David Lewis (1969) introduced sender-receiver games as a way of investigating how meaningful language might evolve from initially random signals. In this report I investigate the conditions under which Lewis signaling games evolve to perfect signaling systems under various learning dynamics. While the 2-state/2- term Lewis signaling game with basic urn learning always approaches a signaling system, I will show that with more than two states suboptimal pooling equilibria can evolve. Inhomogeneous state distributions increase (...) the likelihood of pooling equilibria, but learning strategies with negative reinforcement or certain sorts of mutation can decrease the likelihood of, and even eliminate, pooling equilibria. Both Moran and APR learning strategies (Bereby-Meyer and Erev 1998) are shown to promote successful convergence to signaling systems. A model is presented that illustrates how a language that codes state-act pairs in an order-based grammar might evolve in the context of a Lewis signaling game. The terms, grammar, and the corresponding partitions of the state space co-evolve to generate a language whose structure appears to reflect canonical natural kinds. The evolution of these apparent natural kinds, however, is entirely in service of the rewards that accompany successful distinctions between the sender and receiver. Any metaphysics grounded on the structure of a natural language that evolved in this way would track arbitrary, but pragmatically useful distinctions. (shrink)

The article studies properties of interchangeability of pure, mixed, strict, and strict mixed Nash equilibria. The main result is a sound and complete axiomatic system that describes properties of interchangeability in all four settings. It has been previously shown that the same axiomatic system also describes properties of independence in probability theory, nondeducibility in information flow, and non-interference in concurrency theory.

Using belief elicitation, the paper investigates the process of belief formation and evolution in a signaling game in which a common prior is not induced. Both prior and posterior beliefs of Receivers about Senders’ types are elicited, as well as beliefs of Senders about Receivers’ strategies. In the experiment, subjects often start with diffuse uniform beliefs and update them in view of observations. However, the speed of updating is influenced by the strength of initial beliefs. An interesting result (...) is that beliefs about the prior distribution of types are updated slower than posterior beliefs, which incorporate Senders’ strategies. In the medium run, for some specifications of game parameters, this leads to outcomes being significantly different from the outcomes of the game in which a common prior is induced. It is also shown that elicitation of beliefs does not considerably change the pattern of play in this game. (shrink)

We study a low-rationality learning dynamics called probe and adjust. Our emphasis is on its properties in games of information transfer such as the Lewis signaling game or the Bala-Goyal network game. These games fall into the class of weakly better reply games, in which, starting from any action profile, there is a weakly better reply path to a strict Nash equilibrium. We prove that probe and adjust will be close to strict Nash equilibria (...) in this class of games with arbitrarily high probability. In addition, we compare these asymptotic properties to short-run behavior. (shrink)

Abstract: Knowledge requires more than mere true belief, and we also tend to think it is more valuable. I explain the added value that knowledge contributes if its extra ingredient beyond true belief is tracking . I show that the tracking conditions are the unique conditions on knowledge that achieve for those who fulfill them a strict Nash Equilibrium and an Evolutionarily Stable Strategy in what I call the True Belief Game. The added value of these properties, intuitively, (...) includes preparedness and an expectation of survival advantage. On this view knowledge is valuable not because knowledge persists but because it makes the bearer more likely to maintain an appropriate belief state—possibly nonbelief—through time and changing circumstances. When Socrates concluded that knowledge of the road to Larissa was no more valuable than true belief for the purpose of getting to Larissa, he did not take into account that one might want to be prepared for a possible meeting with a misleading sophist along the way, or for the possibility of road work. (shrink)

We consider modifications to the standard David Lewis signaling game and relax a number of unrealistic implicit assumptions that are often built into the framework. In particular, we motivate and explore various asymmetries that exist between the sender and receiver roles. We find that endowing receivers with a more realistic set of responses significantly decreases the likelihood of signaling, while allowing for unequal selection pressure often has the opposite effect. We argue that the results of this article (...) can also help make sense of a well-known evolutionary puzzle regarding the absence of an evolutionary arms race between sender and receiver in conflict-of-interest signaling games. (shrink)

I introduce an extension of the Lewis-Skyrms signaling game, analysed from a dynamical perspective via simple reinforcement learning. In Lewis’ (Convention, Blackwell, Oxford, 1969) conception of a signaling game, salience is offered as an explanation for how individuals may come to agree upon a linguistic convention. Skyrms (Signals: evolution, learning & information, Oxford University Press, Oxford, 2010a) offers a dynamic explanation of how signaling conventions might arise presupposing no salience whatsoever. The extension of the atomic (...) signaling game examined here—which I will refer to as a salience game—introduces a variable parameter into the atomic signaling game which allows for degrees of salience, thus filling in the continuum between Skyrms’ and Lewis’ models. The model does not presuppose any salience at the outset, but illustrates a process by which accidentally evolved salience is amplified, to the benefit of the players. It is shown that increasing degrees of salience allow populations to avoid sub-optimal pooling equilibria and to coordinate upon conventions more quickly. (shrink)

