To determine what the speaker in a cooperative dialog meant with his assertion, on top of what he explicitly said, it is crucial that we assume that the assertion he gave was optimal. In determining optimal assertions we assume that dialogs are embedded in decision problems (van Rooij 2003) and use backwards induction for calculating them (Benz 2006). In this paper, we show that in terms of our framework we can account for several types of implicatures in a uniform way, (...) suggesting that there is no need for an independent linguistic theory of generalized implicatures. In the final section, we show how we can embed our theory in the framework of signaling games, and how it relates with other game theoretic analyses of implicatures. (shrink)

We present an axiomatic approach for a class of finite, extensive form games of perfect information that makes use of notions like rationality at a node and knowledge at a node. We distinguish between the game theorist's and the players' own theory of the game. The latter is a theory that is sufficient for each player to infer a certain sequence of moves, whereas the former is intended as a justification of such a sequence of moves. While in general the (...) game theorist's theory of the game is not and need not be axiomatized, the players' theory must be an axiomatic one, since we model players as analogous to automatic theorem provers that play the game by inferring (or computing) a sequence of moves. We provide the players with an axiomatic theory sufficient to infer a solution for the game (in our case, the backwards induction equilibrium), and prove its consistency. We then inquire what happens when the theory of the game is augmented with information that a move outside the inferred solution has occurred. We show that a theory that is sufficient for the players to infer a solution and still remains consistent in the face of deviations must be modular. By this we mean that players have distributed knowledge of it. Finally, we show that whenever the theory of the game is group-knowledge (or common knowledge) among the players (i.e., it is the same at each node), a deviation from the solution gives rise to inconsistencies and therefore forces a revision of the theory at later nodes. On the contrary, whenever a theory of the game is modular, a deviation from equilibrium play does not induce a revision of the theory. (shrink)

The Common Prior Assumption (CPA) is central to the economics of information and the foundations of game theory. Recent contributions (Dekel and Gul, 1997, Gul, 1996, Lipman, 1995) have questioned its meaningfulness in situations of incomplete information where there is no ex ante stage and the primitives of the model are the individuals’ belief hierarchies. We address this conceptual issue by providing characterizations of two local versions of the CPA which are in terms of the primitives and, therefore, do not (...) involve a counterfactual and problematic ex ante stage. The characterizations involve three notions: Comprehensive Agreement, no error of beliefs and common belief in no error. Comprehensive Agreement is defined as the absence of “agreement to disagree” about any aspect of beliefs; it is a generalization of Aumann’s (1976) notion of agreement. The entire analysis is carried out locally, that is, with reference to the “true state” (which represents the actual profile of belief hierarchies) and does not rely on the Truth Axiom for individual beliefs. (shrink)

We develop an analysis of discourse anaphora—the relationship between a pronoun and an antecedent earlier in the discourse—using games of partial information. The analysis is extended to include information from a variety of different sources, including lexical semantics, contrastive stress, grammatical relations, and decision theoretic aspects of the context.

David Lewis is widely credited with the first formulation of common knowledge and the first rigorous analysis of convention. However, common knowledge and convention entered mainstream game theory only when they were formulated, later and independently, by other theorists. As a result, some of the most distinctive and valuable features of Lewis' game theory have been overlooked. We re-examine this theory by reconstructing key parts in a more formal way, extending it, and showing how it differs from more recent game (...) theory. In contrast to current theories of common knowledge, Lewis' theory is based on an explicit analysis of the modes of reasoning that are accessible to rational individuals and so can be used to analyse the genesis of common knowledge. Lewis' analysis of convention emphasises the role of inductive reasoning and of salience in the maintenance of conventions over time. Footnotes Earlier versions of this paper were presented at the 13th Amsterdam Colloquium at the University of Amsterdam, at a workshop on social norms at Wissenschaftskolleg zu Berlin, and at seminars at Tilburg University and the University of Bristol. We are grateful for comments from participants at those meetings, from two anonymous referees, and from Michael Bacharach, Nick Bardsley, Cristina Bicchieri, Luc Bovens, Simon Grant, David McCarthy, Shepley Orr, Brian Skyrms, Peter Vanderschraaf, Peter Wakker and Jörgen Weibull. Robert Sugden's work was supported by the Leverhulme Trust. (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)

