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Опубликовано на портале: 28-04-2005John Donald Roberts, Paul R. Milgrom Econometrica. 1990. Vol. 58. No. 6. P. 1255-1277.
We study a class of non-cooperative games that includes many standard oligopoly games,macro economic coordination games, network and production externality games, and others. Forthese games, the sets of rationalizable strategies, pure Nash equilibrium strategies, and correlated equilibrium strategies are non-empty and have identical upper and lower bounds. Also,a large class of dynamic learning processes - including both best-response dynamics and Bayesian learning - lead eventually to behavior that lies between these same bounds. General comparative static and welfare theorems are provided. We study the class of (non-cooperative) supermodular games introduced by Topkis (1979) and further studied by Vives (1988). These are games in which each player's strategy set is partially ordered, the marginal returns to increasing one's strategy rise with increases in the competitors' strategies and, if a player's strategies are multidimensional, the marginal returns to any one component of the player's strategy increase with increases in the other components. The simplest examples of such games arise in oligopoly theory. These include the Cournot duopoly game with a wide range of demand specifications and arbitrary continuous cost functions, Bertrand oligopoly games, R&D racing games, and oligopoly games with endogenous choice of production technologies. Additional applications drawn from industrial organization include the Hendricks-Kovenock (1988) drilling game (in which oil firms decide whether to drill exploratory wells when the information obtained is a public good), network externality games, and certain oligopoly games that arise in connection with the Milgrom-Roberts (1988) model of manufacturing. Other examples include games used to model
Rationalizable Strategic Behavior [статья]
Опубликовано на портале: 30-01-2007B. Douglas Bernheim Econometrica. 2006. Vol. 52. No. 4. P. 1007-1028.
This paper examines the nature of rational choice in strategic games. Although there are many reasons why an agent might select a Nash equilibrium strategy in a particular game, rationality alone does not require him to do so. A natural extension of widely accepted axioms for rational choice under uncertainty to strategic environments generates an alternative class of strategies, labelled "rationalizable." It is argued that no rationalizable strategy can be discarded on the basis of rationality alone, and that all rationally justifiable strategies are members of the rationalizable set. The properties of rationalizable strategies are studied, and refinements are considered.
Опубликовано на портале: 22-01-2007Ehud Lehrer, Ehud Kalai Econometrica. 1993. Vol. 61. No. 5. P. 1019-1045.
Subjective utility maximizers, in an infinitely repeated game, will learn to predict opponents' future strategies and will converge to play according to a Nash equilibrium of the repeated game. Players' initial uncertainty is placed directly on opponents' strategies and the above result is obtained under the assumption that the individual beliefs are compatible with the chosen strategies. An immediate corollary is that, when playing a Harsanyi-Nash equilibrium of a repeated game of incomplete information about opponents' payoff matrices, players will eventually play a Nash equilibrium of the real game, as if they had complete information.
Sequential Equilibria [статья]
Опубликовано на портале: 31-01-2007David M. Kreps, Robert B. Wilson Econometrica. 1982. Vol. 50. No. 4. P. 863-94.
We propose a new criterion for equilibria of extensive games, in the spirit of Selten's perfectness criteria. This criterion requires that players' strategies be sequentially rational: Every decision must be part of an optimal strategy for the remainder of the game. This entails specification of players' beliefs concerning how the game has evolved for each information set, including information sets off the equilibrium path. The properties of sequential equilibria are developed; in particular, we study the topological structure of the set of sequential equilibria. The connections with Selten's trembling-hand perfect equilibria are given.
Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information [статья]
Опубликовано на портале: 30-01-2007Susan Carleton Athey Econometrica. 2001. Vol. 69. No. 4. P. 861-89.
This paper analyzes a class of games of incomplete information where each agent has private information about her own type, and the types are drawn from an atomless joint probability distribution. The main result establishes existence of pure strategy Nash equilibria (PSNE) under a condition we call the single crossing condition (SCC), roughly described as follows: whenever each opponent uses a nondecreasing strategy (in the sense that higher types choose higher actions), a player's best response strategy is also nondecreasing. When the SCC holds, a PSNE exists in every finite-action game. Further, for games with continuous payoffs and a continuum of actions, there exists a sequence of PSNE to finite-action games that converges to a PSNE of the continuum-action game. These convergence and existence results also extend to some classes of games with discontinuous payoffs, such as first-price auctions, where bidders may be heterogeneous and reserve prices are permitted. Finally, the paper characterizes the SCC based on properties of utility functions and probability distributions over types. Applications include first-price, multi-unit, and all-pay auctions; pricing games with incomplete information about costs; and noisy signaling games.
