1.1 Институты как правила: деонтическая сила из коллективной интенциональности

1.2 Институты как равновесия в теории игр: устойчивость из рациональности агентов

Описывается теоретико-игровая традиция институтов как равновесий и базовые понятия теории игр, используемые в данном исследовании.

Vanderschraaf’s inductive deliberation as a source of salience

Vanderschraaf (1995, 1998, 2001) redefined social conventions as CE through inductive learning, positioning conventions as foundational to achieving justice as mutual advantage. He formalized the notion of salience (or focal points) as information partitions and employed the Dirichlet rule¹¹ to show how agents sequentially update their beliefs about others’ strategies to gradually arrive at an equilibrium endogenously, without explicit external signal.

Lewis considered a coordination equilibrium a convention if the players have common knowledge of mutual expectations. Vanderschraaf calls this mutual expectation criterion (MEC). Each agent has a decisive reason to conform to their part of the convention, expecting the other agents to do likewise. Lewis stated that an equilibrium must be a coordination equilibrium to reflect the notion that a person conforming to a convention wants their intention to be seen as such. Vanderschraaf calls it the public intentions criterion (PIC). Furthermore, Lewis argues that common knowledge of the MEC is necessary for a convention. However, as Vanderschraaf notes, it is not sufficient, since common knowledge of the MEC can be satisfied at any strict Nash equilibrium.

According to Vanderschraaf, a convention constitutes a strategy profile \(\sigma^* = (\sigma_1^*, \ldots, \sigma_n^*)\) where each agent \(i\) maximizes expected utility such that \(\mathbb{E}[u_i(\sigma_i^*, \sigma_{-i}^*)] \geq \mathbb{E}[u_i(\sigma_i', \sigma_{-i}^*)]\) for all alternative strategies \(\sigma_i' \neq \sigma_i^*\), ensuring stability against unilateral deviations.

The formation of conventions operates not through cognitively expensive rational deliberation, but through relatively cheap inductive learning mechanisms. Agents employ Dirichlet dynamics to update beliefs about opponents’ strategies. This updating process describes how agents repeatedly revise their beliefs by incorporating new observations of others’ behavior. A deliberational equilibrium is then defined as a fixed point of this learning dynamic, where agents’ beliefs stabilize. The stabilized joint beliefs and strategies that emerge from this iterative updating correspond to what Vanderschraaf calls endogenous correlated equilibrium (ECE)¹²: a CE arising internally from the agents’ inductive learning and mutual belief revision, rather than from an external correlation device as it is usually presented in broader game theory literature¹³. Kôno (2008) has mathematically proven how ECE is possible and that distributions of ECE and exogenous CE are completely different. The Dirichlet dynamics responsible for arriving at ECE is modeled as follows:

\[p_{t+1}(s_{-i}) = \frac{n_{s_{-i}} + \alpha_{s_{-i}}}{\sum_{s'_{-i}} (n_{s'_{-i}} + \alpha_{s'_{-i}})}\]

where \(n_{s_{-i}}\) represents observed strategy profiles and \(\alpha_{s_{-i}}\) denotes prior beliefs (Vanderschraaf, 2018). Repeated interactions lead to path-dependent emergence of focal points, particularly in bargaining scenarios. Two prominent conventions arise: equal division of goods (\(x_i = \frac{1}{n}\)) and egalitarian payoff distributions satisfying \(u_i(x_i) - u_i(d) = u_j(x_j) - u_j(d)\) for all agents \(i,j\), where \(d\) represents disagreement payoffs (Vanderschraaf, 1995).

An important part of Vanderschraaf’s theory of conventions is his contribution to moral philosophy and theory of justice. He grounded principles of justice in conventions that generate Pareto improvements¹⁴ over non-cooperative baselines. A just convention \(\sigma^J\) must satisfy \(u_i(\sigma^J) \geq u_i(\sigma^B)\) for all agents \(i\), where \(\sigma^B\) denotes the baseline equilibrium (Vanderschraaf, 2018).

This requirement addresses the vulnerability objection to justice theories which fail to adequately protect the most vulnerable persons. It does so by ensuring that conventions benefit even the least advantaged participants, creating mutual advantages that stabilize social arrangements. The framework reconciles Humean conventionalism with game theory, demonstrating how justice emerges from repeated coordination problems rather than abstract moral principles¹⁵.

As can be seen, convention as CE allows for more “fair” coordination, even though no pure strategy equilibrium exists as we saw earlier with the “Battle of Sexes” game example. To reiterate, neither of the pure strategy Nash equilibria in this game is “fair”, in the sense that the players receive the same payoff.

This game has a mixed Nash equilibrium at which both agents play their strategies with probability \(\frac 2 3\), yielding an expected payoff of \(\frac 2 3\) for each agent. However, this equilibrium does not satisfy the PIC and is thus not a convention. Nevertheless, there is a correlated equilibrium that is fair to both players and preferable to the pure strategy equilibrium. With a toss of a fair coin, there is a probability space \(\Omega = \{H, W\}\) with “heads” and “tails”. The agents have a common information partition \(\mathscr{H} = \{\{H\},\{W\}\}\) and the correlated strategy combination is denoted as a function \(f: \Omega \rightarrow \{A 1, A 2\} \times \{A 1, A 2\}\) with \(f(H) = (A 1, A 1)\) and \(f(W) = (A 2, A 2)\). Husband has a higher expected payoff with this combination than any of the other strategies, so he will not deviate from it. The expected payoff for Husband is \(2\) if the outcome is \(H\), and \(1\) if it is \(W\).

\[ \begin{aligned} & \left.E\left(u_1 \circ f \mid H\right)=2>0=E\left(u_1(A 2, A 1)\right) \mid H\right), \text { and } \\ & E\left(u_1 \circ f \mid W\right)=1>0=E\left(u_1(A 1, A 2) \mid W\right) \end{aligned} \]

The same holds for the second player. To this end, neither player would want to deviate, since the overall expected payoff at this equilibrium for each player is

\[ E\left(u_k \circ f\right)=\frac{1}{2} \cdot E\left(u_k \circ f \mid H\right)+\frac{1}{2} \cdot E\left(u_k \circ f \mid T\right)=\frac{3}{2} \]

It means that each player prefers the expected payoff from \(f\) to that of the mixed equilibrium.

For Vanderschraaf, a convention is a mapping of “states of the world” to strategy combinations of a noncooperative game (Vanderschraaf, 1995, p. 69):

A game \(\Gamma\) is an ordered triple \((N, S, \mathbf{u})\) consisting of the following elements:

1. A finite set \(N ={\{1,2, …, n\}}\), called the set of players;
2. For each player \(k \in N\), there is a finite set \(S_{k}= \{{A_{k_{1}}, A_{k_{2}},\dots, A_{kn_{k}}}\}\), called the alternative pure strategies for player \(k\). The Cartesian product \(S = S_{1} \times \dots \times S_n\) is called the pure strategy set for the game \(\Gamma\);
3. A map \(\mathbf{u}: S \rightarrow \mathbb{R}^n\), called the payoff function on the pure strategy set. At each strategy combination \(\mathbf{A} = (A_{1j_1}, \dots, A_{nj_{n})}\in S\), player \(k\)’s payoff is given by the \(k\)-th component of the value of \(\mathbf{u}\), that is, player \(k\)’s payoff \(u_k\), at \(\mathbf{A}\) is determined by \[u_k(\mathbf{A}) = I_{k} \circ \mathbf{u} (A_{1j_1}, \dots, A_{nj_n}),\]

where \(I_k(\mathbf{x})\) projects \(\mathbf{x} \in \mathbb{R}^n\) onto its \(k\)-th component.

As Vanderschraaf builds on Aumann’s model (1987), each player has a personal information partition \(\mathscr{H}_k\) of a probability space \(\Omega\). Elementary events on \(\Omega\) are called states of the world. At each state \(\omega\), each player \(k\) knows which element \(H_{kj}\in \mathscr{H}_k\) has occurred, but not which \(\omega\). \(H_kj\) represents \(k\)’s private information about the states of the world. While \(k\) knows the opponent partitions, she does not know their content. A function \(f: \Omega \rightarrow S\) defines a exogenously correlated strategy \(n\)-tuple, such that at each state of the world \(\omega \in \Omega\), each player \(k\) selects a strategy combination \(f(\omega)=(f_1(\omega),\dots,f_n(\omega))\in S\) correlated with the state of the world \(\omega\). Thus, by playing \(f_k(\omega)\), \(k\) follows Bayesian rationality and maximizes expected payoff given private information and expectations regarding opponents.

In addition, given \(\Gamma = (N, S, \mathbf{u})\), \(\Omega\), and the information partitions \(\mathscr{H}\) of \(\Omega\) as defined above, \(f:\Omega \rightarrow S\) is a correlated equilibrium if and only if, for each \(k \in N\),

1. \(f_k\) is an \(\mathscr{H}_k\)-measurable function, that is, for each \(H_{kj}\in \mathscr{H}_k\), \(f_k(\omega)\) is constant for each \(\omega' \in H_kj\), and
2. For each \(\omega \in \Omega\), \[E(u_{k} \circ f|\mathscr{H}_k)(\omega) \geq E(u_{k} \circ (f_{-k}, g_k)|\mathscr{H}_k)(\omega)\]

where \(E\) denotes expectation, ‘\(-k\)’ refer to the result of excluding the \(k\)-th component from an \(n\)-tuple. This holds for any \(\mathscr{H}_k\)-measurable function \(g_{k}: \Omega \rightarrow S_k\). The correlated equilibrium \(f\) is strict if and only if the inequalities are all strict.

The measurability restriction on \(f_k\) means that \(k\) knows her strategy in each \(\omega\). This definition implies that players have common knowledge of the payoff structure, partitions of \(\Omega\), and \(f: \Omega \rightarrow S\), which is needed to compute expected payoffs and reach correlated equilibrium. In addition, if the players possess common knowledge of Bayesian rationality, they will follow their ends of \(f\), expecting others to do the same, since they jointly maximize expected utility in this way.