We develop a logical system that captures two different interpretations of what extensive games model, and we apply this to a long-standing debate in game theory between those who defend the claim that common knowledge of rationality leads to backward induction or subgame perfect (Nash) equilibria and those who reject this claim. We show that a defense of the claim à la Aumann (1995) rests on a conception of extensive game playing as a one-shot event in (...) combination with a principle of rationality that is incompatible with it, while a rejection of the claim à la Reny (1988) assumes a temporally extended, many-moment interpretation of extensive games in combination with implausible belief revision policies. In addition, the logical system provides an original inductive and implicit axiomatization of rationality in extensive games based on relations of dominance rather than the usual direct axiomatization of rationality as maximization of expected utility. (shrink)

The traditional solution concept for noncooperative game theory is the Nash equilibrium, which contains an implicit assumption that players’ probability distributions satisfy t probabilistic independence. However, in games with more than two players, relaxing this assumption results in a more general equilibrium concept based on joint beliefs. This article explores the implications of this joint-beliefs equilibrium concept for two kinds of conflictual coordination games: crisis bargaining and public goods provision. We find that, using updating consistent with Bayes’ rule, (...) players’ beliefs converge to equilibria in joint beliefs which do not satisfy probabilistic independence. In addition, joint beliefs greatly expand the set of mixed equilibria. On the face of it, allowing for joint beliefs might be expected to increase the prospects for coordination. However, we show that if players use joint beliefs, which may be more likely as the number of players increases, then the prospects for coordination in these games declines vis-à-vis independent beliefs. (shrink)

Counterexamples to two results by Stalnaker (Theory and Decision, 1994) are given and a corrected version of one of the two results is proved. Stalnaker's proposed results are: (1) if at the true state of an epistemic model of a perfect information game there is common belief in the rationality of every player and common belief that no player has false beliefs (he calls this joint condition ‘strong rationalizability’), then the true (or actual) strategy profile is path equivalent to (...) a Nash equilibrium; (2) in a normal-form game a strategy profile is strongly rationalizable if and only if it belongs to C8 , the set of profiles that survive the iterative deletion of inferior profiles. (shrink)

Nash Equilibrium is a central concept ingame theory. It has been argued that playing NashEquilibrium strategies is rational advice for agentsinvolved in one-time strategic interactions capturedby non-cooperative game theory. This essaydiscusses arguments for that position: vonNeumann–Morgenstern's argument for their minimaxsolution, the argument from self-enforcingagreements, the argument from the absence ofprobabilities, the transparency-of-reasons argument,the argument from regret, and the argument fromcorrelated equilibrium. All of these argumentseither fail entirely or have a very limited scope.Whatever the use of Nash Equilibrium (...) is, therefore,it is not useful as a rational recommendation inone-time strategic interactions. This is good newsfor Bayesians: although this discussion does notargue directly for the Bayesian idea of rationalityas expected utility maximization, it argues againsta position that has been regarded as a contender insituations of strategic interaction. (shrink)

The problem of cooperation for rational actors comprises two sub problems: the problem of the intentional object (under what description does each actor perceive the situation?) and the problem of common knowledge for finite minds (how much belief iteration is required?). I will argue that subdoxastic signalling can solve the problem of the intentional object as long as this is confined to a simple coordination problem. In a more complex environment like an assurance game signals may become unreliable. Mutual (...) beliefs can then bolster the earlier attained equilibrium. I will first address these two problems by means of an example, in order to draw some more general lessons about combining evolutionary theory and rationality later on. (shrink)

This paper examines the existence of strategic solutions to finite normal form games under the assumption that strategy choices can be described as choices among lotteries where players have security- and potential level preferences over lotteries (e.g., Cohen, Theory and Decision, 33, 101–104, 1992, Gilboa, Journal of Mathematical Psychology, 32, 405–420, 1988, Jaffray, Theory and Decision, 24, 169–200, 1988). Since security- and potential level preferences require discontinuous utility representations, standard existence results for Nash equilibria in mixed strategies ( (...) class='Hi'>Nash, Proceedings of the National Academy of Sciences, 36, 48–49, 1950a, Non-Cooperative Games, Ph.D. Dissertation, Princeton University Press, 1950b) or for equilibria in beliefs (Crawford, Journal of Economic Theory, 50, 127–154, 1990) do not apply. As a key insight this paper proves that non-existence of equilibria in beliefs, and therefore non-existence of Nash equilibria in mixed strategies, is possible in finite games with security- and potential level players. But, as this paper also shows, rationalizable strategies (Bernheim, Econometrica, 52, 1007–1028, 1984, Moulin, Mathematical Social Sciences, 7, 83–102, 1984, Pearce, Econometrica, 52, 1029–1050, 1984) exist for such games. Rationalizability rather than equilibrium in beliefs therefore appears to be a more favorable solution concept for games with security- and potential level players. (shrink)