Strategic Information Transmission [статья]
Опубликовано на портале: 24-01-2007Vincent P. Crawford, Joel Sobel Econometrica. 1982. Vol. 50. No. 6. P. 1431-1451.
This paper develops a model of strategic communication, in which a better-informed Sender (S) sends a possibly noisy signal to a Reciever (R), who then takes an action that determines the welfare of both. We characterize the set of Bayesian Nash equilibria under standart assumptions, and show that equilibrium signaling always takes a strikingly simple form, in which S partitions the support of the (scalar) variable that represents his private information and introduces noise into his signal by reporting, in effect, only which element of the partition his observation actually lies in. We show under further assumptions that before S observes his private information, the equilibrium whose partition has the greatest number of elements is Pareto-superior to all other equilibria, and that if agents coordinate on this equilibrium, R`s equilibrium expected utility rises when agents` preferences become more similar. Since R bases his choice of action on rational expectations, this establishes a sense in which equilibrium signaling is more informative when agents` preferences are more similar.
The Bargaining Problem [статья]
Опубликовано на портале: 08-07-2005John Forbes Nash Econometrica. 1950. Vol. 18. No. 2. P. 155-162.
A new treatment is presented of a classical economic problem, one which occurs in many forms, as bargaining, bilateral monopoly, etc. It may also be regarded as a nonzero-sum two-person game. In this treatment a few general assumptions are made concerning the behavior of a single individual and of a group of two individuals in certain economic environments. From these, the solution (in the sense of this paper) of classical problem may be obtained. In the terms of game theory, values are found for the game. См. также: Two-person cooperative games, автор - Джо Нэш.
The Evolution of Walrasian Behavior [статья]
Опубликовано на портале: 24-01-2007Fernando Vega-Redondo Econometrica. 1997. Vol. 65. No. 2. P. 375-384.
This article describes an evolutionary approach to understanding Walrasian behavior. It avoids any considerations related to the absence of monopoly power or related notion of a large enough population. Walrasian behavior may evolve within any quantity-setting oligopoly producing a homogenous good, provided that the law of demand is satisfied. Evolutionary models may produce interesting behavior that does not correspond to a Nash equilibrium.
Опубликовано на портале: 31-01-2007Dilip Abreu, Prajit K. Dutta, Lones Smith Econometrica. 1994. Vol. 62. No. 4. P. 939-948.
The paper discusses perfect "folk theorems" for infinitely repeated games with complete information. Folk theorems assert that any feasible and individually rational payoff vector of the stage game is a subgame perfect equilibrium payoff in the associated infinitely repeated game with little or no discounting. It is obvious that feasibility and individual rationality are necessary conditions for a payoff vector to be an equilibrium payoff. The content of the folk theorems is that these conditions are also sufficient. Perhaps the first folk theorem type result is due to Friedman (1971) who showed that any feasible payoff which Pareto dominates a Nash equilibrium payoff of the stage game will be an equilibrium payoff in the associated repeated game with sufficiently patient players.
Two-person cooperative games [статья]
Опубликовано на портале: 13-03-2003John Forbes Nash Econometrica. 1953. Vol. 21. No. 1. P. 128-140.
In this paper, the autor extends his previous treatment of «The Bargaining Problem» to a wider class of situations in which threats can play a role/ A new approach is introduced involving the elaboration of the threat concept.
Опубликовано на портале: 22-01-2007Dilip Abreu, Hitoshi Matsushima Econometrica. 1992. Vol. 60. No. 5. P. 993-1008.
The authors investigate the implementation of social choice functions that map to lotteries over alternatives. They require virtual implementation in iteratively undominated strategies. Under very weak domain restrictions, they show that if there are three or more players, any social choice function may be so implemented. The literature on implementation in Nash equilibrium and its refinements is compromised by its reliance on game forms with unnatural features (for example, "integer games") or "modulo" constructions with mixed strategies arbitrarily excluded. In contrast, the authors' results employ finite (consequently "well-behaved") mechanisms and allow for mixed strategies.