A repulsive core force is derived which, assuming π mesons are the field particles, gives binding energies in good agreement with binding energies per nucleon of heavy nuclei. The physical model consists of a field of relatively short range, in which emission of a π meson by a nucleon and subsequent absorption by a neighboring nucleon is equivalent to a potential well. The binding energy at the equilibrium spacing of the nucleons is the self-energy of the π mesons, which (...) is calculated by analogy with classical electric fields. (shrink)

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)

In game theory, the word ‘game’ is used to describe any interdependence between interacting parties, and the Nash equilibrium is a prominent tool for analysing such interactions. I argue that the concept of the Nash equilibrium may also be used in non-gaming contexts. An individual is in a Nash equilibrium if his or her beliefs are consistent with his or her actions. Given that discordance between beliefs and behaviour is a typical cause of psychiatric (...) disorders, individuals who are not in a Nash equilibrium are likely to be affected by such disorders. In this regard, the concept of the Nash equilibrium could aptly be introduced into the medical practitioner’s vocabulary for describing a patient’s mental health status. (shrink)

How does Bayesian reasoning support participation in a game's Nash equilibrium? This paper provides an answer.

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 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)

The prelims comprise: Strategic Interaction Nash Equilibrium Normal‐form Refinements Games in Extensive Form Extensive‐form Refinements Selection by Evolution Notes.

Strong Nash equilibrium and coalition-proof Nash equilibrium rely on the idea that players are allowed to form coalitions and make joint deviations. Both of these notions consider cases in which any coalition can be formed. Accordingly, there may arise “conflicts of interest” that prevent a player from choosing an action that simultaneously meets the requirements of two coalitions to which he or she belongs. Here, we address this observation by studying an organizational framework such that the (...) coalitional structure is motivated by real-life examples where players cannot form some coalitions and formulated in such a way that no conflicts of interest remain. We define an organization as an ordered collection of partitions of the player set such that any partition is coarser than the partitions that precede it. For any given organization, we introduce the notion of organizational Nash equilibrium. We analyze the existence of equilibrium in a subclass of games with strategic complementarities and illustrate how the proposed notion refines the set of Nash equilibria in some examples of normal form games. (shrink)

Game theory is often used to explain behavior. Such explanations often proceed by demonstrating that the behavior in question is a Nash equilibrium. Agents are in Nash equilibrium if each agent’s strategy maximizes her payoff given her opponents’ strategies. Nash equilibriums are fundamentally static, but it is usually assumed that equilibriums will be the outcome of a dynamic process of learning or evolution. This article demonstrates that, even in the most simple setting, this need not (...) be true. In two-strategy games with just a single equilibrium, a family of imitative learning dynamics does not lead to equilibrium. (shrink)

Game theory is usually considered applied mathematics, but a few game‐theoretic results, such as Borel determinacy, were developed by mathematicians for mathematics in a broad sense. These results usually state determinacy, i.e., the existence of a winning strategy in games that involve two players and two outcomes saying who wins. In a multi‐outcome setting, the notion of winning strategy is irrelevant yet usually replaced faithfully with the notion of (pure) Nash equilibrium. This article shows that every determinacy result (...) over an arbitrary game structure, e.g., a tree, is transferable into existence of multi‐outcome (pure) Nash equilibrium over the same game structure. The equilibrium‐transfer theorem requires cardinal or order‐theoretic conditions on the strategy sets and the preferences, respectively, whereas counter‐examples show that every requirement is relevant, albeit possibly improvable. When the outcomes are finitely many, the proof provides an algorithm computing a Nash equilibrium without significant complexity loss compared to the two‐outcome case. As examples of application, this article generalises Borel determinacy, positional determinacy of parity games, and finite‐memory determinacy of Muller games. (shrink)

