David Lewis is widely regarded as the philosopher who introduced the concept of common knowledge. His account of common knowledge differs greatly from most later accounts in philosophy and economy, with the central notion of his theory being ‘having reason to believe’ rather than ‘knowledge’. Unfortunately, Lewis’s account is rather informal, and the argument has a few gaps. This paper assesses two major attempts to formalise Lewis’s account and argues that these formalisations are missing a crucial aspect of this account. (...) Therefore, a new reconstruction is proposed, which explicitly discusses ‘reasons’ and uses a logic inspired by justification logic. (shrink)

This paper investigates the epistemic assumptions that David Lewis makes in his account of social conventions. In particular, I focus on the assumption that the agents have common knowledge of the convention to which they are parties. While evolutionary analyses show that the common knowledge assumption is unnecessary in certain classes of games, Lewis’ original account (and, more recently, Cubitt and Sugden’s reconstruction) stresses the importance of including it in the definition of convention. I discuss arguments pro et contra to (...) argue that, although the assumption might be relevant to a descriptively adequate account of social convention, it is not required for its rational reconstruction. I then point out that Lewis’ account, properly speaking, is of common reason to believe, rather than of common knowledge, and argue that, in order to formalize aptly the distinction between reason to believe and belief, standard formal epistemic models need to be supplemented with so-called awareness structures. Finally, I stress that the notion of knowledge implicit in Lewis’ text involves interesting elements that cannot be captured in the standard propositional formalizations, but need the full expressive force of quantified epistemic logic. (shrink)

In this paper, I outline and defend the view that variations in compliance levels with one and the same norm represent differentnorms about following norms. In support of this claim, I first argue that classic game-theoretic accounts, which define norms as Nash equilibria of noncooperative games, typically consider variations in compliance levels as separate norms. After that, I suggest a more fine-grained, game-theoretic distinction that accounts for degrees of compliance with the same norm and I show how to incorporate such (...) an account into a psychological framework. Finally, the paper examines what given degrees of compliance can reveal about the dynamics underlying the process of norm change. I will argue that they are indicators of different reactions to the introduction of new norms. (shrink)

Signaling games provide basic insights into some fundamental questions concerning the explanation of meaning. They can be analyzed in terms of rational choice theory and in terms of evolutionary game theory. It is argued that an evolutionary approach provides better explanations for the emergence of simple communication systems. To substantiate these arguments, I will look at models similar to those of Skyrms (2000) and Komarova and Niyogi (2004) and study their dynamical properties. My results will lend partial support to the (...) thesis that evolution leads to communication. In general, states of partial communication may evolve with positive probability under standard evolutionary dynamics. However, unlike states of perfect communication, they are unstable relative to neutral drift. (shrink)

Analytic narratives are case studies of historical events and/or institutions that are formed by the combination of the narrative method characteristic of historical and historiographical wor...

This article presents a community-based account of salience as an alternative and a complement to the ‘natural salience’ approach which is endorsed by almost all game theorists who use this concept. While in the naturalistic approach, salience is understood as an objective and natural property of some entities, the community-based account claims that salience is a function of community membership. Building on David Lewis’s theory of common knowledge and on some of its recent refined accounts, I suggest that salience acts (...) as a correlating device in a correlated equilibrium. What is constitutive of salience is common understanding, the fact that agents have common knowledge that they share the same modes of reasoning with respect to a well-identified set of events. I argue that the basis for common understanding is community membership. The relevance of this account stems from the fact that it answers the objection that salience is either unnecessary or unable to account for coordination between rational agents. (shrink)

Economic theories of team reasoning build on the assumption that agents can sometimes behave according to beliefs or preferences attributed to a group or a team. In this paper, I propose a different framework to introduce collective intentionality into game theory. I build on John Searle’s account, which makes collective intentionality constitutive of institutional facts. I show that as soon as one accepts that institutions are required to solve indetermination problems in a game, it is necessary to assume a form (...) of collective intentionality that comes from what I call a common understanding of the situation among the players. This common understanding embodies the epistemic requirements for an institution to be a correlated equilibrium in a game. As a consequence, I question recent claims made by some economists according to which game-theoretic accounts of institutions do not need to assume collective intentionality. (shrink)

:Most game-theoretic accounts of institutions reduce institutions to behavioural patterns the players are incentivized to implement. An alternative account linking institutions to rule-following behaviour in a game-theoretic framework is developed on the basis of David Lewis’s and Ludwig Wittgenstein's respective accounts of conventions and language games. Institutions are formalized as epistemic games where the players share some forms of practical reasoning. An institution is a rule-governed game satisfying three conditions: common understanding, minimal awareness and minimal practical rationality. Common understanding has (...) a strong similarity with Ludwig Wittgenstein's concept of lebensform while minimal awareness and minimal practical rationality capture the idea that rule-following is community-based. (shrink)