We introduce a new class of population games called stable games. These games are characterized by self-defeating externalities: when agents revise their strategies, the improvements in the payoffs of strategies to which revising players are switching are always exceeded by the improvements in the payoffs of strategies which revising players are abandoning. We show that stable games subsume many well-known classes of examples, including zero-sum games, games with an interior ESS, wars of attrition, and concave potential games. We prove that (...) the set of Nash equilibria of any stable game is convex, and offer an elementary proof of existence of equilibrium. Finally, we show that the set of Nash equilibria of a stable game is globally asymptotically stable under a variety of evolutionary dynamics. These convergence results are proved by constructing Lyapunov functions defined in terms of revision potentials—that is, potential functions for the protocols agents follow when they consider switching strategies. (shrink)

In classical game theory the idea that players randomize between their actions according to a particular optimal probability distribution has always been viewed as puzzling. In this paper, we establish a fundamental connection between n-person normal form games and quantum mechanics, which eliminates the conceptual problems of these random strategies. While the two theories have been regarded as distinct, our main theorem proves that if we do not give any other piece of information to a player in a (...) class='Hi'>game, than the payoff matrix—the axiom of “no-supplementary data” holds—then the state of mind of a rational player is algebraically isomorphic to a pure quantum state. The “no supplementary data” axiom is captured in a Lukasiewicz’s three-valued Kripke semantics wherein statements about whether a strategy or a belief of a player is rational are initially indeterminate i.e. neither true, nor false. As a corollary, we show that in a mixed Nash equilibrium, the knowledge structure of a player implies that probabilities must verify the standard “Born rule” postulate of QM. The puzzling “indifference condition” wherein each player must be rationally indifferent between all the pure actions of the support of his equilibrium strategy is resolved by his state of mind being described by a “quantum superposition” prior a player is asked to make a definite choice in a “measurement”. Finally, these results demonstrate that there is an intrinsic limitation to the predictions of game theory, on a par with the “irreducible randomness” of quantum physics. (shrink)

In this article three different types of loss aversion equilibria in bimatrix games are studied. Loss aversion equilibria are Nash equilibria of games where players are loss averse and where the reference points—points below which they consider payoffs to be losses—are endogenous to the equilibrium calculation. The first type is the fixed point loss aversion equilibrium, introduced in Shalev (2000; Int. J. Game Theory 29(2):269) under the name of ‘myopic loss aversion equilibrium.’ There, the players’ (...) reference points depend on the beliefs about their opponents’ strategies. The second type, the maximin loss aversion equilibrium, differs from the fixed point loss aversion equilibrium in that the reference points are only based on the carriers of the strategies, not on the exact probabilities. In the third type, the safety level loss aversion equilibrium, the reference points depend on the values of the own payoff matrices. Finally, a comparative statics analysis is carried out of all three equilibrium concepts in 2 × 2 bimatrix games. It is established when a player benefits from his opponent falsely believing that he is loss averse. (shrink)

We observe that in certain two-player repeated games of incomplete information, where information may be incomplete on both sides, it is possible for an informed player to signal his status as an informed player to the other without revealing any information about the choice of chance. The key to obtaining such a class of games is to relax the assumption that the players’ moves are observable. We show that in such cases players can achieve a kind of signaling that (...) is “zero-knowledge”, in the sense that the other player becomes convinced that her opponent is informed without ever learning the choice of chance. Moreover, such “zero-knowledge signaling” has all of the statistical properties associated with zero-knowledge proofs in intereactive protocols. In particular, under the general assumption that moves are unobservable, such signaling leads to a class of equilibria in repeated games that are separatingin regard to the status of player 1–informed or uninformed–but only for player 2; any other player in a network, being unable to observe the moves of player 2, remains uncertain as to the status of player 1. (shrink)

The paper argues that the Nash Equilibrium Refinement Programme was less successful than its competitor, the Epistemic Programme. The prime criterion of success is the extent to which the programmes were able to reach the key objective guiding non-cooperative game theory for much of the twentieth century, namely, to develop a complete characterisation of the strategic rationality of economic agents in the form of the ultimate solution concept for any normal form and extensive game. The paper explains (...) this in terms of unjustified degrees of mathematisation in Nash Equilibrium Refinement Programme. While this programme’s mathematical models were often inspired by purely mathematical concerns rather than the economic phenomena they were intended to model, the Epistemic Programme’s models were developed with a keen eye to the role beliefs and desires play in strategic interaction between rational economic agents playing games; that is, their interactive epistemology. The Epistemic Programme succeeded in developing mathematical models formalising aspects of strategic interaction that remained implicit in the Nash Equilibrium Refinement Programme owing to an unjustified degree of mathematisation. As a result, the Epistemic Programme is the more successful theory.Keywords: Epistemic Programme; Game theory; Interactive epistemology; Mathematisation; Nash equilibrium. (shrink)

