A Strong Anti-Folk Theorem

We study the properties of finitely complex, symmetric, globally stable, and semi-perfect equilibria. We show that: (1) If a strategy satisfies these properties then players play a Nash equilibrium of the stage game in every period; (2) The set of finitely complex, symmetric, globally stable, semi-perfect equilibrium payoffs in the repeated game equals the set of Nash equilibria payoffs in the stage game; and (3) A strategy vector satisfies these properties in a Pareto optimal way if and only if players play some Pareto optimal Nash equilibrium of the stage game in every stage. Our second main result is a strong anti-Folk Theorem, since, in contrast to what is described by the Folk Theorem, the set of equilibrium payoffs does not expand when the game is repeated.This paper is a revised version of Chapter 3 of my Ph.D. thesis, which has circulated under the title “An Interpretation of Nash Equilibrium Based on the Notion of Social Institutions”.     

Imitation,coordination and the emergence of Nash equilibrium

We consider a learning dynamic in which players imitate and better reply. Sufficient conditions are provided for Nash equilibrium play to emerge over time. The role of imitation in the learning dynamic is discussed through a series of examples. Most interestingly we demonstrate how imitation can ‘help’ the emergence of Nash equilibrium where ‘more rational’ methods do not.     

Equilibrium and effectiveness of two-parameter scoring rules

We study a cardinal model of voting with three alternatives where voters’ von Neumann Morgenstern utilities are private information. We consider voting protocols given by two-parameter scoring rules, as introduced by Myerson (2002). For these voting rules, we show that all symmetric Bayes Nash equilibria are sincere, and have a very specific form. These equilibria are unique for a wide range of model parameters, and we can therefore compare the equilibrium performance of different rules. Computational results regarding the effectiveness of different scoring rules (where effectiveness is captured by a modification of the effectiveness measure proposed in Weber, 1978) suggest that those which most effectively represent voters’ preferences allow for the expression of preference intensity, in contrast to more commonly used rules such as the plurality rule, and the Borda Count. While approval voting allows for the expression of preference intensity, it does not maximize effectiveness as it fails to unambiguously convey voters’ ordinal preference rankings.     

Multicriterion Aerodynamic Shape Design Optimization and Inverse Problems Using Control Theory and Nash Games

Multicriterion design is gaining importance in aeronautics in order to cope with new needs of society. In the literature, contributions to single discipline and/or single-point design optimization abound. The goal of this paper is to introduce a new approach combining the adjoint method with a formulation derived from game theory for multipoint aerodynamic design problems. Transonic flows around lifting airfoils are analyzed via Euler computations. Airfoil shapes are optimized according to various aerodynamic criteria. The notion of player is introduced. In a competitive Nash game, each player attempts to optimize its own criterion through a symmetric exchange of information with others. A Nash equilibrium is reached when each player, constrained by the strategy of the others, cannot improve further its own criterion. Specific real and virtual symmetric Nash games are implemented to set up an optimization strategy for design under conflict. This work has benefited partially from the support of the National Science Foundation of China Grant NSFC-10372040 and Scientific Research Foundation (SRF) for Returned Overseas Chinese Scholars (ROCS) Grant 2003-091. The first author acknowledges the support of INRIA (Institut National de Recherche en Information et en Automatique), France.     

Bargaining with nonanonymous disagreement: Decomposable rules

We analyze bargaining situations where the agents’ payoffs from disagreement depend on who among them breaks down the negotiations. We model such problems as a superset of the standard domain of Nash (1950). We first show that this domain extension creates a very large number of new rules. In particular, decomposable rules (which are extensions of rules from the Nash domain) constitute a nowhere dense subset of all possible rules. For them, we analyze the process through which “good” properties of rules on the Nash domain extend to ours. We then enquire whether the counterparts of some well-known results on the Nash (1950) domain continue to hold for decomposable rules on our extended domain. We first show that an extension of the Kalai-Smorodinsky bargaining rule uniquely satisfies the Kalai and Smorodinsky (1975) properties. This uniqueness result, however, turns out to be an exception. We characterize the uncountably large classes of decomposable rules that survive the Nash (1950), Kalai (1977), and Thomson (1981) properties.     

