An introduction to the special issue on epistemic logic and the foundations of gametheory edited by Michael Bacharach and Philippe Mongin. Contributors are Michael Bacharach, Robert Stalnaker, Salvatore Modica and Aldo Rustichini, Luc Lismont and Philippe Mongin, and Hyun-Song Shin and Timothy Williamson.
This paper critically reviews Ken Binmoreâs non- utilitarian and game theoretic solution to the Arrow problem. Binmoreâs solution belongs to the same family as Rawlsâ maximin criterion and requires the use of Nash bargaining theory, empathetic preferences, and results in evolutionary gametheory. Harsanyi has earlier presented a solution that relies on utilitarianism, which requires some exogenous valuation criterion and is therefore incompatible with liberalism. Binmoreâs rigorous demonstration of the maximin principle for the first time presents (...) a real alternative to a utilitarian solution. (shrink)
Are the recent findings of Behavioural GameTheory (BGT) on unselfish behaviours relevant for the progress of gametheory? Is the methodology of BGT, centred around the attempt to study theoretically players’ utility functions in the light of the feedback that experimental evidence can produce on the theory, a satisfactory one? Or is the creation of various types of ‘social preferences’ just wasteful tinkering? This article compares BGT with the methodology of Rational Game (...) class='Hi'>Theory (RGT). BGT is viewed as a more promising and constructive approach, with regard to the relationship between experimental data and theoretical modelling. However, I also argue that today RGT and BGT are closer to one another than often thought. (shrink)
Rational choice theory enjoys unprecedented popularity and influence in the behavioral and social sciences, but it generates intractable problems when applied to socially interactive decisions. In individual decisions, instrumental rationality is defined in terms of expected utility maximization. This becomes problematic in interactive decisions, when individuals have only partial control over the outcomes, because expected utility maximization is undefined in the absence of assumptions about how the other participants will behave. Gametheory therefore incorporates not only rationality (...) but also common knowledge assumptions, enabling players to anticipate their co-players' strategies. Under these assumptions, disparate anomalies emerge. Instrumental rationality, conventionally interpreted, fails to explain intuitively obvious features of human interaction, yields predictions starkly at variance with experimental findings, and breaks down completely in certain cases. In particular, focal point selection in pure coordination games is inexplicable, though it is easily achieved in practice; the intuitively compelling payoff-dominance principle lacks rational justification; rationality in social dilemmas is self-defeating; a key solution concept for cooperative coalition games is frequently inapplicable; and rational choice in certain sequential games generates contradictions. In experiments, human players behave more cooperatively and receive higher payoffs than strict rationality would permit. Orthodox conceptions of rationality are evidently internally deficient and inadequate for explaining human interaction. Psychological gametheory, based on nonstandard assumptions, is required to solve these problems, and some suggestions along these lines have already been put forward. Key Words: backward induction; Centipede game; common knowledge; cooperation; epistemic reasoning; gametheory; payoff dominance; pure coordination game; rational choice theory; social dilemma. (shrink)
Contents. Introduction. 1. Preliminaries. 2. Normal Form Games. 3. Extensive Games. 4. Applications of GameTheory. 5. The Methodology of GameTheory. Conclusion. Appendix. Bibliography. Index. Does gametheory—the mathematical theory of strategic interaction—provide genuine explanations of human behaviour? Can gametheory be used in economic consultancy or other normative contexts? Explaining Games: The Epistemic Programme in GameTheory—the first monograph on the philosophy of gametheory—is an (...) attempt to combine insights from epistemic logic and the philosophy of science to investigate the applicability of gametheory in such fields as economics, philosophy and strategic consultancy. I prove new mathematical theorems about the beliefs, desires and rationality principles of individual human beings, and explore in detail the logical form of gametheory as it is used in explanatory and normative contexts. I argue that gametheory reduces to rational choice theory if used as an explanatory device, and that gametheory is nonsensical if used as a normative device. A provocative account of the history of gametheory reveals that this is not bad news for all of gametheory, though. Two central research programmes in gametheory tried to find the ultimate characterisation of strategic interaction between rational agents. Yet, while the Nash Equilibrium Refinement Programme has done badly thanks to such research habits as overmathematisation, model-tinkering and introversion, the Epistemic Programme, I argue, has been rather successful in achieving this aim. "The 'epistemic' approach to gametheory has emerged over the past twenty-five years. What is this approach? How does it differ from the conventional equilibrium-based approach to gametheory? What have been its strengths and weaknesses to date? To find out, read this comprehensive and excellently written account". Adam Brandenburger, J. P. Valles Professor of Business Economics and Strategy, Stern School of Business, New York University "Reading Boudewijn de Bruin's book should be rewarding both for game theorists interested in the conceptual foundations of their discipline and for philosophers who want to learn more about formal analysis of strategic interaction. It provides an in-depth logical study of the currently dominant epistemic approaches to non-cooperative games, with an eye both to the attractions and to the serious challenges facing the Epistemic Programme". Wlodek Rabinowicz, Professor of Practical Philosophy, Department of Philosophy, Lund University . (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 gametheory 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; Gametheory; Interactive epistemology; Mathematisation; Nash equilibrium. (shrink)
Focusing on the work of Friedrich von Hayek and Vernon Smith, we discuss some conceptual links between Austrian economics and recent work in behavioral gametheory and experimental economics. After a brief survey of the main methodological aspects of Austrian and experimental economics, we suggest that common views on subjectivism, individualism, and the role of qualitative explanations and predictions in social science may favour a fruitful interaction between these two research programs.
