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A Note On The Existence Of Nash Equilibrium In Games With Discontinuous Payoffs
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Book Synopsis A Note on the Existence of Nash Equilibrium in Games with Discontinuous Payoffs by : Rupert Gatti
Download or read book A Note on the Existence of Nash Equilibrium in Games with Discontinuous Payoffs written by Rupert Gatti and published by . This book was released on 2005 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper generalises the approach taken by Dasgupta & Maskin (1986) and Simon (1989) and provides necessary and sufficient conditions for the existence of pure and mixed strategy Nash equilibrium in games with continuous strategy spaces and discontinuous payoff functions. The conditions can be applied widely, and examples for existence of pure strategy and monotonic equilibria in First-Price auctions are provided. The conditions are also appropriate for ensuring that computer generated equilibrium solutions can be extended to continuous strategy spaces.
Book Synopsis A Note on the Existence of Nash Equilibrium in Games with Discontinuous Payoffs by : John Rupert James Gatti
Download or read book A Note on the Existence of Nash Equilibrium in Games with Discontinuous Payoffs written by John Rupert James Gatti and published by . This book was released on 2005 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Existence and Stability of Nash Equilibrium by : Guilherme Carmona
Download or read book Existence and Stability of Nash Equilibrium written by Guilherme Carmona and published by World Scientific. This book was released on 2013 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book aims at describing the recent developments in the existence and stability of Nash equilibrium. The two topics are central to game theory and economics and have been extensively researched. Recent results on existence and stability of Nash equilibrium are scattered and the relationship between them has not been explained clearly. The book will make these results easily accessible and understandable to researchers in the field. Book jacket.
Book Synopsis Local Payoff Security and the Existence of Nash Equilibrium in Discontinuous Games by : Philip J. Reny
Download or read book Local Payoff Security and the Existence of Nash Equilibrium in Discontinuous Games written by Philip J. Reny and published by . This book was released on 1995 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Existence of Pure-strategy Nash Equilibrium in Games with Payoffs that are Not Quasiconcave by : Michael R. Baye
Download or read book The Existence of Pure-strategy Nash Equilibrium in Games with Payoffs that are Not Quasiconcave written by Michael R. Baye and published by . This book was released on 1990 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Discontinuous Payoffs, Shared Resources, and Games of Fiscal Competition by : Paul Rothstein
Download or read book Discontinuous Payoffs, Shared Resources, and Games of Fiscal Competition written by Paul Rothstein and published by . This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We define a class of games with discontinuous payoffs that we call shared resource games and establish a pure strategy Nash equilibrium existence theorem for these games. We then apply this result to a canonical game of fiscal competition for mobile capital. Other applications are also discussed. Our result for the mobile capital game holds for any finite number of regions, permits general preferences over private and public goods, and does not assume that production technologies have a particular functional form, or are identical in all regions, or satisfy the Inada condition at zero.
Book Synopsis Essays on the Existence of Equilibria in Games by : Idione Meneghel
Download or read book Essays on the Existence of Equilibria in Games written by Idione Meneghel and published by . This book was released on 2013 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The question of existence of a Nash equilibrium is one of the most important questions in game theory. This thesis aims to advance our understanding of the question in two broad directions: 1) by providing weaker sets of sufficient conditions; and 2) by introducing novel techniques, which allow for straightforward proofs and results that give new economic insights. Discontinuous games: This project considers the existence problem in games in which strategy sets are compact and convex, but preferences of the players are represented by numerical functions that may not be continuous. One way to show existence of equilibrium in such games is to apply the 'better reply security' logic, introduced by Reny (1999), combined with some form of quasiconcavity of utility functions. As long as players have securing strategies that are robust to other players' small deviations, one can show that the game has an equilibrium. The novelty of the techniques used relies in combining three main ideas: 1) a local continuous selection of each player's strict upper contour set; 2) the idea of activating different players locally; and 3) a weak notion of convexity of preferences. Bayesian games: Games of incomplete information have been shown to apply to a huge variety of economic, political and other social interactions. Still, the question of existence of equilibria in such games has been largely dealt with on a case-by-case basis. That is, given a particular game with incomplete information, one has to find the equilibrium to prove that it exists. The reason is that the usual tools to prove existence (continuous and quasiconcave payoffs defined on convex and compact strategy sets) do not apply to the general framework of games with incomplete information. This project investigates sufficient conditions for the existence of pure-strategy Nash equilibrium in games of incomplete information. The assumption of nonatomicity of the distribution of types allows for an analysis that does not require convexity assumptions on action spaces and/or payoff functions"--Pages iv-v.
Book Synopsis Refinements of the Nash Equilibrium Concept by : E. van Damme
Download or read book Refinements of the Nash Equilibrium Concept written by E. van Damme and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, noncooperative games are studied. Since in a noncooperative game binding agreements are not possible, the solution of such a game has to be self enforcing, i. e. a Nash equilibrium (NASH [1950,1951J). In general, however, a game may possess many equilibria and so the problem arises which one of these should be chosen as the solution. It was first pointed out explicitly in SELTEN [1965J that I not all Nash equilibria of an extensive form game are qualified to be selected as the solution, since an equilibrium may prescribe irrational behavior at unreached parts of the game tree. Moreover, also for normal form games not all Nash equilibria are eligible, since an equilibrium need not be robust with respect to slight perturba tions in the data of the game. These observations lead to the conclusion that the Nash equilibrium concept has to be refined in order to obtain sensible solutions for every game. In the monograph, various refinements of the Nash equilibrium concept are studied. Some of these have been proposed in the literature, but others are presented here for the first time. The objective is to study the relations between these refine ments;to derive characterizations and to discuss the underlying assumptions. The greater part of the monograph (the chapters 2-5) is devoted to the study of normal form games. Extensive form games are considered in chapter 6.