Inspired by Shalev’s model of loss aversion, we investigate the effect of loss aversion on a bimatrix game where the payoffs in the bimatrix game are characterized by triangular fuzzy variables. First, we define three solution concepts of credibilistic loss aversion Nash equilibria, and their existence theorems are presented. Then, three sufficient and necessary conditions are given to find the credibilistic loss aversion Nash equilibria. Moreover, the relationship among the three credibilistic loss aversion (...) class='Hi'>Nash equilibria is discussed in detail. Finally, for2×2bimatix game with triangular fuzzy payoffs, we investigate the effect of loss aversion coefficients and confidence levels on the three credibilistic loss aversion Nash equilibria. It is found that an increase of loss aversion levels of a player leads to a decrease of his/her own payoff. We also find that the equilibrium utilities of players are decreasing as their own confidence levels when players employ the optimistic value criterion. (shrink)

Since the seminal paper of Nash (Proc Natl Acad Sci USA 36:48–49, 1950) game theoretic literature has focused mostly on equilibrium and not on maximin (minimax) strategies. In a recent paper of Pruzhansky (Int J Game Theory 40:351–365, 2011) it was shown that under fairy general conditions maximin strategies in completely mixed games can guarantee the same expected payoff as completely mixed Nash equilibrium strategies. Based on this finding, the current paper argues that maximin strategies have (...) important properties. For instance, maximin strategies may refine Nash equilibria in subjective mixed strategies. Further, Bayesian rationality of the players may favor maximin strategies more often than Nash equilibrium strategies. The paper concludes with several suggestions for further experimental research that may shed more light on whether maximin behavior can explain reality better than Nash equilibrium. (shrink)

Common wisdom holds that communication is impossible when messages are costless and communicators have totally opposed interests. This article demonstrates that such wisdom is false. Non-convergent dynamics can sustain partial information transfer even in a zero-sum signalling game. In particular, I investigate a signalling game in which messages are free, the state-act payoffs resemble rock–paper–scissors, and senders and receivers adjust their strategies according to the replicator dynamic. This system exhibits Hamiltonian chaos and trajectories do not converge to (...) class='Hi'>equilibria. This persistent out-of-equilibrium behaviour results in messages that do not perfectly reveal the sender's private information, but do transfer information as quantified by the Kullback–Leibler divergence. This finding shows that adaptive dynamics can enable information transmission even though messages at equilibria are meaningless. This suggests a new explanation for the evolution or spontaneous emergence of meaning: non-convergent adaptive dynamics. (shrink)

In this paper I will discuss why (un) marked expressionstypically get an (un)marked interpretation: Horn''sdivision of pragmatic labor. It is argued that it is aconventional fact that we use language this way.This convention will be explained in terms ofthe equilibria of signalling games introduced byLewis (1969), but now in an evolutionary setting. Iwill also relate this signalling game analysis withParikh''s (1991, 2000, 2001) game-theoretical analysis ofsuccessful communication, which in turn is compared withBlutner''s: 2000) bi-directional optimality theory.

A central goal of philosophy of perception is to uncover the nature of sensory capacities. Ideally, we would like an account that specifies what conditions need to be met in order for an organism to count as having the capacity to sense or perceive its environment. And on the assumption that sensory states are the kinds of things that can be accurate or inaccurate, a further goal of philosophy of perception is to identify the accuracy conditions for sensory states. In (...) this paper I recommend a novel approach to these core issues, one that draws heavily on game-theoretic treatments of signaling in nature. A benefit of the approach is that it helps us to understand why biologists attribute sensory powers to such a diverse range of organisms, including plants, fungi, and algae. (shrink)

A strategic equilibrium is a profile of strategies that are each self-supporting given the profile. Strategic equilibria exist in games without Nash equilibria.

In signaling games, a sender has private access to a state of affairs and uses a signal to inform a receiver about that state. If no common association of signals and states is initially available, sender and receiver must coordinate to develop one. How do players divide coordination labor? We show experimentally that, if players switch roles at each communication round, coordination labor is shared. However, in games with fixed roles, coordination labor is divided: Receivers adjust their mappings more (...) frequently, whereas senders maintain the initial code, which is transmitted to receivers and becomes the common code. In a series of computer simulations, player and role asymmetry as observed experimentally were accounted for by a model in which the receiver in the first signaling round has a higher chance of adjusting its code than its partner. From this basic division of labor among players, certain properties of role asymmetry, in particular correlations with game complexity, are seen to follow. (shrink)

In the standard formulation of game theory, agents use mixed strategies in the form of objective and probabilistically precise devices to conceal their actions. We introduce the larger set of probabilistically imprecise devices and study the consequences for the basic results on normal form games. While Nash equilibria remain equilibria in the extended game, there arise new Ellsberg equilibria with distinct outcomes, as we illustrate by negotiation games with three players. We characterize Ellsberg (...) class='Hi'>equilibria in two-person conflict and coordination games. These equilibria turn out to be related to experimental deviations from Nash equilibrium play. (shrink)