This article argues that various deviations from the basic principles of the scientific ethos – primarily the appearance of pseudoscience in scientific communities – can be formulated and explained using specific models of gametheory, such as the prisoner’s dilemma and the iterated prisoner’s dilemma. The article indirectly tackles the deontology of scientific work as well, in which it is assumed that there is no room for moral skepticism, let alone moral anti-realism, in the ethics of scientific communities. (...) Namely, on the basis of the generally accepted dictum of scientific endeavor as the pursuit of knowledge exclusively for knowledge’s sake, scientifically »right« behavior is seen to be clearly defined and distinguishable from scientifically »wrong« behavior. After elucidating the basic principles of gametheory, the article illustrates – by using imaginary and real cases, as well as some views from the philosophyof biology (the units of selection debate) – how this sort of reasoning could be applied in an analysis of the functioning of science. (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’) gametheory 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)
The mathematical tools of gametheory are frequently used in the social sciences and economic consultancy. But how do they explain social phenomena and support prescriptive judgments? And is the use of gametheory really necessary? I analyze the logical form of explanatory and prescriptive game theoretical statements, and argue for two claims: (1) explanatory gametheory can and should be reduced to rational choice theory in all cases; and (2) prescriptive (...) class='Hi'>gametheory gives bad advice in some cases, is reducible to rational choice theory in other cases, while it makes no sense in yet other cases. (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 gametheory, computer science and the philosophy of language.
Marcoux argues that job candidates ought to embellish non-verifiable information on their résumés because it is the best way to coordinate collective action in the résumé ‚game’. I do not dispute his analysis of collective action; I look at the larger picture, which throws light on the role gametheory might play in ethics. I conclude that gametheory’s conclusions have nothing directly to do with ethics. Gametheory suggests the means to certain (...) ends, but the ethics of both the means and ends must be assessed separately before any ethical recommendation can␣be made. Marcoux makes several highly disputable assumptions in order to fit résumés into gametheory; his analysis does not take into account the consequences that embellishing has beyond the submission and assessment of␣résumés; his argument depends on his claim that a résumé system in which everyone embellishes is attainable; and finally, his argument relies on an idealization of human␣motivation, rather than abstraction. I conclude that candidates should never embellish their résumés. (shrink)
In its classical conception, gametheory 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)
A variety of robustness objections have been made against evolutionary gametheory. One of these objections alleges that the games used in the underlying model are too arbitrary and oversimplified to generate a robust model of interesting prosocial behaviors. In this paper, I argue that the robustness objection can be met. However, in order to do so, we must attend to important conceptual issues regarding the nature of fairness, justice, and other moral concepts. Specifically, we must better understand (...) the relationship between moral concepts and formal characterizations of games. (shrink)
In the literature there are at least two main formal structures to deal with situations of interactive epistemology: Kripke models and type spaces. As shown in many papers :149–225, 1999; Battigalli and Siniscalchi in J Econ Theory 106:356–391, 2002; Klein and Pacuit in Stud Log 102:297–319, 2014; Lorini in J Philos Log 42:863–904, 2013), both these frameworks can be used to express epistemic conditions for solution concepts in gametheory. The main result of this paper is a (...) formal comparison between the two and a statement of semantic equivalence with respect to two different logical systems: a doxastic logic for belief and an epistemic–doxastic logic for belief and knowledge. Moreover, a sound and complete axiomatization of these logics with respect to the two equivalent Kripke semantics and type spaces semantics is provided. Finally, a probabilistic extension of the result is also presented. A further result of the paper is a study of the relationship between the epistemic–doxastic logic for belief and knowledge and the logic STIT by Belnap and colleagues. (shrink)
The ‘phenotypic gambit,’ the assumption that we can ignore genetics and look at the fitness of phenotypes to determine the expected evolutionary dynamics of a population, is often used in evolutionary gametheory. However, as this paper will show, an overlooked genotype to phenotype map can qualitatively affect evolution in ways the phenotypic approach cannot predict or explain. This gives us reason to believe that, even in the long-term, correspondences between phenotypic predictions and dynamical outcomes are not robust (...) for all plausible assumptions regarding the underlying genetics of traits. This paper shows important ways in which the phenotypic gambit can fail and how to proceed with evolutionary game theoretic modeling when it does. (shrink)