The noema is one of the most daring and controversial concept of the Husserlian theory of intentionality. It was first introduced by Husserl in 1912, within some research manuscripts, but was only fully developed in Ideen. In this paper I claim that the noema is an ambiguous notion, the result of a theoretical operation, the epoché, whose aim is contradictory. In an effort to keep open the epoché, and therefore maintain distance with respect to every transcendent object, Husserl is forced (...) to multiply intentional objects and complicate the notions of sense and noema. Given that, I propose to overcome the paradoxes of noema through the language of game theory. Game theory offers a very fruitful descriptive model that allows us to save the original Husserlian approach without the contradictions of the epoché. For this reason, I propose to re-interpret intentionality as social game, and the noema as Nash equilibrium. By replying to possible objections, I will show that this approach gives us many theoretical advantages. The general aim of the paper is a global reformulation of the phenomenalogical method. (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)

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)

This paper suggests that Nash equilibrium can be interpreted as a conceptual tool for addressing comparative-statics issues on an aggregate level. Together with additional assumptions, Nash equilibrium helps generate testable predictions about changes or differences of behavior induced by changes or differences of exogenous variables. However, Nash-equilibrium behavior, as such, is not subject to empirical testing. Instead, widespread and persistent behavior is modeled as a Nash equilibrium by assumption. The paper argues that (...) this interpretation is in line with the traditional use of an equilibrium concept in price theory. The suggested interpretation is illustrated with the model of public-goods provision. The paper compares this interpretation of Nash equilibrium with other interpretations and discusses its limits. (shrink)

This paper investigates the existence of pure strategy Nash equilibria in discontinuous and nonquasiconcave games. We introduce a new notion of continuity, called weakly continuous security, which is weaker than the most known weak notions of continuity, including the surrogate point secure of SSYM game of Carbonell-Nicolau and Mclean (Econ Theory, 2018a), the continuous security of Barelli and Meneghel (Econometrica 81:813–824, 2013), C-security of McLennan et al. (Econometrica 79:1643–1664 2011), generalized weakly transfer continuity of Nessah (Economics 47:659–662, 2011), generalized (...) better-reply security of Carmona (Econ Theory 48:1–4, 2011), Barelli and Soza (On the existence of Nash equilibria in discontinuous and qualitative games, 2009), Barelli and Meneghel (Econometrica 81:813–824, 2013), lower single deviation property of Reny (Further results on the existence of Nash equilibria in discontinuous games. University of Chicago, 2009), better-reply security of Reny (Econometrica 67:1029–1056, 1999) and the results of Prokopovych (Econ Theory 48:5–16, 2011, Econ Theory 53:383–402, 2013) and Carmona (J Econ Theory 144:1333–1340, 2009). We show that a compact, convex and weakly continuous secure Hausdorff locally convex topological vector space game has a pure strategy Nash equilibrium. Moreover, it holds in a large class of discontinuous games. (shrink)

Metalogic is an open-ended cognitive, formal methodology pertaining to semantics and information processing. The language that mathematizes metalogic is known as metalanguage and deals with metafunctions purely by extension on patterns. A metalogical process involves an effective enrichment in knowledge as logical statements, and, since human cognition is an inherently logic–based representation of knowledge, a metalogical process will always be aimed at developing the scope of cognition by exploring possible cognitive implications reflected on successive levels of abstraction. Indeed, it is (...) basically impracticable to maintain logic–and–metalogic without paying heed to cognitive theorizing. For it is cognitively irrelevant whether possible conclusions are deduced from some premises before the premises are determined to be true or whether the premises themselves are determined to be true first and, then, the conclusions are deduced from them. In this paper we consider the term metalogic as inherently embodied under the framework referred to as cognitive science and mathematics. We propose a metalogical interpretation of Arrow’s impossibility theorem and, to that end, choice theory is understood as a mental course of action dealing with logic and metalogic issues, in which a possible mathematical approach to model a mental course of action is adopted as a systematic operating method. Nevertheless, if we look closely at the core of Arrow’s impossibility theorem in terms of metalogic, a second fundamental contribution to this framework is represented by the Nash equilibrium. As a result of the foregoing, therefore, we prove the metalogical equivalence between Arrow’s impossibility theorem and the existence of the Nash equilibrium. More specifically, Arrow’s requirements correspond to the Nash equilibrium for finite mixed strategies with no symmetry conditions. To demonstrate this proof, we first verify that Arrow’s set and Nash’s set are isomorphic to each other, both sets being under stated conditions of non–symmetry. Then, the proof is completed by virtue of category theory. Indeed, the two sets are categories that correspond biuniquely to one another and, thus, it is possible to define a covariant functor that preserves their mutual structures. According to this, we show the proof–dedicated metalanguage as a precursor to a special equivalence theorem. (shrink)