The agents refer to a common information partition of the states of the world. While each agent \(k\) has a private information partition \(\mathscr{H}_{k}\) of \(\Omega\), there is a partition of \(\Omega\), namely the intersection \(\mathscr{H}=\cap_{k \in N}\mathscr{H}k\), of the states of the world such that for each \(\omega \in \Omega\), all the agents will know which cell \(H(\omega) \in \mathscr{H}\) occurs. The agents’ expected utilities in the following Definition 3 are conditional on their common partition \(\mathscr{H}\), reflecting the intuition that conventions rely upon information that is public to all.

The agents’ expected utilities are conditioned on their common information common partition \(\mathscr{H}\) of the states of the world, which is the intersection of all their private partitions \(\mathscr{H} = \cap_{k \in N}\mathscr{H}_k\). This reflects that conventions depend on information available to all agents.

Given \(\Gamma=(N, S, \mathbf{u}), \Omega\), and the partition \(\mathscr{H}\) of \(\Omega\) of events that are common knowledge among the players, a function \(f: \Omega \rightarrow S\) is a convention if and only if for each \(\omega \in \Omega\), and for each \(k \in N, f_k\) is \(\mathscr{H}\)-measurable and

\[ E\left(u_k \circ f \mid \mathscr{H}\right)(\omega)>E\left(u_k \circ\left(f_{-j}, g_j\right) \mid \mathscr{H}\right)(\omega) \]

for each \(j \in N\) and for any \(\mathscr{H}\)-measurable function \(g_j: \Omega \rightarrow S_j\).

It means that if any player \(j\) deviates from a convention \(f\), every player \(k \in N\), including \(j\), will be worse off. This definition of convention as a strict correlated equilibrium satisfies the PIC, as all agents are aware of the common partition and the strategies each player is expected to play. Thus, if any opponent mistakenly thinks that a player \(k\) will play a strategy \(g_k(\omega) \neq f_k(\omega)\) other than the one prescribed by \(f\), they may be tempted to deviate, resulting in a worse-off outcome for \(k\). Conversely, if all opponents are aware that \(k\) will play her strategy \(f_k(\omega)\) at each state of the world \(\omega \in \Omega\), then they have a strong incentive to conform with convention \(f(\omega)\), which gives \(k\) an improved outcome.

Overall, Vanderschraaf’s contribution is formalization of salience, hence he uses the common information partition \(\mathscr{H}\) as a necessary restriction to make the definition of convention conform with Lewis’s spirit. The other question is how salience itself emerges. Lewis suggested that pre-game communication, precedent, and environmental cues may lead agents to link their expectations and actions with various “states of the world”, thus achieving equilibrium. However, these sources of salience face the problem of infinite regress, for it is unclear how precedent or pre-game communication occurred in the first place without an established and shared conventional rules. Vanderschraaf, along with Skyrms (Vanderschraaf & Skyrms, 1993), proposed inductive deliberation as a mechanism by which salience is being established. It requires agents to be conditional and works by recursive belief modification. Players can reach a correlated equilibrium without communication by dynamically updating their beliefs using a common inductive rule, even if their beliefs don’t initially allow for an equilibrium.

We see here Bayesian rationality, dynamical updating and capacity for recursive beliefs as features of a certain cognitive architecture of an agent, a characterization of their cognitive capacities which influence their behavior. As we will see later, this implicit notion of agent’s cognitive architecture will be important in the discussion of social ontology in the next chapter.

Another significant extension of Lewis’s theory is related to redefining conventions as ESS and is due mostly to Skyrms.

Skyrms’s evolutionary approach to conventions

Skyrms integrated Lewis’s theory of conventions into an evolutionary framework. He showed how signaling conventions can emerge naturally with adaptive processes like evolution and learning in agents with limited cognitive sophistication which overcomes Lewis’s reliance on common knowledge (Skyrms, 2010a).

Although Skyrms has almost established an entire research program with many followers (Franke, 2014; Huttegger, 2007a, 2007b; LaCroix, 2020a; O’Connor, 2020) and we will take a closer look at his generalization of Lewis’s signaling models later in this section, I suggest he would not have done it without his earlier and less-known contribution to game theory which has to do with generalization of the ESS solution concept.

The ESS, or evolutionary stable strategy, being a foundational solution concept in evolutionary game theory formulated by Smith & Price (1973) is a strategy that, if adopted by majority of population, cannot be invaded by any mutant strategy. Crucially, this concept implies random matching¹⁶, where individuals are paired for strategic interactions independently of their types, such that the probability of encountering any strategy is only proportional to its overall population frequency. While this assumption simplifies analysis and yields elegant theoretical results, it limits the applicability of ESS to well-mixed populations and fails to capture the complexity of structured or socially embedded interactions.

Skyrms recognized that ESS does not generate stable strategies with non-random matching arising from mechanisms like kin selection, signaling systems, spatial or social structures. These correlations induce interactional dependencies increasing the probability of similar-strategy encounters. Such dependencies drastically alter the evolutionary dynamics and can stabilize strategies such as cooperation or signaling conventions that would be unstable or unsustainable under classical ESS assumptions (Skyrms, 1994).

This led Skyrms to establishing “adaptive ratifiable strategy” as a generalization ESS that incorporates the endogenous structure of interactions, making it a more realistic predictor of evolutionary outcomes. A strategy is adaptive-ratifiable if it maximizes expected fitness when it is nearly fixed in the population, taking into account the conditional probabilities of interacting with other strategies. This concept ensures dynamic stability under replicator dynamics where correlation affects interaction frequencies (Skyrms, 1994).

The notion of adaptive ratifiable strategy made another Skyrms’s concept possible. That of “correlated convention” (Skyrms, 2014a), which is conventions as stable yet not necessary Pareto optimal behavioral patterns made possible due to interactional dependencies of any kind between agents. Skyrms explored many possibilities for such correlation like spatial interaction (Alexander & Skyrms, 1999), social structure (Skyrms, 2003), social networks (Skyrms & Pemantle, 2004) and finally signaling systems (Skyrms, 2010b). However, as we will see in the second chapter of the thesis, Skyrms’s “correlation” is different from Vanferschraaf’s.

Skyrms’s approach to conventions differs from Lewis’s in not relying on common knowledge and substituting it with evolutionary pressures which make conventions arise and persist. He showed that even simplest organisms like bacteria can arrive at signaling systems akin to Lewisian conventions with the aid of simple adaptive mechanisms like mutation-selection or reinforcement learning (RL) (Skyrms, 2014a).

Skyrms explored various learning dynamics that enable signaling systems to emerge in populations. For example:

• Simple RL where agents adjust their strategies based on trial-and-error feedback from successful interactions. In a basic Lewis-Skyrms signaling game setup with 2 world states, 2 signals and 2 actions, senders and receivers begin with random dispositions and gradually reinforce successful pairings between states, signals, and actions.

• Win-Stay/Lose-Shift dynamics where agents establish conventions more rapidly than simple reinforcement learning. This dynamic involves sticking with successful strategies while shifting away from unsuccessful ones, enhancing convergence speed and stability.

Skyrms’s framework models conventions as stable equilibria of sender-receiver games that evolve via RL and evolutionary dynamics rather than rational deliberation. Formally, a signaling game involves:

• a set of states of the world \(S = \{s_1, s_2, \ldots, s_n\}\)
• a set of signals \(M = \{m_1, m_2, \ldots, m_k\}\)
• a set of acts \(A = \{a_1, a_2, \ldots, a_l\}\).

The sender observes a state \(s \in S\) and chooses a signal \(m \in M\) to send. The receiver, upon receiving \(m\), chooses an action \(a \in A\). The payoffs \(u_S(s, m, a)\) and \(u_R(s, m, a)\) for sender and receiver respectively depend on how well the receiver’s action matches the state. Unlike Lewis’s model, which assumes common knowledge of salience to coordinate on a unique equilibrium, Skyrms shows that conventions can emerge through adaptive processes even when initial behaviors are random and no focal points exist.

A central concept in Skyrms’ analysis is the informational content of signals, which he quantifies using information-theoretic measures. Given a prior probability distribution over states \(P(S_i)\) and a posterior distribution conditioned on a signal \(m\), denoted \(P(S_i \mid m)\), the information conveyed by \(m\) can be expressed as the vector of log-likelihood ratios:

\[ \left( \log_2 \frac{P(S_1 \mid m)}{P(S_1)}, \log_2 \frac{P(S_2 \mid m)}{P(S_2)}, \ldots, \log_2 \frac{P(S_n \mid m)}{P(S_n)} \right). \]

where \(P(S_i)\) represents prior probabilities of states and \(P(S_i \mid m)\) denotes posterior probabilities conditioned on a signal \(m\). This formalization bridges Lewis’s conceptual framework with mathematical models of communication.

This measure captures how a signal updates the receiver’s conditional strategy choice given the state of the world, thereby guiding action selection (Skyrms, 2010a).

Skyrms further explores signaling equilibria under conditions of partial alignment or conflict of interests between sender and receiver. In such cases, the equilibrium strategies may involve deceptive or partially informative signals. Formally, if a sender’s payoff function \(u_S\) differs from the receiver’s \(u_R\), the equilibrium concept extends to signaling equilibria where strategies \(\sigma_S: S \to \Delta(M)\) and \(\sigma_R: M \to \Delta(A)\) satisfy mutual best responses:

\[ \sigma_S(s) \in \arg\max_{m \in M} \mathbb{E}_{a \sim \sigma_R(m)}[u_S(s, m, a)], \quad \sigma_R(m) \in \arg\max_{a \in A} \mathbb{E}_{s \sim P(\cdot \mid m)}[u_R(s, m, a)], \]

where \(\Delta(X)\) denotes the set of probability distributions over \(X\) (skyrms1996?).

The evolutionary dynamics driving the emergence of conventions are often modeled through RL algorithms such as the Roth-Erev model (Erev & Roth, 1998). Agents maintain propensities \(q_{i}(x)\) for choosing actions \(x\) (signals or responses), which are updated iteratively according to received payoffs:

\[ q_{i}^{t+1}(x) = q_{i}^t(x) + \alpha \cdot \left( r_i^t(x) - q_i^t(x) \right), \]

where \(\alpha\) is a learning rate and \(r_i^t(x)\) is the reward at time \(t\) for action \(x\) (Skyrms, 2010a). Over repeated interactions, these learning dynamics lead to convergence on stable signaling conventions without requiring explicit coordination or rational foresight.