In the last few decades gametheory has emerged as a powerful tool for examining a broad range of philosophical issues. It is unsurprising, then, that gametheory has been taken up as a tool to examine issues in the philosophy of religion. Economist Steven Brams (1982), (1983) and (2007), for example, has given a game theoretic analysis of belief in God, his main argument first published in this journal and then again in both editions (...) of his book, Superior Beings. I have two main aims in this paper, one specific and one general. My specific aim is to show that Brams’ application of gametheory to examine belief in God is, in particular, deeply flawed in two respects. My general aim is to show that any game-theoretic model in which a human being and God are players can only succeed at the cost of abandoning the assumption that God is omnibenevolent. (shrink)
John Maynard Smith was the founder of evolutionary gametheory. He has also been the major influence on the direction of this field, which now pervades behavioural ecology and evolutionary biology. In its original formulation the theory had three components: a set of strategies, a payoff structure, and a concept of evolutionary stability. These three key components are still the basis of the theory, but what is assumed about each component is often different to the original (...) assumptions. We review modern approaches to these components. We emphasis that if a game is considered in isolation, and arbitrary payoffs are assumed, then the payoffs may not be consistent with other components of the system which are not modelled. Modelling the whole system, including not only the focal game, but also the future behaviour of the players and the behaviour of other population members, allows a consistent model to be constructed. We illustrate this in the case of two models of parental care, showing how linking a focal game to other aspects of the system alters what is predicted. (shrink)
This book represents a major contribution to gametheory. It offers this conception of equilibrium in games: strategic equilibrium. This conception arises from a study of expected utility decision principles, which must be revised to take account of the evidence a choice provides concerning its outcome. The argument for these principles distinguishes reasons for action from incentives, and draws on contemporary analyses of counterfactual conditionals. The book also includes a procedure for identifying strategic equilibria in ideal normal-form games. (...) In synthesizing decision theory and gametheory in a powerful way this book will be of particular interest to all philosophers concerned with decision theory and gametheory as well as economists and other social scientists. (shrink)
Game theorists tend to model climate negotiations as a so-called ‘tragedy of the commons’. This is rather worrisome, since the conditions under which such commons problems have historically been solved are almost entirely absent in the case of international greenhouse gas emissions. In this paper, I will argue that the predictive accuracy of the tragedy model might not stem from the model’s inherent match with reality but rather from the model’s ability to make self-fulfilling predictions. I then sketch some (...) possible ways to dispel the tragedy, including (1) recognizing some ways the assumptions of the model fail, (2) taking seriously recent work suggesting that increasing greenhouse gas emissions is not in most nations’ own self-interest, and (3) preferring alternative models like collective risk dilemmas, bargaining games, or cooperative models. (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)
This paper critically examines several game theoretic interpretations of Hobbes' state of nature, including Prisoner's Dilemma and Assurance Game, and argues instead that the best matrix is that of a combination of the two, an Assurance Dilemma. This move is motivated by the fact that Hobbes explicitly notes two distinct personality types, with different preference structures, in the state of nature: dominators and moderates. The former play as if in a Prisoner's Dilemma, the latter play as if in (...) an Assurance Game. But when meeting one another, the Assurance Dilemma represents their differing strategies, and can explain various other features of Hobbes' state of nature, as well as a key informational role played the Sovereign. (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.
IntroductionA quick glance at the opening paragraphs in many of the classic logic textbooks reveals a common view: Logical methods highlight the reasoning patterns of a single agent engaged in some form of mathematical thinking.A sampling from my bookshelf: Shoenfield’s Mathematical Logic: “Logic is the study of reasoning; and mathematical logic is the study of the type of reasoning done by mathematicians”; Enderton’s A Mathematical Introduction of Logic: “Symbolic logic is a mathematical model of deductive thought”; and Chiswell and Hodges (...) Mathematical Logic: “In this course we shall study some ways of proving statements.” However, this traditional view of the “subject matter” of logic is expanding. There is a growing literature using phrases such as “rational interaction” or “information flow” to describe its subject matter while still employing traditional logical methods. The clearest example of this can be found in the work of Johan van Benthem and others on l .. (shrink)
Many weaknesses of gametheory are cured by new models that embody simple cognitive principles, while maintaining the formalism and generality that makes gametheory useful. Social preference models can generate team reasoning by combining reciprocation and correlated equilibrium. Models of limited iterated thinking explain data better than equilibrium models do; and they self-repair problems of implausibility and multiplicity of equilibria.