In the present paper, we consider a bio-economic equilibrium model which describes the dynamics of a fish population fished by several fishermen seeking to maximize their profits. Each fisherman tries to find the fishing effort which maximizes his profit at biological equilibrium without any consultation with others, but all of them have to respect two constraints: (1) the sustainable management of the resources ; and (2) the preservation of the biodiversity. With all these considerations, our problem leads to (...) a generalized Nash equilibrium problem. The objective is to show that even when a fisherman i\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$i$$\end{document} provides a fishing effort equal to twice the fishing effort of a fisherman j\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$j$$\end{document}, then the profit of fisherman i\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$i$$\end{document} is not necessarily double that of fisherman j\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$j$$\end{document}. (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 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)

Donald Capps (2009: 145) suggested the hypothesis that “the Nash equilibrium is descriptive of the normal brain, whereas the game theory formulated by John van Neumann, which Nash’s theory challenges, is descriptive of the schizophrenic brain”. The paper offers arguments in its favor. They are from psychiatry, game theory, set theory, philosophy and theology. The Nash equilibrium corresponds to wholeness, stable emergent properties as well as to representing actual infinity on a material, limited and finite (...) organ as a human brain. (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)

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 model of congestion games is widely used to analyze games related to traffic and communication. A central property of these games is that they are potential games and hence posses a pure Nash equilibrium. In reality, it is often the case that some players cooperatively decide on their joint action in order to maximize the coalition’s total utility. This is modeled by Coalitional Congestion Games. Typical settings include truck drivers who work for the same shipping company, or (...) routers that belong to the same ISP. The formation of coalitions will typically imply that the resulting coalitional congestion game will no longer posses a pure Nash equilibrium. In this paper, we provide conditions under which such games are potential games and posses a pure Nash equilibrium. (shrink)

In the Nash demand game n players announce utility demands, the demands are implemented if they are jointly feasible, and otherwise no one gets anything. If the utilities set is the simplex, the game is called “divide-the-dollar”. Brams and Taylor studied variants of divide-the-dollar, on which they imposed reasonableness conditions. I explore the implications of these conditions on general NDGs. In any reasonable NDG, the egalitarian demand profile cannot be obtained via iterated elimination of weakly dominated strategies. Further, a (...) reasonable NDG may fail to have a Nash equilibrium, even in mixed strategies. In the 2-person case, existence of pure strategy equilibrium is equivalent to the existence of a value, in the sense that each player can secure the egalitarian payoff level independent of his opponent’s play. This result does not extend to reasonable NDGs with more than two players. Interestingly, there are results for reasonable NDGs that hold for two and three players, but not for n≥4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\ge 4$$\end{document} players. (shrink)

Standard models in epistemic game theory make strong assumptions about agents’ knowledge of their own beliefs. Agents are typically assumed to be introspectively omniscient: if an agent believes an event with probability p, she is certain that she believes it with probability p. This paper investigates the extent to which this assumption can be relaxed while preserving some standard epistemic results. Geanakoplos (1989) claims to provide an Agreement Theorem using the “truth” axiom, together with the property of balancedness, a significant (...) relaxation of introspective omniscience. I provide an example which shows that Geanakoplos’s statement is incorrect. I then introduce a new property, local balancedness, which allows us both to correct Geanakoplos’s result, and to extend it to cases where the truth axiom may fail. I exploit this general Agreement Theorem to provide novel epistemic conditions for correlated and Nash equilibrium, both of which relax the assumption of introspective omniscience. In all three cases, the results are also extended to infinite state spaces. (This is Chapter 5 of my 2014 Oxford DPhil (PhD) thesis.). (shrink)