This paper provides a conceptual exploration of the implication of Jeffrey’s rule of belief revision to account for rule-following behavior in a game-theoretic framework. Jeffrey’s rule reflects the fact that in many cases learning something new does not imply that one has full assurance about the true content of the information. In other words, the same information may be both perceived and interpreted in several different ways. I develop an account of rule-following behavior according to which, in the context of (...) strategic interactions, following a rule is defined by two conditions. First, that agents must frame the interaction in a sufficiently similar way and be aware of the same salient properties, i.e. they must have the same partition of the event. Second, they must ascribe to others the same revised probabilities to what they take to be the common partition. In a game-theoretic framework, this also indicates that rule-following behavior cannot be identified merely to the existence of a common prior. (shrink)

Current debates in social ontology are dominated by approaches that view institutions either as rules or as equilibria of strategic games. We argue that these two approaches can be unified within an encompassing theory based on the notion of correlated equilibrium. We show that in a correlated equilibrium each player follows a regulative rule of the form ‘if X then do Y’. We then criticize Searle's claim that constitutive rules of the form ‘X counts as Y in C’ are fundamental (...) building blocks for institutions, showing that such rules can be derived from regulative rules by introducing new institutional terms. Institutional terms are introduced for economy of thought, but are not necessary for the creation of social reality. (shrink)

The Standard View is that, other things equal, speakers’ judgments about the meanings of sentences of their language are correct. After all, we make the meanings, so how wrong can we be about them? The Standard View underlies the Elicitation Method, a typical method in semantic fieldwork, according to which we should work out the truth-conditions of a sentence by eliciting speakers’ judgments about its truth-value in different situations. I put pressure on the Standard View and therefore on the Elicitation (...) Method: for quite straightforward reasons, speakers can be radically mistaken about meanings. -/- Lewis gave a theory of convention in a game-theoretic framework. He showed how conventions could arise from repeated coordination games, and, as a special case, how meanings could arise from repeated signaling games. I put pressure on the Standard View by building on Lewis’s framework. I construct coordination games in which the players can be wrong about their conventions, and signaling games in which the players can be wrong about their messages’ meanings. The key idea is straightforward: knowing your own strategy and payoff needn’t determine what the others do, so leaves room for false beliefs about the convention and meanings. The examples are simple, explicit, new in kind, and based on an independently plausible meta-semantic story. (shrink)

Common knowledge is usually defined as a state in which everyone knows that p, everyone knows that everyone knows that p, and so on, ad infinitum. This definition is usually attributed to David Lewis, despite the fact that his own formulation bears no resemblance to common knowledge as it is usually understood. In this paper, I argue that this concept of common knowledge requires revision. Contrary to usual practice, it turns out to be difficult to model formally because existing models (...) fail to distinguish between full-blown common knowledge and merely finite levels of interactive knowledge. Conceptually, the concept is incompatible with Lewis's intended purpose and obscures the explanatory role played by rational choice models. I propose that the concept of common knowledge be brought better into alignment with Lewis's actual formulation. This reconceptualization of common knowledge suggests a greater focus on explanations that make recourse to the cognitive constraints of real-world agents. (shrink)

The value of solidarity, which is exemplified in noble groups like the Civil Rights Movement along with more mundane teams, families and marriages, is distinctive in part because people are in solidarity over, for or with regard to something, such as common sympathies, interests, values, etc. I use this special feature of solidarity to resolve a longstanding puzzle about enacted social moral rules, which is, aren’t these things just heuristics, rules of thumb or means of coordination that we ‘fetishize’ or (...) ‘worship’ if we stubbornly insist on sticking to them when we can do more good by breaking them? I argue that when we are in a certain kind of solidarity with others, united by social moral rules that we have established among ourselves, the rules we have developed and maintain are a constitutive part of our solidary relationships with one another; and it is part of being in this sort of solidarity with our comrades that we are presumptively required to follow the social moral rules that join us together. Those in the Polish Revolution, for example, were bound by informally enforced rules about publicity, free speech and the use of violence, so following their own rules became a way of standing in a valuable sort of solidarity with one another. I explain why we can have non-instrumental reasons to follow the social moral rules that exist in our own society, improve our rules and even sometimes to break the otherwise good rules that help to unite us. (shrink)

We present a new class of models of players’ reasoning in non-cooperative games, inspired by David Lewis's account of common knowledge. We argue that the models in this class formalize common knowledge of rationality in a way that is distinctive, in virtue of modelling steps of reasoning; and attractive, in virtue of being able to represent coherently common knowledge of any consistent standard of individual decision-theoretic rationality. We contrast our approach with that of Robert Aumann, arguing that the former avoids (...) and diagnoses certain paradoxes to which the latter may give rise when extended in particular ways. (shrink)