In recent years a number of writers have maintained that law can usefully be illuminated by gametheory. Some believe that gametheory can provide guidance in formulating rules for dealing with speciﬁc problems. Others advance the philosophically ambitious contention that we can gain a better understanding and/or appreciation of law by seeing it in terms of game-theoretic ideas. My purpose in this article is to examine some claims of the latter sort, and in particular (...) to ask how distant law can be from the assumptions of gametheory and still be informed by it. Models are not expected to ﬁt precisely what they model, but at some point the deviation is too great and there is a failure to illuminate. (shrink)
The minimax theorem of matrix gametheory is examined from a constructive point of view. It is then shown that the existence of solutions for matrix games cannot be proved constructively, but that a 2-by-2 game with at most one solution has a constructible solution.
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 gametheory only when they were formulated, later and independently, by other theorists. As a result, some of the most distinctive and valuable features of Lewis' gametheory 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 gametheory. 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)
Ken Binmore's previous gametheory textbook, Fun and Games, carved out a significant niche in the advanced undergraduate market; it was intellectually serious and more up-to-date than its competitors, but also accessibly written. Its central thesis was that gametheory allows us to understand many kinds of interactions between people, a point that Binmore amply demonstrated through a rich range of examples and applications. This replacement for the now out-of-date 1991 textbook retains the entertaining examples, but (...) changes the organization to match how gametheory courses are actually taught, making Playing for Real a more versatile text that almost all possible course designs will find easier to use, with less jumping about than before. In addition, the problem sections, already used as a reference by many teachers, have become even more clever and varied, without becoming too technical. Playing for Real will sell into advanced undergraduate courses in gametheory, primarily those in economics, but also courses in the social sciences, and serve as a reference for economists. (shrink)
The paper is a discussion of the interpretation of gametheory. Gametheory is viewed as an abstract inquiry into the concepts used in social reasoning when dealing with situations of conflict and not as an attempt to predict behavior. The first half of the paper..
Ethics is a field in which the gap between words and actions looms large. Gametheory and the empirical methods it inspires look at behavior instead of the lip service people sometimes pay to norms. We believe that this special issue comprises several illustrations of the fruitful application of this approach to ethics.
This commentary focuses on the parts of psychological gametheory dealing with preference, as illustrated by team reasoning, and supports the conclusion that these theoretical notions do not contribute above and beyond existing theory in understanding social interaction. In particular, psychology and games are already bridged by a comprehensive, formal, and inherently psychological theory, interdependence theory (Kelley & Thibaut 1978; Kelley et al. 2003), which has been demonstrated to account for a wide variety of social (...) interaction phenomena. (shrink)
The answer in a nutshell is: Yes, five years ago, but nobody has noticed. Nobody noticed because the majority of social scientists subscribe to one of the following views: (1) the ‘anomalous’ behaviour observed in standard prisoner’s dilemma or ultimatum game experiments has refuted standard gametheory a long time ago; (2) gametheory is flexible enough to accommodate any observed choices by ‘refining’ players’ preferences; or (3) it is just a piece of pure mathematics (...) (a tautology). None of these views is correct. This paper defends the view that GT as commonly understood is not a tautology, that it suffers from important (albeit very recently discovered) empirical anomalies, and that it is not flexible enough to accommodate all the anomalies in its theoretical framework. It also discusses the experiments that finally refuted gametheory, and concludes trying to explain why it took so long for experimental game theorists to design experiments that could adequately test the theory. (shrink)
The development of evolutionary gametheory is closely linked with two interdisciplinary exchanges: the import of gametheory into biology, and the import of biologists’ version of gametheory into economics. This paper traces the history of these two import episodes. In each case the investigation covers what exactly was imported, what the motives for the import were, how the imported elements were put to use, and how they related to existing practices in the (...) respective disciplines. Two conclusions emerged from this study. First, concepts derived from the unity of science discussion or the unification accounts of explanation are too strong and too narrow to be useful for analysing these interdisciplinary exchanges. Secondly, biology and economics—at least in relation to EGT—show significant differences in modelling practices: biologists seek to link EGT models to concrete empirical situations, whereas economists pursue conceptual exploration and possible explanation.Keywords: Models; Evolutionary gametheory; Interdisciplinarity; Unification; Unity of science; Theory import; Biology; Economics. (shrink)
The notion of ‘revealed preference’ is unclear and should be abandoned. Defenders of the theory of revealed preference have misinterpreted legitimate concerns about the testability of economics as the demand that economists eschew reference to (unobservable) subjective states. As attempts to apply revealed-preference theory to gametheory illustrate with particular vividness, this demand is mistaken.
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 gametheory. 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.