Transmission of information in signals and emphasis on informational content of a signal generated a heated debates in philosophy of biology critiquing Skyrms for the lack of causation (Godfrey-Smith, 2020; Harms, 2004; Shea, 2018) and over-reliance on statistical connection instead of functional one.

An interesting part of Skyrms’s extension of Lewis’s signaling game is its implicit reliance on epistemic language of “observing” states of the world and “interpreting” signals for “updating beliefs”. Although Skyrms utterly rejects any Bayesian interpretation of his signaling games (LaCroix, 2020b), he is sometimes interpreted as a incurring epistemology to his agents, especially when his theory is discussed side-by-side with natural theories of mental content (Baraghith, 2019; Harms, 2004; Ruth Garrett Millikan, 1987; Ruth Garrett Millikan & Millikan, 2004): that senders “represent” world states and transmit this public representation to a receiver who then “interprets” it with its own mental states. Consider vervet monkeys’ alarm calls. They can easily be described as involving mental states of “representing” an eagle and sending a certain signal to fellows monkeys who “decode” that public representation and map it onto suitable action. While plausible and the case for most natural theories of mental content like Ruth Garrett Millikan & Millikan (2004), it is not the case for Skyrms.

Although the structure of Lewis-Skyrms game mirrors the flow of information in epistemic contexts (state-signal-action pairings) and it is tempting to treat senders and receivers as conditional, the Skyrmsian agents update their behavioral dispositions rather than beliefs as they do not possess any inference and can only adjust their mappings according to failure rates (Skyrms, 2012).

Skyrms’s sender-receiver system is an information channel focusing on how effective codes (signal-meaning pairings) arise and stabilize, not on agents’ beliefs or intention. His signaling games are mechanistic as Maynard Smith’s, for they take into account only objective, or “ontic”, features of agents like strategy frequency across population or, in case of signaling game, mappings from state to signal and from signal to action in accordance to the rate of coordination failures. Compare Lewis-Skyrms game

with Shannon’s information channel:

Martínez (2019) proposes a “channel-first” view on signaling games and argues that the central behavioral unit of Lewis-Skyrms games is not strategies, but the encoding-decoding pair which is similar to mappings from above.

In this framework, world states, signals and actions can be represented as random variables \(S\), \(M\) and \(A\), each of which is a set of discrete units like states, messages and actions like \([S_1, \dots, S_s]\) together with a probability distribution \([Pr(S_1), \dots Pr(S_s)]\) over them. The same applies to messages and actions.

A sender observes the current state and transmits a signal – one of \(m\) possible signals. The receiver detects this signal and chooses an action, \(A_i\), from a set of available actions. Both the signal sent and the action chosen are random variables.

The probabilities for the random variables are linked through the sender’s and receiver’s strategies which are a probability matrices of signals given world states of acts given signals respectively.

As per criticisms of Skyrms’s approach to Lewisian signaling games, Martínez (2019) argues that Skyrms did not go far enough into information theory and allowed informational analysis only after sender and receiver adopted the strategies which does not explain how they arrived at them. Martinez suggests using Shannon’s rate-distortion function (Shannon, 1948) to show minimum mutual information between states and acts with minimum rate of distortion. It allows him to recast payoffs as distortion indicators in the channel. Seen with this lens, a coordination game of signaling, even that involving deception, as an information channel looks more cooperative.

Overall, Skyrms’s extension of Lewis’s theory of conventions has dropped rationality requirements and introduced a more naturalistic account of signaling systems in a broader context. Crucially, it implies a minimal cognitive architecture (or a lack of it) drastically different from conditional agents of Vanderschraaf.

Gintis

One more influential conceptualization of social norms is due to Gintis who offered a multi-level evolutionary account of social norms that integrates insights from game theory, behavioral economics, evolutionary biology, and complex systems theory. Unlike approaches that treat norms either as equilibrium strategies (Lewis) or as epistemic constructs (Bicchieri), Gintis argued that norms are a form of socially transmitted rule-based behavior that co-evolves with the human capacity for cooperation and punishment, and whose persistence is explained through gene–culture coevolution (Gintis, 2009a; gintis2003?).

Gintis defined a norm as a rule of behavior that is:

1. Universally shared within a reference group,
2. Individually internalized, so that deviation provokes negative emotions like guilt or shame,
3. Enforced through third-party punishment, and
4. Costly to individuals, yet adaptive at the group level (gintis2003?).

The evolutionary viability of such norms arises from the interplay between individual fitness and group selection: although norm-followers may incur costs, groups with strong norm adherence—especially norms of cooperation, fairness, or punishment—outperform less cohesive groups in intergroup competition. This is formalized in models of multi-level selection, where within-group dynamics favor selfishness, but between-group dynamics favor cooperation mediated by norms. As Vlerick (2019) suggests, solutions to coordination problems emerge from within-group dynamics, while solutions to competition ones are largely selected through between-group competition. Within-group dynamics explain why salient coordination rules emerge. When it comes to solving competition problems, however, between-group dynamics play a major role. They select game changing norms that affect the payoff related to the available strategies through punishment or reward to solve free-rider problems which create better equilibria than the ones originally available. It means that social arrangements with norms alter payoff matrices to ensure that self-interested strategies align with group interests, without requiring self-sacrifice. They are shaped by interactions between individuals and between groups, the latter selecting efficient equilibria and the former leading to salient ones. Sanctions are imposed to solve competition problems.

Gintis models norm enforcement and stability through replicator dynamics and public goods games. Suppose \(x_i\) is the share of individuals using strategy \(i\) (e.g., cooperating, defecting, punishing). Let \(f_i\) be the fitness (expected payoff) of strategy \(i\). The replicator equation is:

\[ \dot{x}_i = x_i(f_i - \bar{f}), \]

where \(\bar{f} = \sum_j x_j f_j\) is the population average fitness. A norm is stable when the strategy it encodes becomes evolutionarily stable (resists invasion by mutants) due to its adaptive advantage in group-level performance.

What makes norms distinctive in Gintis’s account is the incorporation of strong reciprocity, a behavioral trait characterized by cooperation with others and punishment of non-cooperators, even at personal cost. Strong reciprocity is empirically observed in cross-cultural behavioral experiments like ultimatum, trust, and public goods games and contradicts the predictions of purely self-interested models (gintis2005?). Gintis treats this trait not as an anomaly but as an evolutionary stable behavioral phenotype, sustained through norm-based socialization and group selection.

A central and innovative concept in Gintis’s theory of social norms is the idea that norms transform not just preferences but the structure of the strategic interaction itself, by modifying agents’ subjective representations of payoffs and actions. This transformation is encoded in what he calls a belief matrix, a mapping of how agents perceive and evaluate their strategic options based on the presence of social norms (Gintis, 2009a, ch. 12; gintis2003?).

In classical game theory, a game is defined by:

• A set of players \(N\),
• A set of strategies \(S_i\) for each player \(i \in N\),
• A utility function \(u_i: S \to \mathbb{R}\) assigning payoffs.

Gintis argues that this framework is incomplete for modeling norm-governed behavior, because it assumes that agents evaluate strategies based on static utility functions. However, norms induce endogenous changes in the utility functions themselves, via socially learned expectations, emotions like guilt or shame, and reputational incentives. These are captured through a modified payoff function:

\[ u'_i(s) = u_i(s) + n_i(s), \]

where \(u'_i\) is the norm-adjusted utility, and \(n_i(s)\) encodes normative valuations of strategy profile \(s\). The function \(n_i\) depends on agent \(i\)’s beliefs about what is expected, appropriate, or punishable—thus forming part of a belief matrix.

The belief matrix is not merely a list of beliefs but a second-order cognitive structure: it encodes how players transform the base game into a normatively laden one. For example, in a Prisoner’s Dilemma, if both players believe that mutual defection is morally wrong and likely to incur reputational loss, their payoff matrix is endogenously transformed into a coordination game or even a Stag Hunt, depending on the intensity of normative beliefs. This resembles Crawford’s and Ostrom’s cooperation games \(\delta\)-parametrized with incurred sanctions which I mentioned earlier.

To formalize this, let \(M\) be the original payoff matrix, and \(B\) be the belief matrix that maps social expectations, punishments, and rewards into numerical modifiers. Then:

\[ M' = M + B \]

where \(M'\) is the norm-governed game actually perceived and enacted by players.

This idea closely parallels Gintis’s general theory of “strongly endogenous games” (Gintis, 2009a, pp. 187–189), in which preferences and payoffs are not fixed but shaped by cultural and institutional context. Here, social norms act as priors or filters that reshape the game. The belief matrix \(B\) may itself evolve over time, via cultural transmission, education, or feedback from repeated play.

Gintis thus provides a mechanism for the cognitive embedding of norms in strategic behavior, bridging the rationalist structure of game theory with evolutionary and cultural psychology. This resembles Bicchieri’ notion of cognitive schemata and hints on its mechanism. Gintis’s approach contrasts sharply with static or exogenous models of norms like Lewis’s conventions, and aligns Gintis with constructivist and dynamic modeling traditions in behavioral economics.

Gintis and Young (Young, 1998) share an interest in the emergence and stability of social norms. Young explains norm stability via stochastic evolutionary dynamics and local interaction, using resistance trees and Markov chains to model convergence to norms. Gintis, by contrast, provides a biocultural account in which norms co-evolve with cognition, social learning, and enforcement institutions. Moreover, while Young focuses on punishment as a strategy, Gintis integrates it as an evolved emotional mechanism, part of the human behavioral repertoire.

Gintis’s theory positions norms as culturally transmitted and biologically grounded mechanisms for sustaining large-scale cooperation. Unlike equilibrium or expectation-based theories, his model embeds norm-following in the coevolution of genes and culture, and explains persistence through multi-level selection. Norms, in his view, are:

• Emotionally regulated,
• Costly but group-beneficial,
• Transmitted via imitation and enforcement, and
• Fundamental to the evolution of human societies.

Stashed changes

Vanderschraaf’s inductive deliberation as a source of salience

Vanderschraaf (1995, 1998, 2001) redefined social conventions as CE through inductive learning, positioning conventions as foundational to achieving justice as mutual advantage. He formalized the notion of salience (or focal points) as information partitions and employed the Dirichlet rule¹⁷ to show how agents sequentially update their beliefs about others’ strategies to gradually arrive at an equilibrium endogenously, without explicit external signal.

