The most important analytical tool in non-cooperative game theory is the concept of a Nash equilibrium, which is a collection of possibly mixed strategies, one for each player, with the property that each player's strategy is a best reply to the strategies of the other players. If we do not go into normative game theory, which concerns itself with the recommendation of strategies, and focus instead entirely on the positive theory of prediction, two alternative interpretations of the Nash equilibrium concept (...) are predominantly available.In the more traditional one, a Nash equilibrium is a prediction of actual play. A game may not have a Nash equilibrium in pure strategies, and a mixed strategy equilibrium may be difficult to incorporate into this interpretation if it involves the idea of actual randomization over equally good pure strategies. In another interpretation originating from Harsanyi, see also Rubinstein, and Aumann and Brandenburger, a Nash equilibrium is a ‘consistent’ collection of probabilistic expectations, conjectures, on the players. It is consistent in the sense that for each player each pure strategy, which has positive probability according to the conjecture about that player, is indeed a best reply to the conjectures about others. (shrink)

Models of idealistic societies pervade the history of political thought from ancient times to the present. How can these models contribute to our thinking about political life in our non-ideal world? Not, as many political theorists have hoped, by performing a normative function -- by giving us reasons to accept particular political principles for the purpose of regulating our thought and behavior. Even still, idealistic models can sharpen our thinking about politics by performing a conceptual function -- by helping us (...) clarify and interpret the concepts we use to describe and evaluate political behavior and institutions. These insights point to a more incisive and judicious approach to political inquiry, in which explanatory and normative modes of thought are tightly intertwined. (The manuscript is under review. I have uploaded the table of contents, chapters 1 and 2, and the bibliography. Chapter summaries are available from my website.). (shrink)

The most common argument against the use of rational choice models outside economics is that they make unrealistic assumptions about individual behavior. We argue that whether the falsity of assumptions matters in a given model depends on which factors are explanatorily relevant. Since the explanatory factors may vary from application to application, effective criticism of economic model building should be based on model-specific arguments showing how the result really depends on the false assumptions. However, some modeling results in imperialistic applications (...) are relatively robust with respect to unrealistic assumptions. Key Words: unrealistic assumptions • economics imperialism • rational choice • as if • robustness. (shrink)

Several game-theoretical lab experiments helped establish the belief that economists are more selfish than non-economists. Since differences in behaviour between experiment participants who are students of economics and those who are not may be observed among junior students as well, it is nowadays widely believed that the origin of the greater selfishness is not the training they undergo, but self-selection. In other words, selfish people voluntarily enrol in economics. Yet, I argue that such explanation is unsatisfactory for several reasons. I (...) also suggest alternative explanations for the observed differences, which have been so far unduly disregarded. (shrink)

This paper uses a game-theoretic framework to formalize the Hayekian notion of equilibrium as the compatibility of plans. To do so, it imposes more structure on the conventional model of strategic games. For each player, it introduces goals, goal-oriented strategies, and the goals’ probabilities of success, from which players’ payoffs are derived. The differences between the compatibility of plans and Nash equilibrium are identified and discussed. Furthermore, it is shown that the notion of compatibility of plans, in general, differs from (...) the notion of Pareto efficiency. Since the compatibility of plans across all players can rarely be achieved in reality, a measurement is introduced to determine various degrees of plan compatibility. Several possible extensions and applications of the model are discussed. (shrink)

Page 1. Economics and Philosophy, 26 291--320 Copyright C Cambridge University Press doi: 10.1017 / S0266267110000386 TWO KINDS OF WE-REASONING RAUL HAKLI, KAARLO MILLER AND RAIMO TUOMELA University of Helsinki.

We generalize the concept of Nash equilibrium in mixed strategies for strategic form games to allow for ambiguity in the players' expectations. In contrast to other contributions, we model ambiguity by means of so-called lower probability measures or belief functions, which makes it possible to distinguish between a player's assessment of ambiguity and his attitude towards ambiguity. We also generalize the concept of trembling hand perfect equilibrium. Finally, we demonstrate that for certain attitudes towards ambiguity it is possible to explain (...) cooperation in the one-shot Prisoner's Dilemma in a way that is in accordance with some recent experimental findings. (shrink)

The paper points out that in dynamic games a player may be better-off if other players do not know his choice of strategy. That is, a player may benefit by not revealing (or not pre-determining) the choice of his action in an information set he (thereby) hopes will not be reached. He would be better-off by exercising his ``right to remain silent'' if he believes –- as the empirical evidence shows –- that players display aversion to ``Knightian uncertainty''. In this (...) case, a player who behaves strategically, may wish to avoid revealing his strategy. This is true under various interpretations of the notion of ``strategy profiles''. (shrink)

Nancy Cartwright claims that "Causality is a hot topic today both in philosophy and economics." She may be right about philosophers, but not when it comes to economists. Cartwright talks about "economics" but nothing she says about it corresponds to what is taught in economics classes. Today, economics is dominated by model builders—but not all models involve econometrics. While all model builders do respect an endogenous-exogenous distinction between variables, this distinction will not be on the basis of which type of (...) variable "causes" which, but on which variables are "determined" (and hence explained) by the model and those which are not. (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)

I argue that standard decision theories, namely causal decision theory and evidential decision theory, both are unsatisfactory. I devise a new decision theory, from which, under certain conditions, standard game theory can be derived.