We introduce a new solution concept, called correlated-belief equilibrium. The difference to Nash equilibrium is that, while each player has correct marginal conjectures about each opponent, it is not necessarily the case that these marginal conjectures are independent. Then, we provide an epistemic foundation and we relate correlated-belief equilibrium with standard solution concepts, such as rationalizability, correlated equilibrium and conjectural equilibrium.

In this paper, we consider Nash implementability in general settings under the assumption that one may abstain. We show that in the case of at least two individuals, any social choice rule is Nash implementable by mechanisms with abstentions if and only if it is Nash implementable. Moreover, we introduce the notions of minimal participation and participation in equilibrium. We then study the possibility of Nash implementability by mechanisms that satisfy minimal participation or participation.

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)

Within a formal epistemic model for simultaneous-move games, we present the following conditions: belief in the opponents’ rationality, stating that a player believes that every opponent chooses an optimal strategy, self-referential beliefs, stating that a player believes that his opponents hold correct beliefs about his own beliefs, projective beliefs, stating that i believes that j’s belief about k’s choice is the same as i’s belief about k’s choice, and conditionally independent beliefs, stating that a player believes that opponents’ types choose (...) their strategies independently. We show that, if a player satisfies BOR, SRB and CIB, and believes that every opponent satisfies BOR, SRB, PB and CIB, then he will choose a Nash strategy. We thus provide a sufficient collection of one-person conditions for Nash strategy choice. We also show that none of these seven conditions can be dropped. (shrink)

Threats to the stability of liberal democracies are of obvious contemporary import. Concern with stability runs through John Rawls’s work. The stability that concerned him was that of fundamental terms of cooperation. Rawls long believed that the terms which would be stable were his two principles, but he eventually conceded that even a well-ordered society was more likely to be characterized by “justice pluralism” than by consensus on his own conception of justice. Contemporary liberal democracies, too, are divided about what (...) justice demands. I believe Rawls’s treatment of stability can help us understand the conditions under which fundamental terms of cooperation can be stable under non-ideal conditions such as ours. But because Rawls never worked through the consequences of his concession, his view needs to be developed before we can draw on it. Rawls’s treatment makes use of elementary game theory. Thus in _Theory of Justice_ he said -- and in _Political Liberalism_ he implied -- that stability would result from citizens with a sense of justice “playing” strategies which combined for what was, in effect, a Nash equilibrium. I argue that his concession requires a new conception of stability and implies that Rawls cannot appeal to a Nash equilibrium to show how stability would be maintained. His concession therefore forces open a troubling gap in his analysis. I fill that gap by proposing a weaker equilibrium concept that serves Rawlsian purposes. I conclude with what this project suggests for challenges facing the fragile liberal democracies of our own time. (shrink)

One approach to achieving cooperation in the one-shot prisoner’s dilemma is Tennenholtz’s (Games Econ Behav 49(2):363–373, 2004) program equilibrium, in which the players of a game submit programs instead of strategies. These programs are then allowed to read each other’s source code to decide which action to take. As shown by Tennenholtz, cooperation is played in an equilibrium of this alternative game. In particular, he proposes that the two players submit the same version of the following program: cooperate (...) if the opponent is an exact copy of this program and defect otherwise. Neither of the two players can benefit from submitting a different program. Unfortunately, this equilibrium is fragile and unlikely to be realized in practice. We thus propose a new, simple program to achieve more robust cooperative program equilibria: cooperate with some small probability. (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.