In studies of multi-agent interaction, especially in game theory, the notion of equilibrium often plays a prominent role. A typical scenario for the belief merging problem is one in which several agents pool their beliefs together to form a consistent "group" picture of the world. The aim of this paper is to define and study new notions of equilibria in belief merging. To do so, we assume the agents arrive at consistency via the use of a social belief (...) removal function, in which each agent, using his own individual removal function, removes some belief from his stock of beliefs. We examine several notions of equilibria in this setting, assuming a general framework for individual belief removal due to Booth et al. We look at their inter-relations as well as prove their existence or otherwise. We also show how our equilibria can be seen as a generalisation of the idea of taking maximal consistent subsets of agents. (shrink)

I consider games with ambiguous payoffs played by non-Expected Utility decision makers. Three equilibrium solutions are studied. Nash equilibrium in which equilibrium mixed strategies must be best responses, Crawford equilibrium in beliefs and pure equilibrium in beliefs in which equilibrium strategies are mixtures of best responses, with the latter restricting best responses to pure actions. I study the interactions between ambiguity preferences on one side and equilibrium properties on the other. I show how the equilibrium concepts differ, computing necessary (...) and sufficient conditions for existence and equivalence. I also show how these solution concepts fare against two fundamental principles of Nash equilibrium in standard games: the principle of indifference and the reduction principle. Given both are central to the computation of Nash equilibrium in games with Expected Utility players, their failure indicates how relaxing the Expected Utility hypothesis may disrupt standard game theoretic results such as the characterization of equilibria in two-player games. (shrink)

Game-theoretic solution concepts such as Nash and Bayesian equilibrium start from an assumption that the players’ sets of possible payoffs, measured in units of von Neumann–Morgenstern utility, are common knowledge, and they go on to define rational behavior in terms of equilibrium strategy profiles that are either pure or independently randomized and which, in applications, are often taken to be uniquely determined or at least tightly constrained. A mechanism through which to obtain a common knowledge of payoff functions (...) measured in units of utility is not part of the model. This paper describes an operational method of constructing a state of common knowledge of the key parameters of the players’ utility functions in terms of conditional small bets on the game’s outcome. When the rationality criterion of joint coherence is applied in this setting, the solution of a game is typically characterized by a convex set of correlated equilibria. In the most general case, where players are risk averse, the parameters of the equilibria are risk-neutral probabilities, interpretable as products of subjective probabilities and relative marginal utilities for money, as in financial markets. Risk aversion generally enlarges the set of equilibria and may present opportunities for Pareto-improving modifications of the rules of the game. (shrink)

Brian Skyrms constructs a theory of "dynamic deliberation" and uses it to investigate rational decision-making in cases of strategic interaction. This illuminating book will be of great interest to all those in many disciplines who use decision theory and game theory to study human behavior and thought. Skyrms begins by discussing the Bayesian theory of individual rational decision and the classical theory of games, which at first glance seem antithetical in the criteria used for determining action. In his effort (...) to show how methods for dealing with information feedback can be productively combined, the author skillfully leads us through the mazes of equilibrium selection, the Nash equilibria for normal and extensive forms, structural stability, causal decision theory, dynamic probability, the revision of beliefs, and, finally, good habits for decision. The author provides many clarifying illustrations and a handy appendix called "Deliberational Dynamics on Your Personal Computer." His powerful model has important implications for understanding the rational origins of convention and the social contract, the logic of nuclear deterrence, the theory of good habits, and the varied strategies of political and economic behavior. (shrink)

We present a dynamic model of the evolution of communication in a Lewis signaling game while systematically varying the degree of common interest between sender and receiver. We show that the level of common interest between sender and receiver is strongly predictive of the amount of information transferred between them. We also discuss a set of rare but interesting cases in which common interest is almost entirely absent, yet substantial information transfer persists in a *cheap talk* regime, and (...) offer a diagnosis of how this may arise. -/- . (shrink)

Evolving signaling systems can be said to induce partitions on the space of world states as they approach equilibrium. Formalizing this claim provides a general framework for understanding what it means for language to “cut nature at its seams”. In order to avoid taking our current best science as providing the adaptive target for all evolving systems, the state space of the world must be characterized exclusively in terms of the coincidence of stimuli and payoffs that drives the evolution (...) of cognitive complexity. Cognition exploits the reliable clustering of events in this space. Using this framework to analyze our ordinary concepts of truth and justification, it appears that while justification can be a simple matter of conforming to historically entrenched strategies, truth cannot be fully specified on the basis of the system’s causal history, but requires a robust clustering in the larger world state space. (shrink)