While fairness is often mentioned as a determinant of ultimatum bargaining behavior, few data sets are available that can test theories that incorporate fairness considerations. This paper tests the reciprocal kindness theory in Rabin (1993 Incorporating fairness into game theory and economics, The American Economic Review 83: 1281-1302) as an application to the one-period ultimatum bargaining game. We report on data from 100 ultimatum games that vary the financial stakes of the game from 1 to 15. Responder behavior is strongly (...) in support of the kindness theory and proposer behavior weakly in support of it. Offer percentages and past offers influence behavior the most, whereas the size of the pie has a marginally significant effect on offer percentages. The data is more in support of reciprocal kindness than alternative theories of equal-split or learning behavior, although the data also weakly support a minimum percentage threshold hypothesis. As a whole, our results together with existing studies suggest that, for smaller stakes games, fairness considerations dominate monetary considerations. This has implications for more complicated naturally occurring bargaining environments in which the financial stakes can vary widely. (shrink)

The paper presents a variation of the EMAIL Game, originally proposed byRubinstein (American Economic Review, 1989), in which coordination ofthe more rewarding-risky joint course of actions is shown to obtain, evenwhen the relevant game is, at most, ``mutual knowledge.'' In the exampleproposed, a mediator is introduced in such a way that two individualsare symmetrically informed, rather than asymmetrically as in Rubinstein,about the game chosen by nature. As long as the message failure probabilityis sufficiently low, with the upper bound being a (...) function of the gamepayoffs, conditional beliefs in the opponent's actions can allow playersto choose a more rewarding-risky action. The result suggests that, forefficient coordination to obtain, the length of interactive knowledge onthe game, possibly up to ``almost common knowledge,'' does not seem to bea major conceptual issue and that emphasis should be focused instead onthe communication protocol and an appropriate relationship between thereliability of communication channels and the payoffs at stake. (shrink)

The mechanisms/abilities of agents compared to the emergent outcomes in three different scenarios from my past work is summarised: the El Farol Game; an Artificial Stock Market; and the Iterated Prisoner’s Dilemma. Within each of these, the presence or absence of some different agent abilities was examined, the results being summarised here – some turning out to be necessary, some not. The ability in terms of the recognition of other agents, either by characteristics or by name is a recurring theme. (...) Some of the difficulties in reaching a systematic understanding of these connections is briefly discussed. (shrink)

A feature of David Lewis's account of conventions in his book "Convention" which has received admiring notices from philosophers is his use of the mathematical theory of games. In this paper I point out a number of serious flaws in Lewis's use of game theory. Lewis's basic claim is that conventions cover 'coordination problems'. I show that game-Theoretical analysis tends to establish that coordination problems in Lewis's sense need not underlie conventions.

We extend previous work on cooperation to some related questions regarding the evolution of simple forms of communication. The evolution of cooperation within the iterated Prisoner's Dilemma has been shown to follow different patterns, with significantly different outcomes, depending on whether the features of the model are classically perfect or stochastically imperfect (Axelrod 1980a, 1980b, 1984, 1985; Axelrod and Hamilton, 1981; Nowak and Sigmund, 1990, 1992; Sigmund 1993). Our results here show that the same holds for communication. Within a simple (...) model, the evolution of communication seems to require a stochastically imperfect world. (shrink)

We continue the work initiated in Herzig and Lorini (J Logic Lang Inform, in press) whose aim is to provide a minimalistic logical framework combining the expressiveness of dynamic logic in which actions are first-class citizens in the object language, with the expressiveness of logics of agency such as STIT and logics of group capabilities such as CL and ATL. We present a logic called ( Deterministic Dynamic logic of Agency ) which supports reasoning about actions and joint actions of (...) agents and coalitions, and agentive and coalitional capabilities. In it is supposed that, once all agents have selected a joint action, the effect of this joint action is deterministic. In order to assess we prove that it embeds Coalition Logic. We then extend with modal operators for agents’ preferences, and show that the resulting logic is sufficiently expressive to capture the game-theoretic concepts of best response and Nash equilibrium. (shrink)