It is usually assumed in game theory that agents who interact strategically with each other are rational, know the strategies open to other agents as well as their payoffs and, moreover, have common knowledge of all the above. In some games, that much information is sufficient for the players to identify a "solution" and play it. The most commonly adopted solution concept is that of Nash equilibrium. A Nash equilibrium is defined a combination of strategies, one (...) for each player, such that no player can profit from a deviation from his strategy if the opponents stick to their strategies. Nash equilibrium is taken to have predictive power, in the sense that in order to predict how rational agents will in fact behave, it is enough to identify the equilibrium patterns of actions. Barring the case in which players have dominant strategies, to play her part in a Nash equilibrium a player must believe that the other players play their part, too. But an intelligent player must immediately realize that she has no ground for this belief. Take the case of a one-shot, simultaneous game. Here all undominated strategies are possible choices, and the beliefs supporting them are possible beliefs, even if this game has a.. (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)

Skyrms has pointed out differences between the results of rational choice theory and evolutionary game theory. This commentary argues that there is a great deal of agreement on the Nash Bargaining Solution, which maximizes the product of player payoffs, in both rational-choice-based and evolution-based theories of equilibrium selection. While evolutionary game theory has the potential to explain how we arrive at the behavioural rules that govern what we do, realistic models will require calibration through laboratory experiments. Indeed, experimental (...) evidence strongly supports the Nash Bargaining Solution. (shrink)

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)

In a pair of controversy provoking papers1, Kadane and Larkey argued that the normative or prescriptive understanding of expected utility theory recommended that participants in a game maximize expected utility given their assessments of the probabilities of the moves that other players would make. They observed that no prescription, norm or standard of Bayesian rationality recommends how they should come to make probability judgments about the choices of other players. For any given player, it is an empirical question as to (...) whether other players are Bayes rational, judge him to be Bayes rational, etc., just as it is an empirical question as to what the other players’ goals and beliefs are. Participants in the game should, of course, use all empirical information available to them about how other players have behaved and how they are likely to behave in the given context of choice. Kadane and Larkey pointed out that rational players could participate in a game meeting these requirements without the game’s terminating with a Nash equilibrium or a result satisfying any other particular solution concept. (shrink)

We add a stage to Nash’s demand game by allowing the greedier player to revise his demand if the demands are not jointly feasible. If he decides to stick to his initial demand, then the game ends and no one receives anything. If he decides to revise it down to 1-x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1-x$$\end{document}, where x is his initial demand, the revised demand is implemented with certainty. The implementation probability changes linearly between these (...) two extreme cases. We derive a condition on the feasible set under which the two-stage game has a unique subgame perfect equilibrium. In this equilibrium, there is first-stage agreement on the egalitarian demands. We also study two n-player versions of the game. In either version, if the underlying bargaining problem is “divide-the-dollar,” then equal division is sustainable in a subgame perfect equilibrium if and only if the number of players is at most four. (shrink)

This paper includes a survey of decision theories directed toward exploring the adequacy of alternative approaches for application to game theoretic reasoning, a review of the classic results of von Neumann and Morgenstern and Nash about equilibrium solutions, an account of a recent challenge to the idea that solutions should be equilibria, and, finally, an explicit reconstruction and defense (using the resources of causal decision theory) of the classic indirect argument for equilibrium solutions.

It is well known that Nash equilibria may not be Pareto-optimal; worse, a unique Nash equilibrium may be Pareto-dominated, as in Prisoners’ Dilemma. By contrast, we prove a previously conjectured result: every finite normal-form game of complete information and common knowledge has at least one Pareto-optimal nonmyopic equilibrium (NME) in pure strategies, which we define and illustrate. The outcome it gives, which depends on where play starts, may or may not coincide with that given by a (...) Nash equilibrium. We use some simple examples to illustrate properties of NMEs—for instance, that NME outcomes are usually, though not always, maximin—and seem likely to foster cooperation in many games. Other approaches for analyzing farsighted strategic behavior in games are compared with the NME analysis. (shrink)