Lewis considered a coordination equilibrium a convention if the players have common knowledge of mutual expectations. Vanderschraaf calls this mutual expectation criterion (MEC). Each agent has a decisive reason to conform to their part of the convention, expecting the other agents to do likewise. Lewis stated that an equilibrium must be a coordination equilibrium to reflect the notion that a person conforming to a convention wants their intention to be seen as such. Vanderschraaf calls it the public intentions criterion (PIC). Furthermore, Lewis argues that common knowledge of the MEC is necessary for a convention. However, as Vanderschraaf notes, it is not sufficient, since common knowledge of the MEC can be satisfied at any strict Nash equilibrium.

According to Vanderschraaf, a convention constitutes a strategy profile \(\sigma^* = (\sigma_1^*, \ldots, \sigma_n^*)\) where each agent \(i\) maximizes expected utility such that \(\mathbb{E}[u_i(\sigma_i^*, \sigma_{-i}^*)] \geq \mathbb{E}[u_i(\sigma_i', \sigma_{-i}^*)]\) for all alternative strategies \(\sigma_i' \neq \sigma_i^*\), ensuring stability against unilateral deviations.

The formation of conventions operates not through cognitively expensive rational deliberation, but through relatively cheap inductive learning mechanisms. Agents employ Dirichlet dynamics to update beliefs about opponents’ strategies. This updating process describes how agents repeatedly revise their beliefs by incorporating new observations of others’ behavior. A deliberational equilibrium is then defined as a fixed point of this learning dynamic, where agents’ beliefs stabilize. The stabilized joint beliefs and strategies that emerge from this iterative updating correspond to what Vanderschraaf calls endogenous correlated equilibrium (ECE)¹⁸: a CE arising internally from the agents’ inductive learning and mutual belief revision, rather than from an external correlation device as it is usually presented in broader game theory literature¹⁹. Kôno (2008) has mathematically proven how ECE is possible and that distributions of ECE and exogenous CE are completely different. The Dirichlet dynamics responsible for arriving at ECE is modeled as follows:

\[p_{t+1}(s_{-i}) = \frac{n_{s_{-i}} + \alpha_{s_{-i}}}{\sum_{s'_{-i}} (n_{s'_{-i}} + \alpha_{s'_{-i}})}\]

where \(n_{s_{-i}}\) represents observed strategy profiles and \(\alpha_{s_{-i}}\) denotes prior beliefs (Vanderschraaf, 2018). Repeated interactions lead to path-dependent emergence of focal points, particularly in bargaining scenarios. Two prominent conventions arise: equal division of goods (\(x_i = \frac{1}{n}\)) and egalitarian payoff distributions satisfying \(u_i(x_i) - u_i(d) = u_j(x_j) - u_j(d)\) for all agents \(i,j\), where \(d\) represents disagreement payoffs (Vanderschraaf, 1995).

An important part of Vanderschraaf’s theory of conventions is his contribution to moral philosophy and theory of justice. He grounded principles of justice in conventions that generate Pareto improvements²⁰ over non-cooperative baselines. A just convention \(\sigma^J\) must satisfy \(u_i(\sigma^J) \geq u_i(\sigma^B)\) for all agents \(i\), where \(\sigma^B\) denotes the baseline equilibrium (Vanderschraaf, 2018).

This requirement addresses the vulnerability objection to justice theories which fail to adequately protect the most vulnerable persons. It does so by ensuring that conventions benefit even the least advantaged participants, creating mutual advantages that stabilize social arrangements. The framework reconciles Humean conventionalism with game theory, demonstrating how justice emerges from repeated coordination problems rather than abstract moral principles²¹.

As can be seen, convention as CE allows for more “fair” coordination, even though no pure strategy equilibrium exists as we saw earlier with the “Battle of Sexes” game example. To reiterate, neither of the pure strategy Nash equilibria in this game is “fair”, in the sense that the players receive the same payoff.

This game has a mixed Nash equilibrium at which both agents play their strategies with probability \(\frac 2 3\), yielding an expected payoff of \(\frac 2 3\) for each agent. However, this equilibrium does not satisfy the PIC and is thus not a convention. Nevertheless, there is a correlated equilibrium that is fair to both players and preferable to the pure strategy equilibrium. With a toss of a fair coin, there is a probability space \(\Omega = \{H, W\}\) with “heads” and “tails”. The agents have a common information partition \(\mathscr{H} = \{\{H\},\{W\}\}\) and the correlated strategy combination is denoted as a function \(f: \Omega \rightarrow \{A 1, A 2\} \times \{A 1, A 2\}\) with \(f(H) = (A 1, A 1)\) and \(f(W) = (A 2, A 2)\). Husband has a higher expected payoff with this combination than any of the other strategies, so he will not deviate from it. The expected payoff for Husband is \(2\) if the outcome is \(H\), and \(1\) if it is \(W\).

\[ \begin{aligned} & \left.E\left(u_1 \circ f \mid H\right)=2>0=E\left(u_1(A 2, A 1)\right) \mid H\right), \text { and } \\ & E\left(u_1 \circ f \mid W\right)=1>0=E\left(u_1(A 1, A 2) \mid W\right) \end{aligned} \]

The same holds for the second player. To this end, neither player would want to deviate, since the overall expected payoff at this equilibrium for each player is

\[ E\left(u_k \circ f\right)=\frac{1}{2} \cdot E\left(u_k \circ f \mid H\right)+\frac{1}{2} \cdot E\left(u_k \circ f \mid T\right)=\frac{3}{2} \]

It means that each player prefers the expected payoff from \(f\) to that of the mixed equilibrium.

For Vanderschraaf, a convention is a mapping of “states of the world” to strategy combinations of a noncooperative game (Vanderschraaf, 1995, p. 69):

A game \(\Gamma\) is an ordered triple \((N, S, \mathbf{u})\) consisting of the following elements:

1. A finite set \(N ={\{1,2, …, n\}}\), called the set of players;
2. For each player \(k \in N\), there is a finite set \(S_{k}= \{{A_{k_{1}}, A_{k_{2}},\dots, A_{kn_{k}}}\}\), called the alternative pure strategies for player \(k\). The Cartesian product \(S = S_{1} \times \dots \times S_n\) is called the pure strategy set for the game \(\Gamma\);
3. A map \(\mathbf{u}: S \rightarrow \mathbb{R}^n\), called the payoff function on the pure strategy set. At each strategy combination \(\mathbf{A} = (A_{1j_1}, \dots, A_{nj_{n})}\in S\), player \(k\)’s payoff is given by the \(k\)-th component of the value of \(\mathbf{u}\), that is, player \(k\)’s payoff \(u_k\), at \(\mathbf{A}\) is determined by \[u_k(\mathbf{A}) = I_{k} \circ \mathbf{u} (A_{1j_1}, \dots, A_{nj_n}),\]

where \(I_k(\mathbf{x})\) projects \(\mathbf{x} \in \mathbb{R}^n\) onto its \(k\)-th component.

As Vanderschraaf builds on Aumann’s model (1987), each player has a personal information partition \(\mathscr{H}_k\) of a probability space \(\Omega\). Elementary events on \(\Omega\) are called states of the world. At each state \(\omega\), each player \(k\) knows which element \(H_{kj}\in \mathscr{H}_k\) has occurred, but not which \(\omega\). \(H_kj\) represents \(k\)’s private information about the states of the world. While \(k\) knows the opponent partitions, she does not know their content. A function \(f: \Omega \rightarrow S\) defines a exogenously correlated strategy \(n\)-tuple, such that at each state of the world \(\omega \in \Omega\), each player \(k\) selects a strategy combination \(f(\omega)=(f_1(\omega),\dots,f_n(\omega))\in S\) correlated with the state of the world \(\omega\). Thus, by playing \(f_k(\omega)\), \(k\) follows Bayesian rationality and maximizes expected payoff given private information and expectations regarding opponents.

In addition, given \(\Gamma = (N, S, \mathbf{u})\), \(\Omega\), and the information partitions \(\mathscr{H}\) of \(\Omega\) as defined above, \(f:\Omega \rightarrow S\) is a correlated equilibrium if and only if, for each \(k \in N\),

1. \(f_k\) is an \(\mathscr{H}_k\)-measurable function, that is, for each \(H_{kj}\in \mathscr{H}_k\), \(f_k(\omega)\) is constant for each \(\omega' \in H_kj\), and
2. For each \(\omega \in \Omega\), \[E(u_{k} \circ f|\mathscr{H}_k)(\omega) \geq E(u_{k} \circ (f_{-k}, g_k)|\mathscr{H}_k)(\omega)\]

where \(E\) denotes expectation, ‘\(-k\)’ refer to the result of excluding the \(k\)-th component from an \(n\)-tuple. This holds for any \(\mathscr{H}_k\)-measurable function \(g_{k}: \Omega \rightarrow S_k\). The correlated equilibrium \(f\) is strict if and only if the inequalities are all strict.

The measurability restriction on \(f_k\) means that \(k\) knows her strategy in each \(\omega\). This definition implies that players have common knowledge of the payoff structure, partitions of \(\Omega\), and \(f: \Omega \rightarrow S\), which is needed to compute expected payoffs and reach correlated equilibrium. In addition, if the players possess common knowledge of Bayesian rationality, they will follow their ends of \(f\), expecting others to do the same, since they jointly maximize expected utility in this way.

The agents refer to a common information partition of the states of the world. While each agent \(k\) has a private information partition \(\mathscr{H}_{k}\) of \(\Omega\), there is a partition of \(\Omega\), namely the intersection \(\mathscr{H}=\cap_{k \in N}\mathscr{H}k\), of the states of the world such that for each \(\omega \in \Omega\), all the agents will know which cell \(H(\omega) \in \mathscr{H}\) occurs. The agents’ expected utilities in the following Definition 3 are conditional on their common partition \(\mathscr{H}\), reflecting the intuition that conventions rely upon information that is public to all.

The agents’ expected utilities are conditioned on their common information common partition \(\mathscr{H}\) of the states of the world, which is the intersection of all their private partitions \(\mathscr{H} = \cap_{k \in N}\mathscr{H}_k\). This reflects that conventions depend on information available to all agents.