The importance of the notion of common knowledge in sustaining cooperative outcomes in strategic situations is well appreciated. However, the systematic analysis of the extent to which small departures from common knowledge affect equilibrium in games has only recently been attempted.We review the main themes in this literature, in particular, the notion of common p-belief. We outline both the analytical issues raised, and the potential applicability of such ideas to game theory, computer science and the philosophy of language.

Recently, natural language pragmatics started to make use of decision-, game-, and information theoretical tools to determine the usefulness of questions and assertions in a quantitative way. In the first part of this paper several of these notions are related with each other. It is shown that under particular natural assumptions the utility of questions and answers reduces to their informativity, and that the ordering relation induced by utility sometimes even reduces to the logical relation of entailment. The second part (...) of the paper shows how different proposals (using either protocols or likelihood functions) to measure the relevance/utility of non-partitional questions come down to the same thing. (shrink)

The paper begins by providing a game-theoretic reconstruction of Gilbert’s (1989) philosophical critique of Lewis (1969) on the role of salience in selecting conventions. Gilbert’s insight is reformulated thus: Nash equilibrium is insufficiently powerful as a solution concept to rationalize conventions for unboundedly rational agents if conventions are solutions to the kinds of games Lewis supposes. Both refinements to NE and appeals to bounded rationality can plug this gap, but lack generality. As Binmore (this issue) argues, evolutive game theory readily (...) explains the origin of conventional behavior, but that is not Lewis’s project. Gilbert’s critique is generalized by reference to Bacharach’s (2006) work on team reasoning in games. The paper then argues that although Lewis’s account of the rationalization of conventions is shown by the reconstruction of Gilbert’s critique to be incomplete, Gilbert is wrong to conclude that classical (‘eductive’) game theory lacks the resources to explain conformity to conventions among people. A game-theoretic account of the dynamics of socialization, based on Ross’s (2005, 2006) idea of ‘game determination’, rationalizes choices of conventional strategies in overlapping generations contexts, provided agents are products of evolutionary selection and know that other players are also such products. (shrink)

This paper uses game theory to try to provide a rational grounding for simple pragmatic inferences, scalar implicatures.

This paper offers a novel ‘changing places’ account of identification in games, where the consequences of role swapping are crucial. First, it illustrates how such an account is consistent with the view, in classical game theory, that only outcomes (and not pathways) are significant. Second, it argues that this account is superior to the ‘pooled resources’ alternative when it comes to dealing with some situations in which many players identify. Third, it shows how such a ‘changing places’ account can be (...) used in games where some of the players identify with one another, but others do not. Finally, it illustrates how the model can handle the notion that identification comes in degrees. (shrink)

The partial cooperation displayed by subjects in the Centipede Game deviates radically from the predictions of traditional game theory. Even standard, infinite population, evolutionary settings have failed to provide an explanation for this behavior. However, recent work in finite population evolutionary models has shown that such settings can produce radically different results from the standard models. This paper examines the evolution of partial cooperation in finite populations. The results reveal a new possible explanation that is not open to the standard (...) models and gives us reason to be cautious when employing these otherwise helpful idealizations. *Received January 2007; revised November 2007. †To contact the author, please write to: Department of Logic and Philosophy of Science, University of California, 3151 Social Science Plaza A, Irvine, CA 92697-5100; e-mail: rsmead@uci.edu. (shrink)

