Abstract. Experimentalists frequently claim that human subjects in the laboratory violate game-theoretic predictions. It is here argued that this claim is usually premature. The paper elaborates on this theme by way of raising some conceptual and methodological issues in connection with the very definition of a game and of players ’ preferences, in particular with respect to potential context dependence, interpersonal preference dependence, backward induction and incomplete information.

We investigate the use of standard statistical models for quantal choice in a game theoretic setting. Players choose strategies based on relative expected utility, and assume other players do so as well. We define a Quantal Response Equilibrium (QRE) as a fixed point of this process, and establish existence. For a logit specification of the error structure, we show that as the error goes to zero, QRE approaches a subset of Nash equilibria and also implies a unique selection from the set of Nash equilibria in generic games. We fit the model to a variety of experimental data sets by using maximum likelihood estimatation.

In this paper, we present a game theoretic framework for bandwidth allocation for elastic services in high-speed net-works. The framework is based on the idea of the Nash bargaining solution from cooperative game theory, which not only provides the rate settings of users that are Pareto optimal from the point of view of the whole system, but are also consistent with the fairness axioms of game theory. We first consider the centralized problem and then show that this procedure can be decentralized so that greedy optimization by users yields the system optimal bandwidth allocations. We propose a distributed algorithm for implementing the optimal and fair bandwidth allocation and provide conditions for its convergence. The paper concludes with the pricing of elastic connections based on users ' bandwidth requirements and users' budget. We show that the above bargaining framework can be used to characterize a rate allocation and a pricing policy which takes into account users ' budget in a fair way and such that the total network revenue is maximized.

This paper is meant to familiarize the audience with some of the fundamental results in the theory of implementation and provide a quick progression to some open questions in the literature.

This paper is a survey and exposition of linear methods for finding Nash equilibria. Above all, these apply to games with two players. In an equilibrium of a twoperson game, the mixed strategy probabilities of one player equalize the expected payoffs for the pure strategies used by the other player. This defines an optimization problem with linear constraints. We do not consider nonlinear methods like simplicial subdivision for approximating fixed points, or systems of inequalities for higher-degree polynomials as they arise for noncooperative games with more than two players. These are surveyed in McKelvey and McLennan (1996)

. We propose the sequence form as a new strategic description for an extensive game with perfect recall. It is similar to the normal form but has linear instead of exponential complexity, and allows a direct representation and efficient computation of behavior strategies. Pure strategies and their mixed strategy probabilities are replaced by sequences of consecutive choices and their realization probabilities. A zero-sum game is solved by a corresponding linear program that has linear size in the size of the game tree. General two-person games are studied in the paper by Koller, Megiddo, and von Stengel in this journal issue. Journal of Economic Literature Classification Number: C72 Keywords. Behavior strategy, equilibrium, extensive game, linear programming, normal form, reduced normal form. 1. Introduction In applications, it is often convenient to describe a game in extensive form. The game tree, with its information sets, possible moves, chance probabilities and payoffs, gives a...

This paper provides deterministic approximation results for stochastic processes that arise when finite populations recurrently play finite games. The processes are Markov chains, and the approximation is defined in continuous time as a system of ordinary differential equations of the type studied in evolutionary game theory. We establish precise connections between the long-run behavior of the discrete stochastic process, for large populations, and its deterministic flow approximation. In particular, we provide probabilistic bounds on exit times from and visitation rates to neighborhoods of attractors to the deterministic flow. We sharpen these results in the special case of ergodic processes.

This paper presents a new lower bound of 2.414 d / √ d on the maximal number of Nash equilibria in d × d bimatrix games, a central concept in game theory. The proof uses an equivalent formulation of the problem in terms of pairs of polytopes with 2d facets in d-space. It refutes a recent conjecture that 2 d −1 is an upper bound, which was proved for d ≤ 4. The first counterexample is a 6×6 game with 75 equilibria. The case d = 5 remains open. The result carries the lower bound closer to the previously known upper bound of 2.6 d / √ d.

In Bagwell (1995) it is claimed that, in models of commitment, "the firstmover advantage is eliminated when there is a slight amount of noise associated with the observation of the first-mover's selection." We show that the validity of this claim depends crucially on the restriction to pure strategy equilibria. The game analyzed by Bagwell always has a mixed equilibrium that is close to the Stackelberg equilibrium when the noise is small. Furthermore, an equilibrium selection theory, that combines elements from the theory of Harsanyi and Selten (1988) with elements from the theory of Harsanyi (1995), actually selects this "noisy Stackelberg equilibrium." Journal of Economic Literature Classification Number: C72. Copyright c fl1997 by Academic Press. This material has been published in Games and Economic Behavior, 21, 282308, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Academic ...

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