Given \(\Gamma=(N, S, \mathbf{u}), \Omega\), and the partition \(\mathscr{H}\) of \(\Omega\) of events that are common knowledge among the players, a function \(f: \Omega \rightarrow S\) is a convention if and only if for each \(\omega \in \Omega\), and for each \(k \in N, f_k\) is \(\mathscr{H}\)-measurable and

\[ E\left(u_k \circ f \mid \mathscr{H}\right)(\omega)>E\left(u_k \circ\left(f_{-j}, g_j\right) \mid \mathscr{H}\right)(\omega) \]

for each \(j \in N\) and for any \(\mathscr{H}\)-measurable function \(g_j: \Omega \rightarrow S_j\).

It means that if any player \(j\) deviates from a convention \(f\), every player \(k \in N\), including \(j\), will be worse off. This definition of convention as a strict correlated equilibrium satisfies the PIC, as all agents are aware of the common partition and the strategies each player is expected to play. Thus, if any opponent mistakenly thinks that a player \(k\) will play a strategy \(g_k(\omega) \neq f_k(\omega)\) other than the one prescribed by \(f\), they may be tempted to deviate, resulting in a worse-off outcome for \(k\). Conversely, if all opponents are aware that \(k\) will play her strategy \(f_k(\omega)\) at each state of the world \(\omega \in \Omega\), then they have a strong incentive to conform with convention \(f(\omega)\), which gives \(k\) an improved outcome.

Overall, Vanderschraaf’s contribution is formalization of salience, hence he uses the common information partition \(\mathscr{H}\) as a necessary restriction to make the definition of convention conform with Lewis’s spirit. The other question is how salience itself emerges. Lewis suggested that pre-game communication, precedent, and environmental cues may lead agents to link their expectations and actions with various “states of the world”, thus achieving equilibrium. However, these sources of salience face the problem of infinite regress, for it is unclear how precedent or pre-game communication occurred in the first place without an established and shared conventional rules. Vanderschraaf, along with Skyrms (Vanderschraaf & Skyrms, 1993), proposed inductive deliberation as a mechanism by which salience is being established. It requires agents to be conditional and works by recursive belief modification. Players can reach a correlated equilibrium without communication by dynamically updating their beliefs using a common inductive rule, even if their beliefs don’t initially allow for an equilibrium.

We see here Bayesian rationality, dynamical updating and capacity for recursive beliefs as features of a certain cognitive architecture of an agent, a characterization of their cognitive capacities which influence their behavior. As we will see later, this implicit notion of agent’s cognitive architecture will be important in the discussion of social ontology in the next chapter.

Another significant extension of Lewis’s theory is related to redefining conventions as ESS and is due mostly to Skyrms.

Skyrms’s evolutionary approach to conventions

Skyrms integrated Lewis’s theory of conventions into an evolutionary framework. He showed how signaling conventions can emerge naturally with adaptive processes like evolution and learning in agents with limited cognitive sophistication which overcomes Lewis’s reliance on common knowledge (Skyrms, 2010a).

Although Skyrms has almost established an entire research program with many followers (Franke, 2014; Huttegger, 2007a, 2007b; LaCroix, 2020a; O’Connor, 2020) and we will take a closer look at his generalization of Lewis’s signaling models later in this section, I suggest he would not have done it without his earlier and less-known contribution to game theory which has to do with generalization of the ESS solution concept.

The ESS, or evolutionary stable strategy, being a foundational solution concept in evolutionary game theory formulated by Smith & Price (1973) is a strategy that, if adopted by majority of population, cannot be invaded by any mutant strategy. Crucially, this concept implies random matching²², where individuals are paired for strategic interactions independently of their types, such that the probability of encountering any strategy is only proportional to its overall population frequency. While this assumption simplifies analysis and yields elegant theoretical results, it limits the applicability of ESS to well-mixed populations and fails to capture the complexity of structured or socially embedded interactions.

Skyrms recognized that ESS does not generate stable strategies with non-random matching arising from mechanisms like kin selection, signaling systems, spatial or social structures. These correlations induce interactional dependencies increasing the probability of similar-strategy encounters. Such dependencies drastically alter the evolutionary dynamics and can stabilize strategies such as cooperation or signaling conventions that would be unstable or unsustainable under classical ESS assumptions (Skyrms, 1994).

This led Skyrms to establishing “adaptive ratifiable strategy” as a generalization ESS that incorporates the endogenous structure of interactions, making it a more realistic predictor of evolutionary outcomes. A strategy is adaptive-ratifiable if it maximizes expected fitness when it is nearly fixed in the population, taking into account the conditional probabilities of interacting with other strategies. This concept ensures dynamic stability under replicator dynamics where correlation affects interaction frequencies (Skyrms, 1994).

The notion of adaptive ratifiable strategy made another Skyrms’s concept possible. That of “correlated convention” (Skyrms, 2014a), which is conventions as stable yet not necessary Pareto optimal behavioral patterns made possible due to interactional dependencies of any kind between agents. Skyrms explored many possibilities for such correlation like spatial interaction (Alexander & Skyrms, 1999), social structure (Skyrms, 2003), social networks (Skyrms & Pemantle, 2004) and finally signaling systems (Skyrms, 2010b). However, as we will see in the second chapter of the thesis, Skyrms’s “correlation” is different from Vanferschraaf’s.

Skyrms’s approach to conventions differs from Lewis’s in not relying on common knowledge and substituting it with evolutionary pressures which make conventions arise and persist. He showed that even simplest organisms like bacteria can arrive at signaling systems akin to Lewisian conventions with the aid of simple adaptive mechanisms like mutation-selection or reinforcement learning (RL) (Skyrms, 2014a).

Skyrms explored various learning dynamics that enable signaling systems to emerge in populations. For example:

• Simple RL where agents adjust their strategies based on trial-and-error feedback from successful interactions. In a basic Lewis-Skyrms signaling game setup with 2 world states, 2 signals and 2 actions, senders and receivers begin with random dispositions and gradually reinforce successful pairings between states, signals, and actions.

• Win-Stay/Lose-Shift dynamics where agents establish conventions more rapidly than simple reinforcement learning. This dynamic involves sticking with successful strategies while shifting away from unsuccessful ones, enhancing convergence speed and stability.

Skyrms’s framework models conventions as stable equilibria of sender-receiver games that evolve via RL and evolutionary dynamics rather than rational deliberation. Formally, a signaling game involves:

• a set of states of the world \(S = \{s_1, s_2, \ldots, s_n\}\)
• a set of signals \(M = \{m_1, m_2, \ldots, m_k\}\)
• a set of acts \(A = \{a_1, a_2, \ldots, a_l\}\).

The sender observes a state \(s \in S\) and chooses a signal \(m \in M\) to send. The receiver, upon receiving \(m\), chooses an action \(a \in A\). The payoffs \(u_S(s, m, a)\) and \(u_R(s, m, a)\) for sender and receiver respectively depend on how well the receiver’s action matches the state. Unlike Lewis’s model, which assumes common knowledge of salience to coordinate on a unique equilibrium, Skyrms shows that conventions can emerge through adaptive processes even when initial behaviors are random and no focal points exist.

A central concept in Skyrms’ analysis is the informational content of signals, which he quantifies using information-theoretic measures. Given a prior probability distribution over states \(P(S_i)\) and a posterior distribution conditioned on a signal \(m\), denoted \(P(S_i \mid m)\), the information conveyed by \(m\) can be expressed as the vector of log-likelihood ratios:

\[ \left( \log_2 \frac{P(S_1 \mid m)}{P(S_1)}, \log_2 \frac{P(S_2 \mid m)}{P(S_2)}, \ldots, \log_2 \frac{P(S_n \mid m)}{P(S_n)} \right). \]

where \(P(S_i)\) represents prior probabilities of states and \(P(S_i \mid m)\) denotes posterior probabilities conditioned on a signal \(m\). This formalization bridges Lewis’s conceptual framework with mathematical models of communication.

This measure captures how a signal updates the receiver’s conditional strategy choice given the state of the world, thereby guiding action selection (Skyrms, 2010a).

Skyrms further explores signaling equilibria under conditions of partial alignment or conflict of interests between sender and receiver. In such cases, the equilibrium strategies may involve deceptive or partially informative signals. Formally, if a sender’s payoff function \(u_S\) differs from the receiver’s \(u_R\), the equilibrium concept extends to signaling equilibria where strategies \(\sigma_S: S \to \Delta(M)\) and \(\sigma_R: M \to \Delta(A)\) satisfy mutual best responses:

\[ \sigma_S(s) \in \arg\max_{m \in M} \mathbb{E}_{a \sim \sigma_R(m)}[u_S(s, m, a)], \quad \sigma_R(m) \in \arg\max_{a \in A} \mathbb{E}_{s \sim P(\cdot \mid m)}[u_R(s, m, a)], \]

where \(\Delta(X)\) denotes the set of probability distributions over \(X\) (skyrms1996?).

The evolutionary dynamics driving the emergence of conventions are often modeled through RL algorithms such as the Roth-Erev model (Erev & Roth, 1998). Agents maintain propensities \(q_{i}(x)\) for choosing actions \(x\) (signals or responses), which are updated iteratively according to received payoffs:

\[ q_{i}^{t+1}(x) = q_{i}^t(x) + \alpha \cdot \left( r_i^t(x) - q_i^t(x) \right), \]

where \(\alpha\) is a learning rate and \(r_i^t(x)\) is the reward at time \(t\) for action \(x\) (Skyrms, 2010a). Over repeated interactions, these learning dynamics lead to convergence on stable signaling conventions without requiring explicit coordination or rational foresight.

Transmission of information in signals and emphasis on informational content of a signal generated a heated debates in philosophy of biology critiquing Skyrms for the lack of causation (Godfrey-Smith, 2020; Harms, 2004; Shea, 2018) and over-reliance on statistical connection instead of functional one.

An interesting part of Skyrms’s extension of Lewis’s signaling game is its implicit reliance on epistemic language of “observing” states of the world and “interpreting” signals for “updating beliefs”. Although Skyrms utterly rejects any Bayesian interpretation of his signaling games (LaCroix, 2020b), he is sometimes interpreted as a incurring epistemology to his agents, especially when his theory is discussed side-by-side with natural theories of mental content (Baraghith, 2019; Harms, 2004; Ruth Garrett Millikan, 1987; Ruth Garrett Millikan & Millikan, 2004): that senders “represent” world states and transmit this public representation to a receiver who then “interprets” it with its own mental states. Consider vervet monkeys’ alarm calls. They can easily be described as involving mental states of “representing” an eagle and sending a certain signal to fellows monkeys who “decode” that public representation and map it onto suitable action. While plausible and the case for most natural theories of mental content like Ruth Garrett Millikan & Millikan (2004), it is not the case for Skyrms.