In this paper, I develop a syntactic framework for the analysis ofstrategic form games that is based on a straightforward combination ofstandard systems of doxastic, probabilistic and conditionalpropositional logic. In particular, for the probabilistic part I makeuse of the axiomatization provided in Fagin and Halpern (1994). The use ofconditionals allows to represent a strategic form game by a logicalformula in a very natural way. Also expected utility maximization can benaturally captured. I use this framework to prove a version of (...) a resulton Nash equilibrium conjectures first presented in Aumann and Brandenburger (1995). (shrink)

The spontaneous emergence of signaling has already been studied in terms of standard evolutionary dynamics of signaling games. Standard evolutionary dynamics is given by the replicator equations. Thus, it is not clear whether the results for standard evolutionary dynamics depend crucially on the functional form of the replicator equations. In this paper I show that the basic results for the replicator dynamics of signaling games carry over to a number of other evolutionary dynamics. ‡This research was supported (...) by the Konrad Lorenz Institute for Evolution and Cognition Research. †To contact the author, please write to: Konrad Lorenz Institute for Evolution and Cognition Research, Adolf Lorenz Gasse 2, A-3422 Altenberg, Austria; e-mail: [email protected]. (shrink)

Signaling games with reinforcement learning have been used to model the evolution of term languages (Lewis 1969, Convention. Cambridge, MA: Harvard University Press; Skyrms 2006, “Signals” Presidential Address. Philosophy of Science Association for PSA). In this article, syntactic games, extensions of David Lewis’s original sender–receiver game, are used to illustrate how a language that exploits available syntactic structure might evolve to code for states of the world. The evolution of a language occurs in the context of available vocabulary (...) and syntax—the role played by each component is compared in the context of simple reinforcement learning. (shrink)

One might think that if the majority of virtue signallers judge that a proposition is true, then there is significant evidence for the truth of that proposition. Given the Condorcet Jury Theorem, individual virtue signallers need not be very reliable for the majority judgment to be very likely to be correct. Thus, even people who are skeptical of the judgments of individual virtue signallers should think that if a majority of them judge that a proposition is true, then that provides (...) significant evidence that the proposition is true. We argue that this is mistaken. Various empirical studies converge on the following point: humans are very conformist in the contexts in which virtue signalling occurs. And stereotypical virtue signallers are even more conformist in such contexts. So we should be skeptical of the claim that virtue signallers are sufficiently independent for the Condorcet Jury Theorem to apply. We do not seek to decisively rule out the relevant application of the Condorcet Jury Theorem. But we do show that careful consideration of the available evidence should make us very skeptical of that application. Consequently, a defense of virtue signalling would need to engage with these findings and show that despite our strong tendencies for conformism, our judgements are sufficiently independent for the Condorcet Jury Theorem to apply. This suggests new directions for the debate about the epistemology of virtue signalling. (shrink)

Why do well‐functioning psychological systems sometimes give rise to absurd beliefs that are radically misaligned with reality? Drawing on signalling theory, I develop and explore the hypothesis that groups often embrace beliefs that are viewed as absurd by outsiders as a means of signalling ingroup commitment. I clarify the game‐theoretic and psychological underpinnings of this hypothesis, I contrast it with similar proposals about the signalling functions of beliefs, and I motivate several psychological and sociological predictions that could be used (...) to distinguish it from alternative explanations of irrational group beliefs. (shrink)

Both the quantity of information and the informational content of a signal are defined in the context of signaling games. Informational content is a generalization of standard philosophical notions of propositional content. It is shown how signals that initially carry no information may spontaneously acquire informational content by evolutionary or learning dynamics. It is shown how information can flow through signaling chains or signaling networks.

In this paper we describe an argumentation-based representation of normal form games, and demonstrate how argumentation can be used to compute pure strategy Nash equilibria. Our approach builds on Modgil’s Extended Argumentation Frameworks. We demonstrate its correctness, showprove several theoretical properties it satisfies, and outline how it can be used to explain why certain strategies are Nash equilibria to a non-expert human user.

We study the handicap principle in terms of the Sir Philip Sidney game. The handicap principle asserts that cost is required to allow for honest signalling in the face of conflicts of interest. We show that the significance of the handicap principle can be challenged from two new directions. Firstly, both the costly signalling equilibrium and certain states of no communication are stable under the replicator dynamics ; however, the latter states are more likely in cases where honest signalling (...) should apply. Secondly, we prove the existence and stability of polymorphisms where players mix between being honest and being deceptive and where signalling costs can be very low. Neither the polymorphisms nor the states of no communication are evolutionarily stable, but they turn out to be more important for standard evolutionary dynamics than the costly signalling equilibrium. (shrink)