Bargaining with nonanonymous disagreement: Decomposable rules

We analyze bargaining situations where the agents’ payoffs from disagreement depend on who among them breaks down the negotiations. We model such problems as a superset of the standard domain of Nash (1950). We first show that this domain extension creates a very large number of new rules. In particular, decomposable rules (which are extensions of rules from the Nash domain) constitute a nowhere dense subset of all possible rules. For them, we analyze the process through which “good” properties of rules on the Nash domain extend to ours. We then enquire whether the counterparts of some well-known results on the Nash (1950) domain continue to hold for decomposable rules on our extended domain. We first show that an extension of the Kalai–Smorodinsky bargaining rule uniquely satisfies the Kalai and Smorodinsky (1975) properties. This uniqueness result, however, turns out to be an exception. We characterize the uncountably large classes of decomposable rules that survive the Nash (1950), Kalai (1977), and Thomson (1981) properties.     

A Characterization of Nash Equilibrium for the Games with Random Payoffs

We consider a two-player random bimatrix game where each player is interested in the payoffs which can be obtained with certain confidence. The payoff function of each player is defined using a chance constraint. We consider the case where the entries of the random payoff matrix of each player jointly follow a multivariate elliptically symmetric distribution. We show an equivalence between the Nash equilibrium problem and the global maximization of a certain mathematical program. The case where the entries of the payoff matrices are independent normal/Cauchy random variables is also considered. The case of independent normally distributed random payoffs can be viewed as a special case of a multivariate elliptically symmetric distributed random payoffs. As for Cauchy distribution, we show that the Nash equilibrium problem is equivalent to the global maximization of a certain quadratic program. Our theoretical results are illustrated by considering randomly generated instances of the game.     

Fictitious play with incomplete learning

In this paper, we consider a case that a game is played repeatedly in an incomplete learning process where each player updates his belief only in the learning periods rather than all the stages. For fictitious play process with incomplete learning, we discuss the absorbability of Nash equilibriums and the consistency of utilities in a finite game and discuss the convergence in a 2×2 game with an identical learning-period set. The main results for incomplete learning models are that, if it is uniformly played, a strict Nash equilibrium is absorbing in a fictitious play process; a fictitious play has the property of utility consistency if it exhibits infrequent switches and players learn frequently enough; a 2×2 game with an identical learning-period set has fictitious play property that any fictitious process for the game converges to equilibrium provided that players learn frequently enough.     

不完全博弈学习过程的虚拟行动规则

本文把博弈学习虚拟行动规则的学习时间一般化,研究不完全学习过程中参与人策略选择的收敛性及效用一致性问题. 分析结果表明：当学习时间不完全时,在学习一致到达的条件下,虚拟行动规则对严格纳什均衡是吸收的; 在学习时间充分及时与虚拟行动非频繁转换的条件下,各参与人的虚拟行动具有效用一致性.     

Observation,Measurement, and Computation in Finite Games

Limitations in agents ability to observe, measure and compute are studied. A formulation in terms of induced changes in the players subjective perception of the game makes it possible to study these phenomena on a common footing with objective variation in the game. We study a model where payoffs undergo continuous variation and players reason about the process from limited local information. Specifically, finite games, and statements about them, are interpreted within sheaf models, which incorporate both variation and a logic of limited observation. Nashs theorem on the existence of equilibrium is not valid unless special observational properties hold, although closely related statements are valid. The possibility of learning to play a mixed strategy Nash equilibrium from observation of past play is also examined within the framework.I thank the referee and associate editor for their comments and suggestions. I also received very helpful suggestions from Josh Epstein. All remaining errors are my own.Received: April 2000 / Revised: December 2003     

Pollution control: A differential game approach

Transnational pollution is formulated as a differential game between two sovereign governments. The symmetric open loop Nash equilibrium is shown to yield more pollution than in a cooperative solution. A model of Stackelberg leadership in pollution control is also investigated. The possibility of limit cycles is illustrated, using bifurcation theory.     