Book Synopsis THE EXISTENCE OF PURE-STRATEGY NASH EQUILIBRIUM IN GAMES WITH PAYOFFS THAT ARE NOT QUASINCONCAVE by : Michael R. BAYE
Download or read book THE EXISTENCE OF PURE-STRATEGY NASH EQUILIBRIUM IN GAMES WITH PAYOFFS THAT ARE NOT QUASINCONCAVE written by Michael R. BAYE and published by . This book was released on 1990 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Existence of Nash Equilibrium in Mixed Strategies for Games where Payoffs Need Not be Continuous in Pure Strategies by : Arthur John Robson
Download or read book Existence of Nash Equilibrium in Mixed Strategies for Games where Payoffs Need Not be Continuous in Pure Strategies written by Arthur John Robson and published by . This book was released on 1990 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stability and Perfection of Nash Equilibria by : Eric van Damme
Download or read book Stability and Perfection of Nash Equilibria written by Eric van Damme and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last decade has seen a steady increase in the application of concepts from noncooperative game theory to such diverse fields as economics, political science, law, operations research, biology and social psychology. As a byproduct of this increased activity, there has been a growing awareness of the fact that the basic noncooperative solution concept, that of Nash equilibrium, suffers from severe drawbacks. The two main shortcomings of this concept are the following: (i) In extensive form games, a Nash strategy may prescribe off the equilibrium path behavior that is manifestly irrational. (Specifically, Nash equilibria may involve incredible threats), (ii) Nash equilibria need not be robust with respect to small perturbations in the data of the game. Confronted with the growing evidence to the detriment of the Nash concept, game theorists were prompted to search for more refined equilibrium notions with better properties and they have come up with a wide array of alternative solution concepts. This book surveys the most important refinements that have been introduced. Its objectives are fourfold (i) to illustrate desirable properties as well as drawbacks of the various equilibrium notions by means of simple specific examples, (ii) to study the relationships between the various refinements, (iii) to derive simplifying characterizations, and (iv) to discuss the plausibility of the assumptions underlying the concepts.
Book Synopsis The Existence of Pure-strategy Nash Equilibrium in Games with Payoffs that are Not Quasiconcave by : Michael R. Baye
Download or read book The Existence of Pure-strategy Nash Equilibrium in Games with Payoffs that are Not Quasiconcave written by Michael R. Baye and published by . This book was released on 1990 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nash Equilibrium in Discontinuous Games by : Philip Reny
Download or read book Nash Equilibrium in Discontinuous Games written by Philip Reny and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We provide several generalizations of the various equilibrium existence results in Reny (1999), Barelli and Meneghel (2013), and McLennan, Monteiro, and Tourky (2011). We also provide an example demonstrating that a natural additional generalization is not possible. All of the theorems yielding existence of pure strategy Nash equilibria here are stated in terms of the players' preference relations over joint strategies. Hence, in contrast to virtually all of the previous work in the area the present results for pure strategy equilibria are entirely ordinal, as they should be.
Book Synopsis Existence of Equilibria in Constrained Discontinuous Games by : Adib Bagh
Download or read book Existence of Equilibria in Constrained Discontinuous Games written by Adib Bagh and published by . This book was released on 2019 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: We establish the existence of pure strategy equilibria in games with discontinuous payoffs where the set of feasible actions of each player varies, also in a discontinuous fashion, as a function of the actions of the other players. Such games are used in modeling abstract economies and other games where players share common constraints. Our approach circumvents the difficulties that arise from the presence of discontinuities by modifying the original problem and allowing the players to use strategies that possibly lie outside their feasible sets. We then show that each modified game has "epsilon-equilibria points. Under certain conditions, and as the extent of modification becomes smaller and smaller and " approaches zero, the "epsilon-equilibria points of the modified games will converge to a strategy profile that is an equilibrium of the original game. Hence, we obtain a set of sufficient conditions for the existence of pure equilibria of the original game. We apply our results to a number of classic games that have discontinuous payoffs and discontinuous constraintcorrespondences.
Book Synopsis Symposium on Existence of Nash Equilibria in Discontinuous Games by : Guilherme Carmona
Download or read book Symposium on Existence of Nash Equilibria in Discontinuous Games written by Guilherme Carmona and published by . This book was released on 2011 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Existence of Equilibria in Incomplete Information Games with Disturbed Payoffs by : Brian John Crone
Download or read book Existence of Equilibria in Incomplete Information Games with Disturbed Payoffs written by Brian John Crone and published by . This book was released on 1990 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Existence of Equilibria in Cournotian Games with Utility Functions that are Discontinuous at the Origin by : Pierre von Mouche
Download or read book Existence of Equilibria in Cournotian Games with Utility Functions that are Discontinuous at the Origin written by Pierre von Mouche and published by . This book was released on 2014 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the Nash equilibrium existence problem for Cournotian games and we provide two results for it. The first is compatible with utility functions that are discontinuous at the origin, but requires the nonemptiness of best-replies at the origin (and in some sense is known); the second requires the discontinuity of utility functions at the origin and the emptiness of best-replies at the origin (and to the best of our knowledge is not known). Both results are proved by reducing the Nash equilibrium existence problem to a simple fixpoint existence problem for a real function defined on a real interval. The results are then applied to Cournot oligopolies and winner-take-all contest games; various examples illustrate the novelty of the results obtained.