As the content of propositional attitudes, propositions are usually taken to help explain the behavior of rational agents. However, a closer look at signaling games suggests otherwise: rational agents often acquire partial beliefs, and many of their signals are ambiguous. Signaling games also suggest that it is rational for agents to mix their behavior in response to partial beliefs and ambiguous signals. But as I show in this paper, propositions cannot help explain the mixing behavior of rational agents: (...) to explain mixing behavior, we need a probabilistic notion of content. I also show that a probabilistic notion of content renders propositions explanatorily idle in the case of unambiguous signals and full beliefs as well. My suggestion is thus that we should abandon propositions in explanations of rational behavior and adopt instead a probabilistic notion of content. The notion of probabilistic content ultimately provides a simpler framework for explanations of rational behavior than the notion of propositional content. (shrink)

#1 NEW YORK TIMES BESTSELLER • A bold work from the author of The Black Swan that challenges many of our long-held beliefs about risk and reward, politics and religion, finance and personal responsibility In his most provocative and practical book yet, one of the foremost thinkers of our time redefines what it means to understand the world, succeed in a profession, contribute to a fair and just society, detect nonsense, and influence others. Citing examples ranging from Hammurabi to Seneca, (...) Antaeus the Giant to Donald Trump, Nassim Nicholas Taleb shows how the willingness to accept one’s own risks is an essential attribute of heroes, saints, and flourishing people in all walks of life. As always both accessible and iconoclastic, Taleb challenges long-held beliefs about the values of those who spearhead military interventions, make financial investments, and propagate religious faiths. Among his insights: • For social justice, focus on symmetry and risk sharing. You cannot make profits and transfer the risks to others, as bankers and large corporations do. You cannot get rich without owning your own risk and paying for your own losses. Forcing skin in the game corrects this asymmetry better than thousands of laws and regulations. • Ethical rules aren’t universal. You’re part of a group larger than you, but it’s still smaller than humanity in general. • Minorities, not majorities, run the world. The world is not run by consensus but by stubborn minorities imposing their tastes and ethics on others. • You can be an intellectual yet still be an idiot. “Educated philistines” have been wrong on everything from Stalinism to Iraq to low-carb diets. • Beware of complicated solutions (that someone was paid to find). A simple barbell can build muscle better than expensive new machines. • True religion is commitment, not just faith. How much you believe in something is manifested only by what you’re willing to risk for it. The phrase “skin in the game” is one we have often heard but rarely stopped to truly dissect. It is the backbone of risk management, but it’s also an astonishingly rich worldview that, as Taleb shows in this book, applies to all aspects of our lives. As Taleb says, “The symmetry of skin in the game is a simple rule that’s necessary for fairness and justice, and the ultimate BS-buster,” and “Never trust anyone who doesn’t have skin in the game. Without it, fools and crooks will benefit, and their mistakes will never come back to haunt them.”. (shrink)

We give derivations of two formal models of Gricean Quantity implicature and strong exhaustivity in bidirectional optimality theory and in a signalling games framework. We show that, under a unifying model based on signalling games, these interpretative strategies are game-theoretic equilibria when the speaker is known to be respectively minimally and maximally expert in the matter at hand. That is, in this framework the optimal strategy for communication depends on the degree of knowledge the speaker is known to (...) have concerning the question she is answering. In addition, and most importantly, we give a game-theoretic characterisation of the interpretation rule Grice (formalising Quantity implicature), showing that under natural conditions this interpretation rule occurs in the unique equilibrium play of the signalling game. (shrink)

Eric Posner’s signaling theory of social norms holds that individuals adopt social norms in order to signal that they have a low discount rate , and are therefore reliable long-term cooperative partners. This paper radically expands Posner’s theory by incorporating internalization into his model . I do this by tethering Posner’s theory to an evolutionary model. I argue that internalization is an adaptive quality that enhances the individual’s ability to play Posner’s signaling game and was thus selected (...) for. The idea that internalization is evolutionarily conditioned is not new; however, linking this to Posner’s theory of discount rate signals is, and doing so offers tremendous explanatory potential.Part I identifies the limitations of Posner’s purely rational choice approach, argues for the necessity of including internalization, and then proposes a model that does so – what I call the Expanded Signaling Model of Norms . Part II examines the problems that arise when we embrace such a model. How this model answers some key criticisms plaguing sociobiology is also briefly explored. Part III then examines existing criticisms of Posner’s theory, demonstrating how the Expanded Signaling Model clearly resolves these issues. The paper concludes that incorporating internalization into Posner’s signaling model greatly broadens the explanatory reach of Posner’s theory, providing a measure of clarity and predictability regarding how and why norms are internalized – an important insight, as these beliefs form the normative underpinning to law. (shrink)

Deliberation about what to do in any context requires reasoning about what will or would happen in various alternative situations, including situations that the agent knows will never in fact be realized. In contexts that involve two or more agents who have to take account of each others' deliberation, the counterfactual reasoning may become quite complex. When I deliberate, I have to consider not only what the causal effects would be of alternative choices that I might make, but also what (...) other agents might believe about the potential effects of my choices, and how their alternative possible actions might affect my beliefs. Counterfactual possibilities are implicit in the models that game theorists and decision theorists have developed – in the alternative branches in the trees that model extensive form games and the different cells of the matrices of strategic form representations – but much of the reasoning about those possibilities remains in the informal commentary on and motivation for the models developed. Puzzlement is sometimes expressed by game theorists about the relevance of what happens in a game ‘off the equilibrium path’: of what would happen if what is both true and known by the players to be true were instead false. (shrink)

