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The Existence Of Pure Strategy Nash Equilibrium In Games With Payoffs That Are Not Quasiconcave
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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 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 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 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 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 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.
Download or read book Game Theory written by Drew Fudenberg and published by MIT Press. This book was released on 1991-08-29 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced text introduces the principles of noncooperative game theory in a direct and uncomplicated style that will acquaint students with the broad spectrum of the field while highlighting and explaining what they need to know at any given point. This advanced text introduces the principles of noncooperative game theory—including strategic form games, Nash equilibria, subgame perfection, repeated games, and games of incomplete information—in a direct and uncomplicated style that will acquaint students with the broad spectrum of the field while highlighting and explaining what they need to know at any given point. The analytic material is accompanied by many applications, examples, and exercises. The theory of noncooperative games studies the behavior of agents in any situation where each agent's optimal choice may depend on a forecast of the opponents' choices. "Noncooperative" refers to choices that are based on the participant's perceived selfinterest. Although game theory has been applied to many fields, Fudenberg and Tirole focus on the kinds of game theory that have been most useful in the study of economic problems. They also include some applications to political science. The fourteen chapters are grouped in parts that cover static games of complete information, dynamic games of complete information, static games of incomplete information, dynamic games of incomplete information, and advanced topics.
Book Synopsis The Purification Problem for Constrained Games with Incomplete Information by : Helmut Meister
Download or read book The Purification Problem for Constrained Games with Incomplete Information written by Helmut Meister and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 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 On the Existence of Pure Strategy Nash Equilibria in Two Person Discrete Games by : Indrajit Mallick
Download or read book On the Existence of Pure Strategy Nash Equilibria in Two Person Discrete Games written by Indrajit Mallick and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We construct a generalized two-person discrete strategy static game of complete information where continuity, convexity and compactness cannot be invoked to show the existence of Pure Strategy Nash Equilibrium. We show that, when Best Responses are unique from both sides, a condition of Minimal Acyclicity is necessary and sufficient for the existence of Pure Strategy Nash Equilibria.
Book Synopsis Diagonal Payoff Security and Equilibrium Existence in Quasi-symmetric Discontinuous Games by : Christian Ewerhart
Download or read book Diagonal Payoff Security and Equilibrium Existence in Quasi-symmetric Discontinuous Games written by Christian Ewerhart and published by . This book was released on 2022 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Previous evidence shows that better insurance coverage increases medical expenditure. However, formal studies on the effect of spending on health outcomes, and especially mental health, are lacking. To fill this gap, we reanalyze data from the Rand Health Insurance Experiment and estimate a joint non-linear model of spending and mental health. We address the endogeneity of spending in a flexible copula regression model with Bernoulli and Tweedie margins and discuss its implementation in the freely available GJRM R package. Results confirm the importance of accounting for endogeneity: in the joint model, a $1000 spending in mental care is estimated to reduce the probability of low mental health by 1.3 percentage points, but this effect is not statistically significant. Ignoring endogeneity leads to a spurious (upwardly biased) estimate.Payoff security combined with reciprocal upper semicontinuity is sufficient for better-reply security, and consequently for the existence of a pure strategy Nash equilibrium in compact, quasiconcave games by Reny's (1999) theorem. Analogously, diagonal payoff security combined with upper semicontinuity of the diagonal payoff function has been widely understood to be sufficient for diagonal better-reply security, and consequently for the existence of a symmetric pure strategy Nash equilibrium in compact, diagonally quasiconcave, quasi-symmetric games. We show by example that this is incorrect. Specifically, diagonal better-reply security may fail to hold, and a symmetric pure strategy equilibrium may fail to exist, if some player's payoff function lacks lower semicontinuity, with respect to the opponents' symmetric strategy profile, at all strategy profiles reached from a non-equilibrium profile on the diagonal by a unilateral better response of that player. These difficulties disappear, both in the game and in its mixed extension, if the lower bound on a player's payoff in the definition of diagonal payoff security is raised to reflect the higher levels that arbitrary better responses may achieve. We also discuss the relationship between our strengthened condition and diagonal payoff security.
Book Synopsis Game Theoretic Problems in Network Economics and Mechanism Design Solutions by : Y. Narahari
Download or read book Game Theoretic Problems in Network Economics and Mechanism Design Solutions written by Y. Narahari and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph focuses on exploring game theoretic modeling and mechanism design for problem solving in Internet and network economics. For the first time, the main theoretical issues and applications of mechanism design are bound together in a single text.
Book Synopsis Foundations in Microeconomic Theory by : Matthew O. Jackson
Download or read book Foundations in Microeconomic Theory written by Matthew O. Jackson and published by Springer Science & Business Media. This book was released on 2008-11-30 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects papers from Hugo Sonnenschein's students. It aims to demonstrate his tremendous impact as an advisor. The papers span decades and present some of the most important articles in microeconomic theory. Each paper is accompanied with a preface by the student providing background on the paper and indicating Hugo's influence on its genesis. The papers all lie in microeconomic theory, and moreover all make fundamental contributions to the foundations of the theory.
Book Synopsis Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2013 Edition by :
Download or read book Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 1198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Mathematical Analysis. The editors have built Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Mathematical Analysis in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Book Synopsis Theory and Applications of Dynamic Games by : Elena Parilina
Download or read book Theory and Applications of Dynamic Games written by Elena Parilina and published by Springer Nature. This book was released on 2022-11-23 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a comprehensive overview of noncooperative and cooperative dynamic games involving uncertain parameter values, with the stochastic process being described by an event tree. Primarily intended for graduate students of economics, management science and engineering, the book is self-contained, as it defines and illustrates all relevant concepts originally introduced in static games before extending them to a dynamic framework. It subsequently addresses the sustainability of cooperative contracts over time and introduces a range of mechanisms to help avoid such agreements breaking down before reaching maturity. To illustrate the concepts discussed, the book provides various examples of how dynamic games played over event trees can be applied to environmental economics, management science, and engineering.
Book Synopsis On the Existence of Pure Strategy Nash Equilibria in Large Games by : Guilherme Carmona
Download or read book On the Existence of Pure Strategy Nash Equilibria in Large Games written by Guilherme Carmona and published by . This book was released on 2006 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider an asymptotic version of Mas-Colell's theorem on the existence of pure strategy Nash equilibria in large games. Our result states that, if players' payoff functions are selected from an equicontinuous family, then all sufficiently large games have an pure, equilibrium for all gt; 0. We also show that our result is equivalent to Mas-Colell's existence theorem, implying that it can properly be considered as its asymptotic version.