Although the structure of Lewis-Skyrms game mirrors the flow of information in epistemic contexts (state-signal-action pairings) and it is tempting to treat senders and receivers as conditional, the Skyrmsian agents update their behavioral dispositions rather than beliefs as they do not possess any inference and can only adjust their mappings according to failure rates (Skyrms, 2012).

Skyrms’s sender-receiver system is an information channel focusing on how effective codes (signal-meaning pairings) arise and stabilize, not on agents’ beliefs or intention. His signaling games are mechanistic as Maynard Smith’s, for they take into account only objective, or “ontic”, features of agents like strategy frequency across population or, in case of signaling game, mappings from state to signal and from signal to action in accordance to the rate of coordination failures. Compare Lewis-Skyrms game

with Shannon’s information channel:

Martínez (2019) proposes a “channel-first” view on signaling games and argues that the central behavioral unit of Lewis-Skyrms games is not strategies, but the encoding-decoding pair which is similar to mappings from above.

In this framework, world states, signals and actions can be represented as random variables \(S\), \(M\) and \(A\), each of which is a set of discrete units like states, messages and actions like \([S_1, \dots, S_s]\) together with a probability distribution \([Pr(S_1), \dots Pr(S_s)]\) over them. The same applies to messages and actions.

A sender observes the current state and transmits a signal – one of \(m\) possible signals. The receiver detects this signal and chooses an action, \(A_i\), from a set of available actions. Both the signal sent and the action chosen are random variables.

The probabilities for the random variables are linked through the sender’s and receiver’s strategies which are a probability matrices of signals given world states of acts given signals respectively.

As per criticisms of Skyrms’s approach to Lewisian signaling games, Martínez (2019) argues that Skyrms did not go far enough into information theory and allowed informational analysis only after sender and receiver adopted the strategies which does not explain how they arrived at them. Martinez suggests using Shannon’s rate-distortion function (Shannon, 1948) to show minimum mutual information between states and acts with minimum rate of distortion. It allows him to recast payoffs as distortion indicators in the channel. Seen with this lens, a coordination game of signaling, even that involving deception, as an information channel looks more cooperative.

Overall, Skyrms’s extension of Lewis’s theory of conventions has dropped rationality requirements and introduced a more naturalistic account of signaling systems in a broader context. Crucially, it implies a minimal cognitive architecture (or a lack of it) drastically different from conditional agents of Vanderschraaf.

Gintis

One more influential conceptualization of social norms is due to Gintis who offered a multi-level evolutionary account of social norms that integrates insights from game theory, behavioral economics, evolutionary biology, and complex systems theory. Unlike approaches that treat norms either as equilibrium strategies (Lewis) or as epistemic constructs (Bicchieri), Gintis argued that norms are a form of socially transmitted rule-based behavior that co-evolves with the human capacity for cooperation and punishment, and whose persistence is explained through gene–culture coevolution (Gintis, 2009a; gintis2003?).

Gintis defined a norm as a rule of behavior that is:

1. Universally shared within a reference group,
2. Individually internalized, so that deviation provokes negative emotions like guilt or shame,
3. Enforced through third-party punishment, and
4. Costly to individuals, yet adaptive at the group level (gintis2003?).

The evolutionary viability of such norms arises from the interplay between individual fitness and group selection: although norm-followers may incur costs, groups with strong norm adherence—especially norms of cooperation, fairness, or punishment—outperform less cohesive groups in intergroup competition. This is formalized in models of multi-level selection, where within-group dynamics favor selfishness, but between-group dynamics favor cooperation mediated by norms. As Vlerick (2019) suggests, solutions to coordination problems emerge from within-group dynamics, while solutions to competition ones are largely selected through between-group competition. Within-group dynamics explain why salient coordination rules emerge. When it comes to solving competition problems, however, between-group dynamics play a major role. They select game changing norms that affect the payoff related to the available strategies through punishment or reward to solve free-rider problems which create better equilibria than the ones originally available. It means that social arrangements with norms alter payoff matrices to ensure that self-interested strategies align with group interests, without requiring self-sacrifice. They are shaped by interactions between individuals and between groups, the latter selecting efficient equilibria and the former leading to salient ones. Sanctions are imposed to solve competition problems.

Gintis models norm enforcement and stability through replicator dynamics and public goods games. Suppose \(x_i\) is the share of individuals using strategy \(i\) (e.g., cooperating, defecting, punishing). Let \(f_i\) be the fitness (expected payoff) of strategy \(i\). The replicator equation is:

\[ \dot{x}_i = x_i(f_i - \bar{f}), \]

where \(\bar{f} = \sum_j x_j f_j\) is the population average fitness. A norm is stable when the strategy it encodes becomes evolutionarily stable (resists invasion by mutants) due to its adaptive advantage in group-level performance.

What makes norms distinctive in Gintis’s account is the incorporation of strong reciprocity, a behavioral trait characterized by cooperation with others and punishment of non-cooperators, even at personal cost. Strong reciprocity is empirically observed in cross-cultural behavioral experiments like ultimatum, trust, and public goods games and contradicts the predictions of purely self-interested models (gintis2005?). Gintis treats this trait not as an anomaly but as an evolutionary stable behavioral phenotype, sustained through norm-based socialization and group selection.

A central and innovative concept in Gintis’s theory of social norms is the idea that norms transform not just preferences but the structure of the strategic interaction itself, by modifying agents’ subjective representations of payoffs and actions. This transformation is encoded in what he calls a belief matrix, a mapping of how agents perceive and evaluate their strategic options based on the presence of social norms (Gintis, 2009a, ch. 12; gintis2003?).

In classical game theory, a game is defined by:

• A set of players \(N\),
• A set of strategies \(S_i\) for each player \(i \in N\),
• A utility function \(u_i: S \to \mathbb{R}\) assigning payoffs.

Gintis argues that this framework is incomplete for modeling norm-governed behavior, because it assumes that agents evaluate strategies based on static utility functions. However, norms induce endogenous changes in the utility functions themselves, via socially learned expectations, emotions like guilt or shame, and reputational incentives. These are captured through a modified payoff function:

\[ u'_i(s) = u_i(s) + n_i(s), \]

where \(u'_i\) is the norm-adjusted utility, and \(n_i(s)\) encodes normative valuations of strategy profile \(s\). The function \(n_i\) depends on agent \(i\)’s beliefs about what is expected, appropriate, or punishable—thus forming part of a belief matrix.

The belief matrix is not merely a list of beliefs but a second-order cognitive structure: it encodes how players transform the base game into a normatively laden one. For example, in a Prisoner’s Dilemma, if both players believe that mutual defection is morally wrong and likely to incur reputational loss, their payoff matrix is endogenously transformed into a coordination game or even a Stag Hunt, depending on the intensity of normative beliefs. This resembles Crawford’s and Ostrom’s cooperation games \(\delta\)-parametrized with incurred sanctions which I mentioned earlier.

To formalize this, let \(M\) be the original payoff matrix, and \(B\) be the belief matrix that maps social expectations, punishments, and rewards into numerical modifiers. Then:

\[ M' = M + B \]

where \(M'\) is the norm-governed game actually perceived and enacted by players.

This idea closely parallels Gintis’s general theory of “strongly endogenous games” (Gintis, 2009a, pp. 187–189), in which preferences and payoffs are not fixed but shaped by cultural and institutional context. Here, social norms act as priors or filters that reshape the game. The belief matrix \(B\) may itself evolve over time, via cultural transmission, education, or feedback from repeated play.

Gintis thus provides a mechanism for the cognitive embedding of norms in strategic behavior, bridging the rationalist structure of game theory with evolutionary and cultural psychology. This resembles Bicchieri’ notion of cognitive schemata and hints on its mechanism. Gintis’s approach contrasts sharply with static or exogenous models of norms like Lewis’s conventions, and aligns Gintis with constructivist and dynamic modeling traditions in behavioral economics.

Gintis and Young (Young, 1998) share an interest in the emergence and stability of social norms. Young explains norm stability via stochastic evolutionary dynamics and local interaction, using resistance trees and Markov chains to model convergence to norms. Gintis, by contrast, provides a biocultural account in which norms co-evolve with cognition, social learning, and enforcement institutions. Moreover, while Young focuses on punishment as a strategy, Gintis integrates it as an evolved emotional mechanism, part of the human behavioral repertoire.

Gintis’s theory positions norms as culturally transmitted and biologically grounded mechanisms for sustaining large-scale cooperation. Unlike equilibrium or expectation-based theories, his model embeds norm-following in the coevolution of genes and culture, and explains persistence through multi-level selection. Norms, in his view, are:

• Emotionally regulated,
• Costly but group-beneficial,
• Transmitted via imitation and enforcement, and
• Fundamental to the evolution of human societies.

1.3 ✅ Синтез и его амбивалентность: теория «правил-в-равновесии» Франческо Гуалы

Описывается теория правил-в-равновесии (ПвР) Франческо Гуалы, её критика со стороны коллег, а также критика автора, направленная на лакуны в аргументации и, следовательно, нелегитимные теоретические выводы ПвР.

2.1. Круг в определении: институт как скрытая предпосылка института

Описывается ключевая проблема теории Гуалы: институт как правило-в-равновесии требует существования готовой конвенции, решающей конфликт.

2.1.2 Подмена условной стратегии готовой абстрактной конвенцией

• Даже приняв методологическую разницу игр, мы видим, что Гуала сравнивает игру с конфликтом с игрой на координацию, не изменяя матрицы и незаметно устраняя конфликт внутри Ястреба-Голубя:
  • Пример с животными (ЯГБ): Чистая игра с конфликтом. Условная стратегия «Буржуа» — это решение, которое предстоит найти в рамках игры. Никаких внешне данных правил нет.
  • Пример с людьми («выпас скота»): Гуала описывает это так: «Племена пасли скот по разные стороны реки. Река высохла. Теперь они продолжают пасти скот по воображаемой линии».
  • Ключевой момент: Фраза «продолжают пасти» содержит готовую конвенцию. Но откуда она взялась? В момент, когда река высохла, перед племенами встала точно такая же игра с конфликтом, как у животных (ЯГБ за новый ресурс). Гуала пропускает этот момент и начинает анализ с того, что конвенция уже существует.