In its classical conception, game theory aspires to be a determinate decision theory for games, understood as elements of a structurally specified domain. Its aim is to determine for each game in the domain a complete solution to each player's decision problem, a solution valid for all real-world instantiations, regardless of context. "Permissiveness" would constrain the theory to designate as admissible for a player any conjecture consistent with the function's designation of admissible strategies for the other players. Given (...) permissiveness and other appropriate constraints, solution sets must contain only Nash equilibria and at least one pure-strategy equilibrium, and there is no solution to games in which no symmetry invariant set of pure-strategy equilibria forms a Cartesian product. These results imply that the classical program is unrealizable. Moreover, the program is implicitly committed to permissiveness, through its common-knowledge assumptions and its commitment to equilibrium. The resulting incoherence deeply undermines the classical conception in a way that consolidates a long series of contextualist criticisms. (shrink)

This dissertation investigates some philosophical issues using computational models. Chapter 1 presents a Lewis-Skyrms signaling game that can exhibit a type of compositionality novel to the signaling game literature. The structure of the signaling game is motivated by an analogy to the alarm calls of putty-nosed monkeys (Cercopithecus nictitans). Putty-nosed monkeys display a compositional system of alarm calls with a semantics that is sensitive to the ordering of terms. This sensitivity to the ordering of (...) terms has not been previously modeled with a Lewis-Skyrms signaling game literature. Signaling games are valued for showing how communicative systems can arise with minimal learning tools. Simulation results show that basic (Roth-Erev) reinforcement learning is sufficient for the acquisition of a compositional signaling system sensitive to the ordering of terms. Chapter 2 investigates social epistemology in the context of an effect of cognitive biases called the illusory truth effect. The illusory truth effect is exhibited when repeated exposure to a statement increases an individual's credence in that statement. While most investigations of the illusory truth effect focus on individuals' belief formation, humans typically form beliefs within a social structure. This is particularly relevant because various social structures can give rise to repeated exposure to statements; e.g. a popular book might recurringly be discussed in one's social circle, or one or two foundational papers might always be cited by a particular lab. So, how does the illusory truth effect influence learning and belief formation in a group? This chapter uses network models to investigate this question. These models show that the illusory truth effect can be very detrimental to a group's belief formation. The effect causes networks to prematurely settle on a belief, in part, through repeated exposure to data points that are not independently generated. Previous research has indicated that the probability of such failures is near zero when networks are large or scientists are forced to explore unpopular and risky science. However, simulation results show that the harmful consequences of the illusory truth effect are robust even in large networks with mandatory exploration. Finally, Chapter 3 shows how a rudimentary type of abstraction can obtain in Lewis-Skyrms signaling games. Here, abstraction is understood as occurring when different particulars take on the same functional role. Some abstraction may be guided by innate biases, and the chapter develops an analogy of reasoning about strategic thinking in chess to highlight some epistemic concerns that are raised by the presentation of abstraction. Concretely, the signaling game models of this chapter are developed in the context of two tasks that are much simpler than strategizing in chess. The first task is a transitive inference task that has been substantially studied in both humans and non-human animals. General features of the models developed for the transitive inference task are then carried over to a model for the second task of learning rudimentary grammatical structures. This second task is based on studies of human infants and non-human primates' ability to learn ``nonsense grammars". Closing discussion highlights some strengths of the abstraction exhibited in the Lewis-Skyrms signaling game models. (shrink)

Compositionality is a key design feature of human language: the meaning of complex expressions is, for the most part, systematically constructed from the meanings of its parts and their manner of composition. This paper demonstrates that rudimentary forms of compositional communicative behavior can emerge from a variant of reinforcement learning applied to signaling games. This helps explain how compositionality could have emerged gradually: if unsophisticated agents can evolve prevalent dispositions to communicate compositional-like, there is a direct evolutionary benefit for (...) adaptations that exploit the systematicity in form-meaning mappings more rigorously. (shrink)

We give derivations of two formal models of Gricean Quantity implicature and strong exhaustivity in bidirectional optimality theory and in a signalling games framework. We show that, under a unifying model based on signalling games, these interpretative strategies are game-theoretic equilibria when the speaker is known to be respectively minimally and maximally expert in the matter at hand. That is, in this framework the optimal strategy for communication depends on the degree of knowledge the speaker is known to (...) have concerning the question she is answering. In addition, and most importantly, we give a game-theoretic characterisation of the interpretation rule Grice (formalising Quantity implicature), showing that under natural conditions this interpretation rule occurs in the unique equilibrium play of the signalling game. (shrink)