An Ethical Interpretation of the Nash Choice Rule

This paper provides an ethical intepretation of the Nash choice rule. In a setting in which (cardinal) utilities are interpersonally comparable, this procedure is characterised by an impartiality requirement and by the assumption that choices are not responsive to the agents' relative ability to convert resources into utility.     

On Stalnaker's Notion of Strong Rationalizability and Nash Equilibrium in Perfect Information Games

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 C , the set of profiles that survive the iterative deletion of inferior profiles.     

Arbitrage,rationality, and equilibrium

No-arbitrage is the fundamental principle of economic rationality which unifies normative decision theory, game theory, and market theory. In economic environments where money is available as a medium of measurement and exchange, no-arbitrage is synonymous with subjective expected utility maximization in personal decisions, competitive equilibria in capital markets and exchange economies, and correlated equilibria in noncooperative games. The arbitrage principle directly characterizes rationality at the market level; the appearance of deliberate optimization by individual agents is a consequence of their adaptation to the market. Concepts of equilibrium behavior in games and markets can thus be reconciled with the ideas that individual rationality is bounded, that agents use evolutionarily-shaped decision rules rather than numerical optimization algorithms, and that personal probabilities and utilities are inseparable and to some extent indeterminate. Risk-neutral probability distributions, interpretable as products of probabilities and marginal utilities, play a central role as observable quantities in economic systems.     

Nash Equilibrium with Lower Probabilities

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.     

Five legitimate definitions of correlated equilibrium in games with incomplete information

Aumann's (1987) theorem shows that correlated equilibrium is an expression of Bayesian rationality. We extend this result to games with incomplete information.First, we rely on Harsanyi's (1967) model and represent the underlying multiperson decision problem as a fixed game with imperfect information. We survey four definitions of correlated equilibrium which have appeared in the literature. We show that these definitions are not equivalent to each other. We prove that one of them fits Aumann's framework; the agents normal form correlated equilibrium is an expression of Bayesian rationality in games with incomplete information.We also follow a universal Bayesian approach based on Mertens and Zamir's (1985) construction of the universal beliefs space. Hierarchies of beliefs over independent variables (states of nature) and dependent variables (actions) are then constructed simultaneously. We establish that the universal set of Bayesian solutions satisfies another extension of Aumann's theorem.We get the following corollary: once the types of the players are not fixed by the model, the various definitions of correlated equilibrium previously considered are equivalent.     

理性与非理性的博弈:现代投资决策理论的演进

理性与非理性的纷争构成了现代投资决策理论演化的主要脉络。本文从古典经济学对理性的最初描述开始,系统讨论了博弈论框架下的理性特征、理性预期对现代金融理论发展的影响、有限理性修正、凯恩斯批判、噪音交易的存在性以及行为金融学关于投资者非理性行为的解释,最后分析了理性与非理性的经济学本质,对现代金融决策理论发展的脉络进行了全面理论梳理。     

On the evaluation of solution concepts

It is proposed that solution concepts for games should be evaluated in a way that is analogous to the way a logic is evaluated by a model theory for the language. A solution concept defines a set of strategy profiles, as a logic defines a set of theorems. A model theoretic analysis for a game defines a class of models, which are abstract representations of particular plays of the game. Given an appropriate definition of a model, one can show that various solution concepts are characterized by intuitively natural classes of models in the same sense that the set of theorems of a logic is characterized by a class of models of the language. Sketches of characterization results of this kind are given for rationalizability, Nash equilibrium, and for a refinement of rationalizability —strong rationalizability — that has some features of an equilibrium concept. It is shown that strong rationalizability is equivalent to Nash equilibrium in perfect information games. Extensions of the model theoretic framework that represent belief revision and that permit the characterization of other solution concepts are explored informally.     

An axiomatic basis of accounting: A structuralist reconstruction

Set-theoretic axiomatizations are given for a model of accounting with double classification, and a general core-model for accounting. The empirical status, and representational role of systems of accounts, as well as the problem of how to assign correct values to the goods accounted, are analyzed in precise terms. A net of special laws based on the core-model is described.     