Social interaction is both ubiquitous and central to understanding human behavior. Such interactions depend, we argue, on shared intentionality: the parties must form a common understanding of an ambiguous interaction. Yet how can shared intentionality arise? Many well-known accounts of social cognition, including those involving “mind-reading,” typically fall into circularity and/or regress. For example, A’s beliefs and behavior may depend on her prediction of B’s beliefs and behavior, but B’s beliefs and behavior depend in turn on her prediction of A’s (...) beliefs and behavior. One possibility is to embrace circularity and take shared intentionality as imposing consistency conditions on beliefs and behavior, but typically there are many possible solutions and no clear criteria for choosing between them. We argue that addressing these challenges requires some form of we-reasoning, but that this raises the puzzle of how the collective agent arises from the individual agents. This puzzle can be solved by proposing that the will of the collective agent arises from a simulated process of bargaining: agents must infer what they would agree, were they able to communicate. This model explains how, and which, shared intentions are formed. We also propose that such “virtual bargaining” may be fundamental to understanding social interactions. (shrink)

This paper examines the perceptual and reasoning processes that underpin regularities in behaviour. A distinction is made between situations as they are, or as described by an omniscient external observer, and situations as agents see or frame them. Different frames can stem from differences in culture, experience and personality, as well as from other context-specific factors. Drawing upon David Lewis’s Convention, I show that consistency between reasoning and experience does not preclude individuals from understanding the same state of affairs differently, (...) and that agents’ beliefs about others’ beliefs may well be wrong. As a result, cases may occur in which conventions are sustained by false but mutually consistent and self-confirming beliefs. (shrink)

Game theory is the mathematical study of strategy and conflict. It has wide applications in economics, political science, sociology, and, to some extent, in philosophy. Where rational choice theory or decision theory is concerned with individual agents facing games against nature, game theory deals with games in which all players have preference orderings over the possible outcomes of the game. This paper gives an informal introduction to the theory and a survey of applications in diverse branches of philosophy. No criticism (...) is reviewed. Game theory is shown at work in discussions about epistemological dependence, liberalism and efficiency, Hume’s concept of convention, morality and rationality, and distributive justice and egalitarianism. A guide to the literature provides hints at applications in collective intentionality, epistemology, ethics, history of philosophy, logic, philosophy of language, and political philosophy. (shrink)

The central philosophical task posed by conventions is to analyze what they are and how they differ from mere regularities of action and cognition. Subsidiary questions include: How do conventions arise? How are they sustained? How do we select between alternative conventions? Why should one conform to convention? What social good, if any, do conventions serve? How does convention relate to such notions as rule, norm, custom, practice, institution, and social contract? Apart from its intrinsic interest, convention is important because (...) philosophers frequently invoke it when discussing other topics. A favorite philosophical gambit is to argue that, perhaps despite appearances to the contrary, some phenomenon ultimately results from convention. Notable candidates include: property, government, justice, law, morality, linguistic meaning, necessity, ontology, mathematics, and logic. (shrink)

One of the conceptual limitations of the orthodox game theory is its inability to offer definitive theoretical predictions concerning the outcomes of noncooperative games with multiple rationalizable outcomes. This prompted the emergence of goal-directed theories of reasoning – the team reasoning theory and the theory of hypothetical bargaining. Both theories suggest that people resolve non-cooperative games by using a reasoning algorithm which allows them to identify mutually advantageous solutions of non-cooperative games. The primary aim of this thesis is to enrich (...) the current debate on goaldirected reasoning theories by studying the extent to which the principles of the bargaining theory can be used to formally characterize the concept of mutual advantage in a way which is compatible with some of the conceptually compelling principles of orthodox game theory, such as individual rationality, incentive compatibility, and non-comparability of decision-makers’ personal payoffs. I discuss two formal characterizations of the concept of mutual advantage derived from the aforementioned goal-directed reasoning theories: A measure of mutual advantage developed in collaboration with Jurgis Karpus, which is broadly in line with the notion of mutual advantage suggested by Sugden, and the benefit-equilibrating bargaining solution function, which is broadly in line with the principles underlying Conley and Wilkie’s solution for Pareto optimal point selection problems with finite choice sets. I discuss the formal properties of each solution, as well as its theoretical predictions in a number of games. I also explore each solution concept’s compatibility with orthodox game theory. I also discuss the limitations of the aforementioned goal-directed reasoning theories. I argue that each theory offers a compelling explanation of how a certain type of decision-maker identifies the mutually advantageous solutions of non-cooperative games, but neither of them offers a definitive answer to the question of how people coordinate their actions in non-cooperative social interactions. (shrink)