Virtual bargaining theory suggests that social agents aim to resolve non-cooperative games by identifying the strategy profile which they would agree to play if they could openly bargain. The theory thus offers an explanation of how social agents resolve games with multiple Nash equilibria. One of the main questions pertaining to this theory is how the principles of the bargaining theory could be applied in the analysis of hypothetical bargaining in non-cooperative games. I propose a bargaining model based on (...) the benefit-equilibrating bargaining solution concept for non-cooperative games, broadly in line with the principles underlying Conley and Wilkie's ordinal egalitarian solution for Pareto optimal point selection problems with finite choice sets. I provide formal characterizations of the ordinal and the cardinal versions of BES, discuss their application to n-player games, and compare model's theoretical predictions with the data available from several experiments involving `pie games'. (shrink)

With a focus on the areas of theory, literature, culture, society and film, this collection of essays examines, questions and broadens the applicability of Postcolonialism and Islam from a multifaceted and cross-disciplinary perspective.Topics covered include the relationship between Postcolonialism and Orientalism, theoretical perspectives on Postcolonialism and Islam, the position of Islam within postcolonial literature, Muslim identity in British and European contexts, and the role of Islam in colonial and postcolonial cinema in Egypt and India. At a time at which Islam (...) continues to be at the centre of increasingly heated and frenzied political and academic deliberations, Postcolonialism and Islam offers a framework around which the debate on Muslims in the modern world can be centred.Transgressing geographical, disciplinary and theoretical boundaries, this book is an invaluable resource for students of Islamic Studies, Cultural Studies, Sociolgy and Literature. (shrink)

The Archaeology of Semiotics and the social order of things is edited by George Nash and George Children and brings together 15 thought-provoking chapters from contributors around the world. A sequel to an earlier volume published in 1997, it tackles the problem of understanding how complex communities interact with landscape and shows how the rules concerning landscape constitute a recognised and readable grammar. The mechanisms underlying landscape grammar are both physical and mental, being based in part on the mindset (...) of the individual; the same landscape can thus evoke different meanings for different people and at different times. People's perception has greatly influenced the construction of landscapes over millennia but, until recently, the potential of this area has been largely untapped. Apart from chapters focusing solely upon human interaction with landscape, there are several which skilfully integrate artefacts and place with landscape (e.g. Gheorghiu and Sognnes). Other chapters look at the way people have marked the landscape through such mechanisms as rock-art (e.g. Clegg, Devereux, Estévez, Fossati, Kelleher and Skier). Rock-art establishes personal and communal identity in relation to landscape and it is clear that other forms of visual expression were in place which distinctively created special places within the landscape. Landscape constructs can bind cultures together; bringing the old ways of reading the landscape into contemporary life (e.g. Smiseth). Defining early and late prehistoric landscapes and segregating these into, say, mundane domestic and ritualised spaces rely on both clear and subtle archaeologies and in this volume distinct monument clustering and ritualised linearity are considered (e.g. Mason and Nash). A volume such as this cannot escape the influence of New World approaches, such as anthropology, and in many respects chapters by Bender, Muller and Merritt give context to other chapters within the book. Finally, one must consider text as a means of constructing landscape and this is considered by Heyd, who eloquently deconstructs the travel diary of a 17th century Japanese poet. This will be an important volume for archaeologists, landscape scholars and students. The many approaches used are tried and tested, forming an invaluable resource and not just another edited book. (shrink)

"Teaching College Students How to Solve Real-Life Moral Dilemmas" will speak to the sometimes confounding, real-life, moral challenges that quarterlife students actually face each and every day of their lives. It will spell out an original, all-inclusive approach to thinking about, and applying, ethical problem-solving that takes into consideration people's acts, intentions, circumstances, principles, background beliefs, religio-spiritualities, consequences, virtues and vices, narratives, communities, and the relevant institutional and political structures. This approach doesn't tell students exactly what to do as much (...) as it evokes important information in order to help them think more deeply and expansively about ethical issues in order to resolve actual ethical dilemmas. There is no text like it on the market today. "Teaching College Students How to Solve Real-Life Moral Dilemmas" can be used in a variety of ethics courses. (shrink)