协调博弈的摆动均衡：企业核心层关系的一个分析

一、问题的提出 本文的关注对象是企业。 在理论领域,企业是由合约组织形成的,合约是不完全的,不完全 的合约为企业运行带来很多不确定性,一些关注这一问题的企业理论, 探讨了弥补合约不完全性的途径:例如关系合同理论,通过将"关系"引 入合约来考察合约的运行;剩余控制权理论则试图通过明确剩余权利 的归属,使得合约得以完全,等等。但是合约真的能由此变完全吗? 在现实领域,以雇佣合约为例,通过在FD公司长时间地参与观     

Simple Characterizations of the Nash and Kalai/smorodinsky Solutions

In this study we introduce two new properties, the Midpoint Outcome on a Linear Frontier (MOLF) and Balanced Focal Point (BFP) properties, to replace the Weak Pareto Optimality (WPO), Symmetry (SYM) and Independence of Equivalent Utility Representations (IEUR) properties in the axiomatic characterizations of the two most prominent solution concepts, namely the Nash and Kalai/Smorodinsky solutions, respectively.     

Choice under risk and the security factor: An axiomatic model

The particular attention paid by decision makers to the security level ensured by each decision under risk, which is responsible for the certainty effect, can be taken into account by weakening the independence and continuity axioms of expected utility theory. In the resulting model, preferences depend on: (i) the security level, (ii) the expected utility, offered by each decision. Choices are partially determined by security level comparison and completed by the maximization of a function, which express the existing tradeoffs between expected utility and security level, and is, at a given security level, an affine function of the expected utility. In the model, risk neutrality at a given security level implies risk aversion.     

Refinements of Nash Equilibrium: A critique

Rational play of Noncooperative Games is investigated under the assumptions that a particular form of Best Reply Principle holds, each player has at least one rational strategy and all strategies are either rational or irrational. These assumptions are shown to imply that (a) some weakly dominated strategies are rational (b) recursive reasoning can be misleading (c) only a Strict Nash Equilibrium can be a solution. A Supplementary Best Reply Principle is formulated. It sheds further light on which games have solutions and on rational play in games without them. The relationship between these results and those of other authors is discussed.     

Learning to cooperate with Pavlov an adaptive strategy for the iterated Prisoner's Dilemma with noise

Conflict of interest may be modeled, heuristically, by the iterated Prisoner's Dilemma game. Although several researchers have shown that the Tit-For-Tat strategy can encourage the evolution of cooperation, this strategy can never outscore any opponent and it does poorly against its clone in a noisy environment. Here we examine the family of Pavlovian strategies which adapts its play by positive and negative conditioning, much as many animals do. Mutual cooperation will evolve in a contest with Pavlov against a wide variety of opponents and in particular against its clone. And the strategy is quite stable in a noisy environment. Although this strategy cooperates and retaliates, as does Tit-For-Tat, it is not forgiving; Pavlov will exploit altruistic strategies until he is punished by mutual defection. Moreover, Pavlovian strategies are natural models for many real life conflict-of-interest encounters as well as human and computer simulations.     

Pavlov and the prisoner's dilemma

Our Pavlov learns by conditioned response, through rewards and punishments, to cooperate or defect. We analyze the behavior of an extended play Prisoner's Dilemma with Pavlov against various opponents and compute the time and cost to train Pavlov to cooperate. Among our results is that Pavlov and his clone would learn to cooperate more rapidly than if Pavlov played against the Tit for Tat strategy. This fact has implications for the evolution of cooperation.     

An extension of the Nash bargaining problem and the Nash social welfare function

This paper provides an extension of Nash's bargaining model. The extension permits the domain of a solution function to contain non-convex sets. First, it is shown that the proposed extension is a mathematical generalization of Nash's bargaining problem. Next, some relations between the extension and the Nash social welfare function are developed. The formal equivalence of the two constructs is demonstrated, and the intuitive significance of the results is discussed.I am indebted to S. Ishikawa for helpful comments on an earlier draft and to K. Nakamura for helpful discussions. Any errors that remain are of course my responsibility.     