In one-shot public goods dilemmas, defection is the strictly dominant strategy. However, agents with cooperative strategies can do well if (1) agents are `translucent' (that is, if agents can fallibly recognize the strategy other agents play ex ante ) and (2) an institutional structure allows `assortation' such that cooperative agents can increase the likelihood of playing with their own kind. The model developed in this article shows that even weak levels of translucency suffice if cooperators are able to pool their (...) information to exclude defectors. Computer simulations confirm this claim. The results imply that conditional cooperation can be a successful strategy given translucency and `assortation', even if the game has a one-shot character. The article discusses implications for moral theory against the backdrop of `virtual self-regard' and the concept of moral integrity. Key Words: public good • game theory • prisoner's dilemma • translucency • assortation • group formation • group identity • integrity • altruism. (shrink)

Abstract Orthodox decision theory presupposes that agency is invested in individuals. An opposing literature allows team agency to be invested in teams whose members use distinctive modes of team reasoning. This paper offers a new conceptual framework, inspired by David Lewis's analysis of common reasons for belief, within which team reasoning can be represented. It shows how individuals can independently endorse a principle of team reasoning which prescribes acting as a team member conditional on assurance that others have endorsed the (...) same principle. It argues that there can be such assurance even when no individual has an obligation to act on team reasoning. *This paper originated in a lecture that I gave at a Colloquium on Collective Intentions at Erasmus University Rotterdam. I thank participants, and particularly Govert den Hartogh, for comments. The analysis presented in this paper is an offshoot of a larger project, which uses David Lewis's work as the starting point for a reconstruction of the foundations of game theory. That project is joint work with Robin Cubitt. The specific idea of using this approach to analyse team reasoning grew out of a discussion with Michael Bratman. My work was supported by the Leverhulme Trust. (shrink)

Individual rational action consists of (i) knowing what you want, (ii) taking proper steps to approach what you want as closely as possible, within the confines of the law. This one can learn, although some people are more skilled in it than others. Modern democracies are set up in such a way that they leave as much room as possible for individual rational action. Education for citizenship is sometimes taken to be: getting young citizens acquainted with the legal possibilities for (...) maximizing their individual interests. How about collective rational action? Game theory shows that if people engage in individual rational action, the common good suffers. This is known as ‘the tragedy of the commons’. It was also known in Antiquity: ”What is common to the greatest number has the least care bestowed upon it” (Aristotle). To understand the issues involved we will analyse the notions of ”common knowledge”, ”individual commitment” and ”collective intention”. (shrink)

Recently, natural language pragmatics started to make use of decision-, game-, and information theoretical tools to determine the usefulness of questions and assertions in a quantitative way. In the first part of this paper several of these notions are related with each other. It is shown that under particular natural assumptions the utility of questions and answers reduces to their informativity, and that the ordering relation induced by utility sometimes even reduces to the logical relation of entailment. The second part (...) of the paper shows how different proposals (using either protocols or likelihood functions) to measure the relevance/utility of non-partitional questions come down to the same thing. (shrink)

Aconvention is a state in which agents coordinate their activity, not as the result of an explicit agreement, but because their expectations are aligned so that each individual believes that all will act so as to achieve coordination for mutual benefit. Since agents are said to follow a convention if they coordinate without explicit agreement, the notion raises fundamental questions: (1) Why do certain conventions remain stable over time?, and (2) How does a convention emerge in the first place? In (...) a pioneering study, Lewis (1969) addresses these questions by applyingnoncooperative game theory. Lewis defines a convention as aNash coordination equilibrium of a noncooperative game that issalient, that is, it is somehow conspicuous to the agents so that all expect one another to conform with the equilibrium. This paper presents a new game theoretic definition of conventions, which formalizes the notion of salience and which also generalizes the class of conventions Lewis discusses in his work. I define a convention as acorrelated equilibrium (Aumann 1974, 1987) satisfying apublic intentions criterion: Every agent wants his intended action to becommon knowledge. I argue that many conventions correspond to correlated equilibria that are not Nash equilibria, and that this is consistent with Lewis' general viewpoint. Finally, I argue that game theoretic characterizations of convention, such as Lewis' and my own, help to explain a convention's stability, but that a fully satisfactory account of the emergence of convention requires a theory of equilibrium selection beyond the scope of Lewis' work. (shrink)