Single Crossing Properties and the Existence of Pure Strategy Nash Equilibria in Games of Incomplete Information PDF Download
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Author: Susan Athey
Publisher:
ISBN:
Category :
Languages : en
Pages : 46
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Book Description
Author: Susan Athey
Publisher:
ISBN:
Category :
Languages : en
Pages : 46
Get Book Here
Book Description
Author: Susan Athey
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
This paper derives sufficient conditions for a class of games of incomplete information, such as first price auctions, to have pure strategy Nash equilibria (PSNE). The paper treats games between two or more heterogeneous agents, each with private information about his own type (for example, a bidder's value for an object of a firm's marginal cost of production), and the types are drawn from an atomless joint probability distribution which potentially allows for correlation between types. Agents' utility may depend directly on the realizations of other agents' types, as in Milgrom and Weber's (1982) formulation of the "mineral rights" auction. The restriction we consider is that each player's expected payoffs satisfy the following single crossing condition: whenever each opponent uses a nondecreasing strategy (that is, an opponent who has a higher type chooses a higher action), then a player's best response strategy is also nondecreasing in her type. The paper has two main results. The first result shows that, when players are restricted to choose among a finite set of actions (for example, bidding or pricing where the smallest unit is a penny), games where players' objective functions satisfy this single crossing condition will have PSNE. The second result demonstrates that when players' utility functions are continuous, as well as in mineral rights auction games and other games where "winning" creates a discontinuity in payoffs, the existence result can be extended to the case where players choose from a continuum of actions. The paper then applies the theory to several classes of games, providing conditions on utility functions and joint distributions over types under which each class of games satisfies the single crossing condition. In particular, the single crossing condition is shown to hold in all first-price, private value auctions with potentially heterogeneous, risk-averse bidders, with either independent or affiliated values, and with reserve prices which may differ across bidders; mineral rights auctions with two heterogeneous bidders and affiliated values; a class of pricing games with incomplete information about costs; a class of all-pay auction games; and a class of noisy signaling games. Finally, the formulation of the problem introduced in this paper suggests a straightforward algorithm for numerically computing equilibrium bidding strategies in games such as first price auctions, and we present numerical analyses of several auctions under alternative assumptions about the joint distribution of types.
Author: Susan Athey
Publisher:
ISBN:
Category : Game theory
Languages : en
Pages : 46
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Book Description
Author: Petyon Young
Publisher: Elsevier
ISBN: 0444537678
Category : Mathematics
Languages : en
Pages : 1025
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Book Description
The ability to understand and predict behavior in strategic situations, in which an individual’s success in making choices depends on the choices of others, has been the domain of game theory since the 1950s. Developing the theories at the heart of game theory has resulted in 8 Nobel Prizes and insights that researchers in many fields continue to develop. In Volume 4, top scholars synthesize and analyze mainstream scholarship on games and economic behavior, providing an updated account of developments in game theory since the 2002 publication of Volume 3, which only covers work through the mid 1990s. Focuses on innovation in games and economic behavior Presents coherent summaries of subjects in game theory Makes details about game theory accessible to scholars in fields outside economics
Author: Luis C. Corchón
Publisher: Edward Elgar Publishing
ISBN: 178536328X
Category : Business & Economics
Languages : en
Pages : 567
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Book Description
The first volume of this wide-ranging Handbook contains original contributions by world-class specialists. It provides up-to-date surveys of the main game-theoretic tools commonly used to model industrial organization topics. The Handbook covers numerous subjects in detail including, among others, the tools of lattice programming, supermodular and aggregative games, monopolistic competition, horizontal and vertically differentiated good models, dynamic and Stackelberg games, entry games, evolutionary games with adaptive players, asymmetric information, moral hazard, learning and information sharing models.
Author: Michael R. Baye
Publisher:
ISBN:
Category :
Languages : en
Pages : 62
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Author: Xavier Vives
Publisher: MIT Press (MA)
ISBN: 9780262220606
Category : Business & Economics
Languages : en
Pages : 446
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Book Description
Applies a modern game-theoretic approach to develop a theory of oligopoly pricing. The text relates classic contributions to the field of modern game theory and discusses basic game-theoretic tools and equilibrium, paying particular attention to developments in the theory of supermodular games.
Author: Karl Schmedders
Publisher: Newnes
ISBN: 0080931782
Category : Business & Economics
Languages : en
Pages : 680
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Book Description
Handbook of Computational Economics summarizes recent advances in economic thought, revealing some of the potential offered by modern computational methods. With computational power increasing in hardware and algorithms, many economists are closing the gap between economic practice and the frontiers of computational mathematics. In their efforts to accelerate the incorporation of computational power into mainstream research, contributors to this volume update the improvements in algorithms that have sharpened econometric tools, solution methods for dynamic optimization and equilibrium models, and applications to public finance, macroeconomics, and auctions. They also cover the switch to massive parallelism in the creation of more powerful computers, with advances in the development of high-power and high-throughput computing. Much more can be done to expand the value of computational modeling in economics. In conjunction with volume one (1996) and volume two (2006), this volume offers a remarkable picture of the recent development of economics as a science as well as an exciting preview of its future potential. Samples different styles and approaches, reflecting the breadth of computational economics as practiced today Focuses on problems with few well-developed solutions in the literature of other disciplines Emphasizes the potential for increasing the value of computational modeling in economics
Author: Helmut Meister
Publisher: Springer Science & Business Media
ISBN: 3642502784
Category : Business & Economics
Languages : en
Pages : 127
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Book Description
The approach presented in this book combines two aspects of generalizations of the noncooperative game as developed by Nash. First, players choose their acts dependent on certain information variables, and second there are constraints on the sets of decisions for players. After the derivation of a general (Nash)equilibrium existence theorem, some results from purification theory are used to prove the existence of an approximate equilibrium in pure strategies, that is in nonrandomized decision functions. For some types of payoff-functions and constraints, these games prove to have an (exact) equilibrium in pure strategies. The reason for considering constrained games with incomplete information is that, apart from their game-theoretic importance, they have rather widespread application. Market games with a continuum of traders as well as some statistical decision problems are covered with this approach.
Author:
Publisher:
ISBN:
Category : Economics, Mathematical
Languages : en
Pages : 740
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