• Что должно быть объясняемым (explanandum)? Возникновение и устойчивость принудительной социальной структуры (например, границы, права собственности).
• Что Гуала использует как объясняющее (explanans)? Уже существующую, работающую социальную структуру (конвенцию о разделе по реке), которую он встраивает в начальные условия своей модели.
• Итог: Он строит теорию, где институт (как готовая конвенция) является предпосылкой для объяснения института (как устойчивого равновесия). Это логический круг (petitio principii). Он объясняет институт через самого себя. Это фатально, потому что весь пафос Гуалы — показать, как правила и равновесия совместно порождают институты. Но в его ключевом примере правило («паси на своей стороне») не порождается игрой — .оно дано ей изначально как часть истории
• Вывод 1: Гуала не моделирует возникновение института. Он моделирует воспроизводство уже существующего института в слегка изменившихся условиях (река исчезла, но «правило» осталось). Его модель объясняет не «почему есть граница», а «почему сохраняется инерция уже существующей конвенции о границе, если физический маркер исчез». Это другая, более простая проблема.
• Если рассмортреть пример Гуалы с выпасом скота как настоящую ЯГБ (без предустановленной конвенции в виде реки как границы), то там будет и равновесие, и правило — но не в онтологическом смысле уже существующей конвенции, а как условная стратегия.
• Вывод 2: Это ставит под вопрос необходимость правил для определения института. Возможно, правила не необходимы.

2.2. Неустойчивость коррелированного равновесия: правило без санкции в условиях неполной информации

• Рассматривается реалистичная игра ЯГБ без предустановленной конвенции в качестве равновесия
• Находится байесовское равновесие в этой игре с неполной информацией.
• Показывается, что оно отличается от коррелированного равновесия, и что стратегия «всегда посылать сигнал “Владелец” и играть по правилу Буржуа-стратегии» строго выгоднее, чем простая условная стратегия Буржуа.
• Делается вывод, что КР недостаточно для описания института.

Центральный тезис Гуалы — что КР адекватно описывает устойчивость института. Однако это не так, поскольку работает только в случае допущения о полной информации в игре. Чтобы это показать, представляем игры в развернутой форме и находим байесовское равновесие.

Стратегия Буржуа в ЯГБ является КР в игре с полной информацией — если типы игроков наблюдаемы обоими игроками. Чтобы это показать, введём понятия истории игры и информационного множества.

История \(h \in H\) — конечная последовательность ходов (или узлов дерева) игры в развёрнутой форме \(h = (a_1, a_2,\dots, a_k)\). Информационное множество \(I_R\) — это набор неразличимых для получателя историй игры. Если \(|I_R| > 1\), то получатель не знает, в каком узле игры он находится, что усложняет принятие решения. В ЯГБ в примере Гуалы с животными: \[ \begin{gathered} h_1 = \{\theta_1, m_1\} \\ h_2 = \{\theta_2, m_2\} \\ I_R = \{h\} \end{gathered} \] Поскольку \(I_R = 1\) (истории эквивалентны, так как идентичны по форме), получатель сигнала точно знает, в каком узле игры находится.

А в примере Гуалы с племенами: \[I_R(m_1) = \{h, (\theta_2, m_1)\}\]

Тип отправителя неразличим для получателя сигнала — он видит один и тот же сигнал «я владелец» и когда отправитель действительно «владелец», и когда он «чужак», что обозначено на схеме пунктирной линией. Это создаёт неопределённость и лазейку для эксплуатации получателя.

Поскольку получатель не может различить, в каком узле игры находится и кто его оппонент по реальному типу, отправитель сигнала может всегда посылать сигнал «я — владелец», даже не являясь им фактически.

Введём новую стратегию «Блефующий» и рассчитаем средние платежи согласно стандартным условиям игры «Ястреб-Голубь», где стоимость конфликта выше ценности ресурса \(C > V\), и каждый игрок может быть либо захватчиком, либо владельцем (Maynard Smith, 1982):

1. Буржуа (B) — честная стратегия:
   • Сигналит свой истинный тип.
   • На сигнал «владелец» → Голубь.
   • На сигнал «захватчик» → Ястреб.
2. Блефующий — обманывающая стратегия:
   • Всегда сигналит «владелец».
   • На сигнал «владелец» → Голубь.
   • На сигнал «захватчик» → Ястреб.

Встреча M vs B:

M тип	B тип	Сигналы	Действия	Платёж M
Владелец	Захватчик	(Владелец, Захватчик)	Ястреб, Голубь	V
Захватчик	Владелец	(Владелец, Владелец)	Голубь, Голубь	V/2

Встреча B vs. B

B тип	B тип	Сигналы	Действия	Платёж M
Владелец	Захватчик	(Владелец, Захватчик)	Голубь, Голубь	V/2
Захватчик	Владелец	(Захватчик, Владелец)	Голубь, Голубь	V/2

Средний платёж M: \[ EU(M,B) = \frac12 \cdot \frac{V}{2} + \frac12 \cdot V = \frac{3V}{4} \]

Выигрыш «Блефующего» строго больше выигрыша Буржуа: \(\frac{3V}{4} > \frac{V}{2}\) при \(C > V\) (и, следовательно, \(V - C < 0\)).

• следование правилу (то есть условной стратегии Буржуа в КР) — не лучший ответ. Вместо этого можно сблефовать и получить больший выигрыш
• чтобы условная стратегия стала КР, нужен модификатор платежа для стратегии блефа: Гуала его либо уже предполагает встроенным в игру (делая институт черным ящиком), либо игнорирует:

\[\frac{3V}{4} - \delta \geq \frac{V}{2} \]

Это означает, что санкция за блеф \(\delta\) должна превышать ожидаемую выгоду от блефа, равную \(\frac{V}{4}\). Значит, институт может быть устойчивым даже при малых санкциях, однако КР все равно этого не объясняет.

• Вывод: концепция коррелированного равновесия недостаточна для описания устойчивости института — для нее принципиальна защита от блефа при неполной информации. КР схватывает лишь финальное состояние работающего института в игре с полной информацией. Поэтому нужна нужна динамическая устойчивость равновесия, которая может объяснить, как стратегия может возникнуть и закрепиться через динамический процесс (обучение, имитация, эволюционный отбор).
• Институт в человеческом обществе не может быть смоделирован как коррелированное равновесие в игре с объективными, проверяемыми сигналами (как у Гуалы). Реальный институт — это попытка установить что-то вроде КР в игре со стратегическими, ненадёжными сигналами.

Общий вывод: Теория «правил-в-равновесии» не выполняет своей основной задачи — объяснить принудительную силу институтов. Она либо тавтологична, либо описывает невозможный объект.

Вывод главы: необходимость динамической онтологии, исходящей из до-институционального состояния и не предполагающая существования готовой конвенции, которая интегрирует и равновесия, и правила в смысле Сёрла.

3.1. \(\delta\)-параметр как необходимое условие локальной устойчивости

• Поскольку оригинальная игра ЯГБ уже включает в себя термины «захватчик» и «владелец», которые можно трактовать институционально — как наличие или отсутствие уже закрепленного права собственности, мы начнем с симметричной игры Ястреб-Голубь
• Опираясь на эволюционную динамику Скирмса, мы говорим, что условная Буржуа-стратегия, зависимая от информационной асимметрии (сигнала) появляется в игре как результат адаптации в популяции, даже если агенты не обладают понятием собственности.
• Это позволяет получить понятие коррелированной конвенции. Однако она, как мы показали в прошлой главе, предполагает полноту информации.
• Если убрать полноту информации, Буржуа-стратегия перестанет быть ЭСС
• Так же, как и в главе 2 с КР, здесь возникает необходимость компенсации блефа — дельта-параметр
• Это позволяет нам сказать, что устойчивость института не зависит от конкретного равновесия — и ЭСС, и КР в ЯГБ рушатся при неполной информации. Значит, сущность института — не в равновесии.

3.2. Проблема масштаба: от одной игры к популяции. Параметр \(r\) и надёжность компенсации блефа

• Если положить не одну игру, а несколько идентичных игр, в каждой из которых санкция не гарантирована, то дельты (и ее размера) становится недостаточно
• Если в каждой игре дельта либо применена, либо нет (что выражено бинарной случайной величиной E), то эффективная дельта во всех играх будет \(\delta \cdot \r\), где \(r\) — эмпирическая частота реализации дельты в игре (санкция применена)
• Это позволяет показать, что при низкой надежности компенсации блефа \(r\) во популяции игр Буржуа-стратегия не может быть глобальной ЭСС → равновесие разрушается

3.3. Взаимная информация \(I\) о компенсации блефа как мера связности идентичных стратегических ситуаций

• Для поддержания Буржуа-стратегии как глобальной ЭСС нужен механизм или устройство для повышения надёжности санкции \(r\)
• Функция этого механизма — повышение статистической связности (корреляции) или взаимной информации между фактами применения дельты в каждой из игр. Иначе говоря, нужен канал информации между играми, делающий применение санкции после нарушения предсказуемым.
• Подобный механизм и составляет глубинную онтологическую основу институа.

