Всего статей в данном разделе : 69
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.
Опубликовано на портале: 24-01-2007Roger B. Myerson International Journal of Game Theory. 1978. Vol. 7. No. 2. P. 73-80.
Selten's concept of perfect equilibrium for normal form games is reviewed, and a new concept of proper equilibrium is defined. It is shown that the proper equilibria form a nonempty subset of the perfect equilibria, which in turn form a subset of the Nash equilibria. An example is given to show that these inclusions may be strict.
Reputation and Imperfect Information [статья]
Опубликовано на портале: 31-01-2007David M. Kreps, Robert B. Wilson Journal of Economic Theory. 1982. Vol. 27. No. 2. P. 253-279.
A common observation in the informal literature of economics (and elsewhere) is that is multistage games, players may seek early in the game to acquire a reputation for being tough or benevolent or something else. But this phenomenon is not observed in some formal game-theoretic analyses of finite games, such as Selten's finitely repeated chain-store game or in the finitely repeated prisoners' dilemma. We reexamine Selten's model, adding to it a small amount of imperfect (or incomplete) information about players' payoffs, and we find that this addition is sufficient to give rise to the reputation effect that one intuitively expects.
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.
Sequentially Optimal Auctions [статья]
Опубликовано на портале: 30-01-2007Daniel R. Vincent, R. Preston McAfee Games and Economic Behavior. 1997. Vol. 18. No. 2.
We examine equlibria in sequential auctions where a seller can post a reserve price but, if the auction fails to result in a sale, can commit keeping the object off the market only for an exogenously fixed period of time. We restrict attention to enviornments where bidders have independent private values and where the support of the bidder types lies strictly above the valuation of the seller. In the case where the seller sells by second price auction in each period, there is a unique perfect Bayesian equilbrium. A form of revenue equivalence is shown. There exists a perfect Bayesian equilibrium of repeated first price auctions with the feature that in every period, the seller's expected revenue from the continuation is the same in either auction mechanism. As the length of time the seller can commit to keeping the object off the market goes to zero, seller expected revenues converge to those of a static auction with no reserve price. As the number of bidders becomes large, the seller expected revenue approaches the revenue from an optimal static auction. We also characterize a parametrized auction game in which the simple equilibrium reserve price policy of the seller mirrors a policy commonly used by many auctioneers.
Опубликовано на портале: 31-01-2007David M. Kreps, In-Koo Cho Quarterly Journal of Economics. 1987. Vol. 102. No. 2. P. 179-221.
Games in which one party conveys private information to a second through messages typically admit large numbers of sequential equilibria, as the second party may entertain a wealth of beliefs in response to out-of-equilibrium messages. By restricting those out-of equilibrium beliefs, one can sometimes eliminate many unintuitive equilibria. We present a number of formal restrictions of this sort, investigate their behavior in specific examples, and relate these restrictions to Kohlberg and Mertens` notion of stability.
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: 22-01-2007Eric S. Maskin, Partha Sarathi Dasgupta Review of Economic Studies. 1986. Vol. 53. No. 1. P. 1-26.
The article presents information about the existence of equilibrium in discontinuous economic games. In this paper and its sequel presents study the existence of Nash equilibrium in games where agents' payoff functions are discontinuous. The enquiry is motivated by a number of recent studies that have uncovered serious existence problems in seemingly innocuous economic games. In the sequel to this paper, authors have explained the utility function in the economic games referred to earlier are neither continuous nor quasi-concave. However, they demonstrate that the payoff functions in mildly modified versions of these constructs exhibit two weaker forms of continuity which, together with the requirement of quasi-concavity, suffice for the existence of an equilibrium. From this one may conclude that, at least in the modified versions of these models, discontinuities in the payoff functions are not the real source of the problem. Rather, it is the failure of the payoff functions to the quasi-concave which is "responsible" for the non-existence of equilibrium. These observations bear on the existence of Nash equilibrium in pure strategies.
The Fisherman's Problem: Exploring the Tension between Cooperative and Non-Cooperative Concepts in a Simple Game [статья]
Опубликовано на портале: 07-07-2005Klaus Abbink, Ron Darziv, Zohar Gilula, Harel Goren, Bernd Irlenbusch, Arnon Keren, Bettina Rockenbach, Abdolkarim Sadrieh, Reinhard Selten, Shmuel Zamir Journal of Economic Psychology. 2003. Vol. 24. No. 4. P. 425-445.
We introduce and experiment the Fisherman's Game in which the application of economic theory leads to four different benchmarks. Non-cooperative sequential rationality predicts one extreme outcome while the core (which coincides with the competitive market equilibrium) predicts the other extreme. Intermediate, disjoint outcomes are predicted by fairness utility models and the Shapley value. None of the four benchmarks fully explains the observed behavior. However, since elements of both cooperative and non-cooperative game theory are crucial for organizing our data, we conclude that effort towards bridging the gap between the various concepts is a promising approach for future economic research.
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.
Опубликовано на портале: 27-02-2004Elizabeth Hoffman, K. McCabe, Vernon L. Smith Experimental Economics. 2000. Vol. 3. No. 1. P. 5-9.
In this paper we report the results of additional exchange ultimatum game experiments conducted at the same time as the exchange ultimatum game experiments reported in Hoffman et al. (Games and Economic Behavior, 7(3), pp. 346-380, 1994). In these additional experiments, we use instructions to change an impersonal exchange situation to a personal exchange situation. To do this, we prompt sellers to consider what choices their buyers will make. Game theory would predict that thinking about the situation would lead sellers to make smaller offers to buyers. In contrast, we find a significant increase in seller offers to buyers. This result suggests that encouraging sellers to thinking about buyer choices focuses their attention on the strategic interaction with humans who think they way they do in personal exchange situations, and who may punish them for unacceptable behavior, and not on the logic of the game theoretic structure of the problem.
The lab man [статья]
Опубликовано на портале: 27-02-2004Vernon L. Smith Finance & Development. 2003. Vol. 40. No. 1. P. 6-9.
For a man who has built his reputation on controlled experiments to test market theories in the laboratory, Nobel Prize winner Vernon Smith is a bit of a free spirit. Smith pioneered the use of experiments conducted in the controlled environment of the laboratory to test economic theories, in particular why markets work the way they do. Smith is passionate in his commitment to laboratory testing in economics. Laboratory experiments do not provide policymakers with iron-clad answers to key economic questions but do offer a quick, cost-effective way to identify market and policy flaws before ideas and theories become major public policy initiatives. Participants in Smith's experiments come from many fields and include corporate executives, market traders, graduate students, and trained economists.