Evolutionary and asymptotic stability in symmetric multi-player games

We provide a classification of symmetric three-player games with two strategies and investigate evolutionary and asymptotic stability (in the replicator dynamics) of their Nash equilibria. We discuss similarities and differences between two-player and multi-player games. In particular, we construct examples which exhibit a novel behavior not found in two-player games.Received October 2001/Revised May 2003     

Homogeneous Customers Renege from Invisible Queues at Random Times under Deteriorating Waiting Conditions

We consider a memoryless first-come first-served queue in which customers' waiting costs are increasing and convex with time. Hence, customers may opt to renege if service has not commenced after waiting for some time. We assume a homogeneous population of customers and we look for their symmetric Nash equilibrium reneging strategy. Besides the model parameters, customers are aware only, if they are in service or not, and they recall for how long they are have been waiting. They are informed of nothing else. We show that under some assumptions on customers' utility function, Nash equilibrium prescribes reneging after random times. We give a closed form expression for the resulting distribution. In particular, its support is an interval (in which it has a density) and it has at most two atoms (at the edges of the interval). Moreover, this equilibrium is unique. Finally, we indicate a case in which Nash equilibrium prescribes a deterministic reneging time.     

Nonsymmetric Nash solutions and replications of 2-person bargaining

A 2-person fixed threat bargaining problem is considered. A full characterization of the solutions which satisfy all of Nash's axioms except for the axiom of symmetry is given. It is also shown that these nonsymmetric Nash solutions are precisely the solutions that arise from symmetric Nash solutions through replications.     

On Nash Equilibrium Strategy of Two-person Zero-sum Games with Trapezoidal Fuzzy Payoffs

In this paper, we investigate Nash equilibrium strategy of two-person zero-sum games with fuzzy payoffs. Based on fuzzy max order, Maeda and Cunlin constructed several models in symmetric triangular and asymmetric triangular fuzzy environment, respectively. We extended their models in trapezoidal fuzzy environment and proposed the existence of equilibrium strategies for these models. We also established the relation between Pareto Nash equilibrium strategy and parametric bi-matrix game. In addition, numerical examples are presented to find Pareto Nash equilibrium strategy and weak Pareto Nash equilibrium strategy from bi-matrix game.     

Equilibrium in a war of attrition with an option to fight decisively

We develop a symmetric incomplete-information continuous-time two-player war-of-attrition game with an option to fight decisively. We show that there exists an essentially unique symmetric Bayesian Nash equilibrium. Under equilibrium, the game does not end immediately, and a costly delay persists even with the availability of the fighting option that ends the game if chosen. In addition, there exists a critical time in which a fight occurs unless a player resigns before that time.     

Variational inequality formulation for the games with random payoffs

We consider an n-player non-cooperative game with random payoffs and continuous strategy set for each player. The random payoffs of each player are defined using a finite dimensional random vector. We formulate this problem as a chance-constrained game by defining the payoff function of each player using a chance constraint. We first consider the case where the continuous strategy set of each player does not depend on the strategies of other players. If a random vector defining the payoffs of each player follows a multivariate elliptically symmetric distribution, we show that there exists a Nash equilibrium. We characterize the set of Nash equilibria using the solution set of a variational inequality (VI) problem. Next, we consider the case where the continuous strategy set of each player is defined by a shared constraint set. In this case, we show that there exists a generalized Nash equilibrium for elliptically symmetric distributed payoffs. Under certain conditions, we characterize the set of a generalized Nash equilibria using the solution set of a VI problem. As an application, the random payoff games arising from electricity market are studied under chance-constrained game framework.     

土木工程投标报价模型研究(英文)

本文主要研究单一不可分土木工程的n人投标报价模型.报价高低不是是否中标的唯一决定性因素,施工方案和工程报价为赢得工程施工合同共同发挥组合效应,并且在一定条件下,通过工程竟标,中标价会趋于Nash平衡.