The paper is an addition to the intensionalist approach to decision theory, with emphasis on game theoretic modelling. Extensionality in games is an a priori requirement that players exhibit the same behavior in all algebraically equivalent games on pain of irrationality. Intensionalism denies that it is always irrational to play differently in differently represented but algebraically equivalent versions of a game. I offer a framework to integrate game non-extensionality with the more familiar idea of linguistic non-extensionality from philosophy of language, (...) followed by applications of it based on toy examples of well-known game models. I argue that the notion of what I call “Intensional Nash Equilibrium” is, in effect, very useful in understanding human decision-making. (shrink)

We develop a theory of joint intention in contexts in which participants have mixed motives that can manifest in all-things-considered reasons to deviate from contributing to the desired project, e.g., contexts with collective action problems. Our theory is based on strategic equilibrium-based reasoning, which links the characterization of joint intention in terms of individual intentions with conditions on strategy profiles of the underlying strategic games. We use elements of equilibrium reasoning to construct a counterfactual account of joint intention in the (...) mixed-motive contexts, which extends the reach of the notion of joint intention considerably beyond that of previous formulations. (shrink)

p. cm. — (Zeuthen lecture book series) Includes bibliographical references (p. ) and index. ISBN 0-262-18187-8 (hardcover : alk. paper). — ISBN 0-262-68100-5 (pbk. : alk. paper) 1. Decision-making. 2. Economic man. 3. Game theory. 4. Rational expectations (Economic theory) I. Title. II. Series.

Contents. Introduction. 1. Preliminaries. 2. Normal Form Games. 3. Extensive Games. 4. Applications of Game Theory. 5. The Methodology of Game Theory. Conclusion. Appendix. Bibliography. Index. Does game theory—the mathematical theory of strategic interaction—provide genuine explanations of human behaviour? Can game theory be used in economic consultancy or other normative contexts? Explaining Games: The Epistemic Programme in Game Theory—the first monograph on the philosophy of game theory—is an attempt to combine insights from epistemic logic and the philosophy of science to (...) investigate the applicability of game theory 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 game theory as it is used in explanatory and normative contexts. I argue that game theory reduces to rational choice theory if used as an explanatory device, and that game theory is nonsensical if used as a normative device. A provocative account of the history of game theory reveals that this is not bad news for all of game theory, though. Two central research programmes in game theory 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 game theory has emerged over the past twenty-five years. What is this approach? How does it differ from the conventional equilibrium-based approach to game theory? 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)

from now on , was to point out that the model commonly used to describe . a decision problem with imperfect recall suffers from major ambiguities in its interpretation. We claimed that several issues which were immaterial in decision problems with perfect recall may be of importance in the analysis of decision problems with imperfect recall. The issues that we raised can be summarized by the following questions.

We model differences among agents in their ability to recognize temporal patterns of prices. Using the concept of DeBruijn sequences in two dynamic models of markets, we demonstrate the existence of equilibria in which prices fluctuate in a pattern that is independent of the fundamentals and that can be recognized only by the more competent agents. (JEL: C7, D4.

We argue that in extensive decision problems (extensive games with a single player) with imperfect recall care must be taken in interpreting information sets and strategies. Alternative interpretations allow for different kinds of analysis. We address the following issues: 1. randomization at information sets; 2. consistent beliefs; 3. time consistency of optimal plans; 4. the multiselves approach to decision making. We illustrate our discussion through an example that we call the ‘‘paradox of the absentminded driver.’’ Journal of Economic Literature Classification (...) Numbers: C7, D0. 1997 Academic Press. (shrink)

(2) Mental preferences: These describe the mental attitude of an individual toward the objects. They can be defined in contexts which do not involve actual choice. In particular, preferences can describe tastes (such as a preference for one season over another) or can refer to situations which are only hypothetical (such as the possible courses of action available to an individual were he to become Emperor of Rome) or which the individual does not fully control (such as a game situation (...) in which a player has preferences over the entire set of outcomes). (shrink)

I give an informal presentation of the evolutionary game theoretic approach to the conventions that constitute linguistic meaning. The aim is to give a philosophical interpretation of the project, which accounts for the role of game theoretic mathematics in explaining linguistic phenomena. I articulate the main virtue of this sort of account, which is its psychological economy, and I point to the casual mechanisms that are the ground of the application of evolutionary game theory to linguistic phenomena. Lastly, I consider (...) the objection that the account cannot explain predication, logic, and compositionality. (shrink)

This chapter presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent’s belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics are re-examined within (...) the semantics, such as inductive skepticism, the logic of discovery, Duhem’s problem, the articulation of theories by auxiliary hypotheses, the role of serendipity in scientific knowledge, Fitch’s paradox, deductive closure of knowability, whether one can know inductively that one knows inductively, whether one can know inductively that one does not know inductively, and whether expert instruction can spread common inductive knowledge—as opposed to mere, true belief—through a community of gullible pupils. (shrink)

The concept of rationality, predominantly in the guise of rational choice theory, plays a key role in the social sciences. Yet, whilst rational choice theory is usually understood as part of positive political science, it is also widely employed within normative political theories. In this paper, we examine how allegedly positive rational choice arguments can find application within normative political theories. To this effect, we distinguish between two interpretations of rationality ascriptions, one empirical, the other normative. Since, as we demonstrate, (...) empirical readings of the rationality assumption cannot convincingly explain the role of rational choice arguments in normative theories, we argue that the rationality assumption should be given a normative interpretation. We conclude by considering what this result implies for the use of rational choice arguments in normative and positive political science. (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)