3.4. Формальное определение: институт, протоинститут, конвенция

• Формально, институт в нашей концепции — это сеть дельта-стабилизированных равновесий в условных стратегиях с высокой взаимной информацией.
• Прото-институт (как часть определения института) — .это равновесие в условных стратегиях (неважно, коррелированное, байесовское, ЭСС) в расширенной игре с неполной информацией и конфликтом интересов, которое является Парето-улучшением по отношению к существующему равновесию в базовой (не расширенной) игре
  • Эквивалентная ситуация — множество игр с таким равновесием, но с низкой взаимной информацией: применение санкции в одной ситуации ничего не говорит об ее применении в другой.
• для существования института нужны:
  • ситуация с конфликтом интересов (описываемые играми ЯГБ, дилемма заключенного, битва полов)
  • условная стратегия, решающая конфликт и связанная с чистыми стратегиями (а не как у Гуалы)
  • \(\delta\)-параметр — модификатор платежа для стратегии, эксплуатирующей условную стратегию
  • равновесие в условных стратегиях (неважно, какое)
  • множество структурно идентичных игровых ситуаций с равновесием и дельтой
  • любой механизм или устройство, повышающий взаимную информацию (или статистическую корреляцию) о применении санкции между игровыми ситуациями

4.1 Институт и протоинститут: значение параметров \(\delta\) и \(I\)

• Масштабирование существующей санкции — онтологическая суть института.
• Если санкция для компенсации блефа необходима эволюционно в ситуации неполной информации, то масштабирование этой санкции — нет.
  • Это означает, что в него инвестируют те, кто хотят обладать монополией на дельту (это дает критический угол нашей теории, позволяя эмпирически смотреть на источники статистической связности санкций в конкретном классе ситуаций)
• Если каналы доставки и масштабирования санкции — суть института, то они должны быть до-институциональными. Они онтологически примитивны и выполняют одну или несколько функций:
  • Социальная память и репутация («В этом племени все знаютб что Х — обманщик»)
  • Физическая связанность территории (возможность быстро дойти до нарушителя)
  • Наблюдаемость действий (открытая местность, где всё видно)
• Любой механизм или устройство, обеспечивающие одну или больше функций (память, физическая доступность, наблюдаемость), может служить эмпирическим каналом «доставки» санкции.
  • Каналы доставки санкции являются интерсубъективно интерпретируемыми материальными носителями или социальными технологиями (все знают, что они кодируют дельту):
    • Физические артефакты: дорожные знаки, униформа, печати, камеры, стены, оружие.
    • Социальные технологии: ритуалы, процедуры, публичные казни, формализованные речи (клятвы, приговоры).
    • Символические системы: письменные кодексы, базы данных, репутационные рейтинги.
• При этом, и за локальную дельту, и за каналы доставки дельты можно конкурировать. Это позволяет объяснить многие феномены от клановых войн (борьба конкретных локальных дельт) до политической борьбы (борьба за право насаждать одну дельту глобально)

4.2 Статус равновесий

Равновесия необходимы, но недостаточны для определения института:

• равновесие действительно отражает стабильное состояние социальной системы, однако для института оно невозможно без модификатора платежа — вне зависимости от типа устойчивости (ЭСС, КР)
• это означает, что равновесие не схватывает сущность института само по себе
• вместо этого, санкция, компенсирующая блеф схватывает суть института
• однако даже дельты недостаточно самой по себе, поскольку она решает конфликт локально, и нужна корреляция не только стратегий внутри игры, но и корреляция применения санкций между играми
• 🔥 интуиция института как корреляции стратегии, встречаемая в литературе (Gintis, 2009b; Guala & Hindriks, 2015; Vanderschraaf, 2017), верна, но неточна — институт требует не только скоррелированных стратегий, но и скоррелированных фактов наказания за отклонения от этих скоррелированных стратегий, иначе это просто конвенция, а не институт.

4.3 Статус правил

• Правила не имеют собтвенной онтологии в нашей концепции, но могут служить удобными интерфейсами к этапам развития сети, определяемыми значением параметров \(\delta\) и \(I\):
  • Условная стратегия в игре с конфликтом за ресурс может быть описана как регулятивное правило «если…, то…», которое агент использует как рецепт действия — так, как предполагает Гуала. Однако это не добавляет ничего в онтологию — это просто условная стратегия
  • Конститутивное и регулятивное правило действительно идентичны по форме (как предполагает Гуала), но первое несводимо ко второму. Конститутивное правило — это та же самая условная стратегия в игре с конфликтом за ресурс, только ставшая общим знанием в сети игр благодаря высоко взаимной информации \(I\) о применении санкции: «Я знаю, что все знают, что если пришел первым на холм, то можешь пасти стадо, иначе последует рейд от другого племени».
  • При достижении высокой взаимной информации о применении санкции между игровыми ситуациями санкция обретает новый смысл — она теперь не за блеф в локальной стратегической ситуации, а за игнорирование общего знания о применении санкции. Это согласуется с идеей Сёрла о деонтических силах конститутивного правила.
  • Это объясняет эмердженцию автономного социального порядка без магии, как это есть у Серла или Дюркгейма в социологии
• Если сеть игр — онтологический «бэкенд» института, то правила с их различением конститутивных и регулятивных — пользовательский интерфейс, делающий описание более удобным и в терминах агентов, и в терминах внешнего наблюдателя.
• Правила — эпистемическия «плагин» для удобства описания онтологии, а не онтологический примитив, как полагал Сёрль. Однако это не умаляет важность его интуиции.

5.1. Диагностика тупика: почему «правила-в-равновесии» не решают проблему принудительной силы

• Краткий итог критики Гуалы: Теория Гуалы страдает не просто логическим кругом, а онтологической статичностью. Она принимает как данность то, что требует объяснения — готовую конвенцию («паси на своей стороне реки»), и описывает не генезис института, а его инерционное воспроизводство. Это следствие реифицирующей онтологии, где правило и равновесие — готовые сущности.
• Ключевой пробел: Игнорирование проблемы неполной информации (блефа) и, что критически важно, проблемы масштабирования локальной стабильности на множество взаимодействий. Его коррелированное равновесие (КР) — это описание состояния системы, а не механизм её устойчивости в реалистичных условиях.

5.2. Предложенное решение: параметрическая социальная онтология \(\delta/I\)-сетей и её фундаментальные параметры

• Смена онтологической оптики: Вместо сущностей (правила, равновесия) предлагается каркас, основанный на динамических параметрах, описывающих условия устойчивости.
  • Параметр \(\delta\): Решает локальную проблему блефа. Это необходимое условие устойчивости любого равновесия (будь то ЭСС или КР) в единичной игре с конфликтом и неполной информацией. Он вводит в онтологию силовой/санкционный компонент как фундаментальный.
  • Параметр \(I\) (взаимная информация): Решает глобальную проблему масштаба. Он фиксирует неопределенность (\(r\)) применения санкции \(\delta\) в популяции игр. Высокое I означает наличие каналов, делающих применение санкции предсказуемым и связным в разных ситуациях. Это вводит в онтологию информационно-сетевой компонент как фундаментальный.
• Новые определения как следствие:
  • Протоинститут: Устойчивое равновесие, обеспеченное \(\delta\) в локальной игре (I низко или нерелевантно).
  • Институт (в строгом смысле): Связная сеть \(\delta\)-стабилизированных равновесий, характеризуемая высоким значением I между её узлами (стратегическими ситуациями). Институт — это не вещь, а паттерн связности в пространстве параметров \(\delta\) и I.

5.3. Методологическая рефлексия: статус теории и её позиция в философии науки

• Реализм без реификации (Структурный реализм): Теория не является инструменталистской. Параметры \(\delta\) и I описывают объективные, каузально действующие структуры (паттерны связности и силы), необходимые для объяснения наблюдаемой устойчивости социальных порядков. Реальны не правила, а эти лежащие в их основе каузально-информационные паттерны (Dennett, 1991; Ladyman, Ross, Spurrett, & Collier, 2007).
• Объяснение через лучшее объяснение (IBE, inference to the best explanation): Вся конструкция является выводом к наилучшему объяснению (IBE). Объясняется устойчивость сложных форм координации вопреки неопределенности и оппортунизму за счет существования сетей с высокими \(\delta\) и I. Это объяснение лучше альтернатив (Сёрл, Гуала), так как оно:

1. Ненадуманно (non-ad hoc): параметры \(\delta\) и I вводятся как решение четко формализованных проблем (блеф, масштаб).
2. Объединяюще (unificatory): охватывает и «деонтическую силу» (через предсказуемость санкции при высоком I), и «устойчивость равновесия» (через \(\delta\)).
3. Эмпирически ориентированно: задает новые единицы анализа (\(\delta\), I, сетевые каналы).

5.4. Продуктивность теории \(\delta/I\)-сетей как исследовательской программы: обратная совместимость с эмпирикой

• Операционализация понятий: главное методологическое новшество — перевод философской онтологии в потенциально измеримые концепты. \(\delta\) может быть операционализирован как издержки/риски нарушения (от штрафов до потери репутации). I может быть операционализирован через сетевой анализ каналов коммуникации, мониторинга и принуждения (от скорости распространения сплетен до плотности CCTV).
• Сдвиг фокуса для эмпирических исследований: Теория предлагает социологам искать не «правила» или «нормы», а:

1. Источники \(\delta\): Кто/что и как может накладывать издержки?
2. Каналы, повышающие I: Как информация о применении \(\delta\) передается между ситуациями? (Социальные сети, СМИ, судебная система, ритуалы).
3. Точки разрыва сетей: Где I падает, превращая институт в кластер нестабильных протоинститутов?

5.5. Ограничения и направления дальнейшего развития

• Теория объясняет условия устойчивости принудительного социального порядка, а не его конкретное символическое содержание, смыслы или историческую траекторию. Это .онтологический и методологический каркас, а не полная социальная метафизика

• Направления развития:

1. Математическое: Уточнение моделей перехода от I к r (надежности).
2. Алгоритмическое: использование теории для решения насущных проблем обучения с подкреплением в мультиагентных системах
3. Эмпирическое: Разработка методов измерения \(\delta\) и I в конкретных кейсах (например, сравнительный анализ институтов в онлайн-сообществах vs. традиционных обществах).
4. Теоретическое: Интеграция с концепциями легитимности (как фактор, снижающий требуемый порог \(\delta\)) и изучение динамики конкуренции за контроль над сетевыми узлами.

Представленная теория совершает тройной вклад:

• В социальную онтологию — она преодолевает тупик синтеза через переход от онтологии реифицированных сущностей (правила, равновесия) к онтологии фундаментальных каузально-информационных параметров (\(\delta\), I).
• В методологию социальных наук — она предлагает не просто новую интерпретацию институтов, а новый, потенциально операционализируемый концептуальный каркас, который переводит философские вопросы о природе социального порядка в плоскость конкретных исследовательских программ, фокусирующихся на силе, информации и сетевой связности.
• В исследования мультиагентных систем — она может быть апробирована для решения дилеммы блефа в проблемах обучения с подкреплением

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