Endogenizing the order of moves in matrix games

Players often have flexibility in when they move and thus whether a game is played simultaneously or sequentially may be endogenously determined. For 2 × 2 games, we analyze this using an extended game. In a stage prior to actual play, players choose in which of two periods to move. A player moving at the first opportunity knows when his opponent will move. A player moving at the second turn learns the first mover's action. If both select the same turn, they play a simultaneous move subgame.If both players have dominant strategies in the basic game, equilibrium payoffs in the basic and extended games are identical. If only one player has a dominant strategy or if the unique equilibrium in the basic game is in mixed strategies, then the extended game equilibrium payoffs differ if and only if some pair of pure strategies Pareto dominates the basic game simultaneous play payoffs. If so, sequential play attains the Pareto dominating payoffs. The mixed strategy equilibrium occurs only when it is not Pareto dominated by some pair of pure strategies.In an alternative extended game, players cannot observe delay by opponents at the first turn. Results for 2×2 games are essentially the same as with observable delay, differing only when only one player has a dominant strategy.     

Applied general equilibrium analysis of trade liberalisation on land-based sectors in Malaysia and Indonesia

This paper presents general equilibrium evaluations of forest sector trade for Southeast Asian exporters. The four scenarios examined range from the 1994 Uruguay Round tariff reductions to a complete liberalisation of forest and agricultural products trade. We find that simultaneous reductions in forest and agricultural sector tariffs make Indonesia and Malaysia worse off. For Indonesia, this is due to the fall in forest rent and agricultural tariff revenues. Malaysia has the highest ratio of agricultural imports to total land-based sector imports, the rise in agricultural prices thus hits Malaysian consumers the hardest.We find that terms of trade effect omitted from the partial equilibrium framework may reduce the welfare calculations for Malaysia and Indonesia in the forest sector trade by as much as 106 and 58%, respectively. This points to the importance of general equilibrium modelling in the logging industry. The same applies to other sector specific analyses where trade is concentrated between few countries.     

Effective choice in the single-shot Prisoner's Dilemma tournament

This paper discusses the results of a single-shot Prisoner's Dilemma computer tournament. In the single-shot Prisoner's Dilemma tournament each pair of players interacts only once. But players can establish and detect reputations because they know how their current opponent has behaved in previous games with other players. The results show that cooperation is worthwhile, even in single-shot games, provided the outcomes of previous games are common knowledge.Reality is a game, but you shouldn't take a game for reality(Pragmaticist Proverb)     

现实的摧毁与理想的建构--卢梭政治哲学方法论简论

卢梭以先验理性主义为指导 ,运用分析还原与理智重建的方法 ,提出了以“公意”为基础的契约理论 ,体现了摧毁与重建的方法论思想。卢梭政治理论本身是一贯的 ,但理论与实践之间却存在难以弥合的裂痕。这是因为先验理性的范导功能被约简到建构功能之中 ,从而使得价值的关切压倒了实践层面的具体操作。     

The individual rationality of maintaining a sense of justice

Let us say that an individual possesses aprincipled preference if she prefers satisfying her preferences without violating the principles of justice governing her community to satisfying her preferences by violating these principles. Although living among possessors of principled preferences benefits individuals, maintaining such a preference is individually costly. Further, individuals can benefit from others possessing principled preferences without themselves possessing one. In this paper, I argue that occupying a choice situation which mirrors key aspects of our own situation, maximizing rationality requires individuals to develop and maintain principled preferences.To establish that maintaining a principled preference is individually rational for the occupants of such a choice situation, I define a range of individual strategies for them, model their choice of individual strategies as a game, and argue that this game involves an equilibrium in which all of its participants would choose to develop and maintain a principled preference.