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Author: Jungwook Kim (Economist)
Publisher:
ISBN:
Category :
Languages : en
Pages : 106
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Book Description
Author: Jungwook Kim (Economist)
Publisher:
ISBN:
Category :
Languages : en
Pages : 106
Get Book Here
Book Description
Author: Ziwei Wang
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
The study of game theory has advanced our understanding of strategic interactions and economic behaviors. In applications, we economists often use parsimonious game-theoretic models to help us make sharp predictions. However, these models are associated with strong, sometimes unwarranted, common knowledge assumptions about players' payoffs and information. In order to make our predictions realistic and reliable, we need to embed these models into larger and more comprehensive ones, and then perform analysis that are robust to the relaxation of common knowledge assumptions. This dissertation contains three chapters that study various game-theoretic frameworks with incomplete information and investigate the implications of weakened assumptions. The first chapter proposes a new notion of stability to study matching markets with one-sided incomplete information. A key contribution is to formulate a proper definition of uninformed agents' endogenous beliefs and a self-consistency condition on those beliefs. We define a criterion of stability for a given set of outcomes, and then iteratively apply this criterion to remove outcomes that cannot be deemed stable. Our solution concept, the set of rationalizable stable outcomes, is the limit of this procedure. We prove the existence of rationalizable stable outcomes using a fixed-point characterization. We then provide two additional characterizations of our solution concept. The first characterization links the non-equilibrium approach we pursue to the equilibrium approach pioneered by Liu (2020). The second one reveals the epistemic assumptions implicit in the iterative definition. In the second chapter, we study standard auctions and compare their minimum expected revenues across all information structures. We show that, for a given symmetric common prior of values among bidders, if the seller is uncertain about the correct model of bidders' interim beliefs and evaluates her expected revenue by the worst-case scenario, the all-pay auction performs weakly worse than does the first-price auction. Specifically, we first provide a revenue equivalence result of standard auction formats under the "worst-case" information structure constructed in Bergemann et al. (2017a), which implies that the minimum expected revenue of the all-pay auction never exceeds that of a first-price auction. We then construct an example to illustrate that the all-pay auction can generate strictly lower expected revenue in some cases. The third chapter studies predictions that are robust against higher order payoff uncertainty in dynamic games. Common knowledge among players is captured by a preference-information structure, while a type space is used as a concise model of players' initial beliefs. We formulate an interim version of extensive form rationalizability (EFR) and use this solution concept as the starting point of our robustness analysis. Employing a collection-based approach, we provide conditions that fully characterize (i) what refinements of EFR are robust, (ii) when a Structure Theorem (Weinstein and Yildiz, 2007) of EFR holds, and (iii) when the prediction of EFR is generically unique. We then apply these results to study robust refinements of EFR when there is higher order uncertainty about privacy of information or about observability of actions. These applications demonstrate the power of our results and generate interesting observations in dynamic environments.
Author: Idione Meneghel
Publisher:
ISBN:
Category : Game theory
Languages : en
Pages : 35
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"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.
Author: Robert J. Aumann
Publisher: MIT Press
ISBN: 9780262011471
Category : Business & Economics
Languages : en
Pages : 372
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The basic model studied throughout the book is one in which players ignorant about the game being played must learn what they can from the actions of the others.
Author: George R. Feiwel
Publisher: SUNY Press
ISBN: 9780873959421
Category : Business & Economics
Languages : en
Pages : 512
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This important book and its companion volume, Issues in Contemporary Microeconomics and Welfare, capture and convey the spirit, fundamental issues, underlying tensions, rich variety, accomplishments, and failures in contemporary economics. It presents economics as a dynamic subject, showing its strengths and limitations, exploring alternative approaches, and tracing the sources of differences. The essays include original contributions by the theorists themselves; major interpretations, reflections, and assessments by leading economists, and evaluations of particular areas by rising young scholars.
Author: The late John F. Nash
Publisher: Edward Elgar Publishing
ISBN: 9781781956298
Category : Business & Economics
Languages : en
Pages : 116
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Book Description
'This short volume is very welcome . . . Most importantly, on pages 32-33, the volume reprints as an appendix to the journal article based on Nash's Princeton doctoral dissertation on non-cooperative games a section of the thesis on "motivation and interpretation" that was omitted from the article. An editorial note remarks mildly that "The missing section is of considerable interest". This section, not available in any other published source, makes the present volume indispensable for research libraries . . . Nash's Essays on Game Theory, dating from his years as a Princeton graduate student . . . has a lasting impact on economics and related fields unmatched by any series of articles written in such a brief time . . . To economists, his name will always bring to mind his game theory papers of the early 1950s. It is good to have these conveniently reprinted in this volume.' - Robert W. Dimand, The Economic Journal 'The news that John Nash was to share the 1994 Nobel Prize for Economics with John Harsanyi and Reinhard Selten was doubly welcome. It signalled not only that the brilliant achievements of his youth were to be recognized in a manner consistent with their significance, but that the long illness that clouded his later years had fallen into remission. I hope that this collection of his economic papers will serve as another reminder that John Nash has rejoined the intellectual community to which he has contributed so much.' - From the introduction by Ken Binmore Essays on Game Theory is a unique collection of seven of John Nash's essays which highlight his pioneering contribution to game theory in economics. Featuring a comprehensive introduction by Ken Binmore which explains and summarizes John Nash's achievements in the field of non-cooperative and cooperative game theory, this book will be an indispensable reference for scholars and will be welcomed by those with an interest in game theory and its applications to the social sciences.
Author: Nimrod Megiddo
Publisher: Springer Science & Business Media
ISBN: 1461226481
Category : Mathematics
Languages : en
Pages : 209
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Book Description
This volume presents a collection of papers on game theory dedicated to Michael Maschler. Through his dedication and contributions to game theory, Maschler has become an important figure particularly in the area of cooperative games. Game theory has since become an important subject in operations research, economics and management science. As befits such a volume, the main themes covered are cooperative games, coalitions, repeated games, and a cost allocation games. All the contributions are authoritative surveys of a particular topic, so together they will present an invaluable overview of the field to all those working on game theory problems.
Author: Lucas Pahl
Publisher:
ISBN:
Category : Game theory
Languages : en
Pages : 120
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"This thesis consists of two essays on game theory. Chapter 1 considers an infinitely repeated three-player Bayesian game with lack of information on two sides, in which an informed player plays two zero-sum games simultaneously at each stage against two uninformed players. This is a generalization of Aumann, Maschler, and Stearns (1995) two-player zero-sum one-sided, incomplete information model. Under a correlated prior, the informed player faces the problem of how to optimally disclose information among two uninformed players in order to maximize his long term average payoffs. The objective is to understand the adverse effects of "information spillover" from one game to the other in the equilibrium payoff set of the informed player. We provide conditions under which the informed player can fully overcome such adverse effects, and show that in some cases the adverse effects are unsurmountable and severe. Chapter 2 develops a theory of index of equilibria for a more general class of games than finite normal-form games and presents an application to extensive-form games. Whenever equivalent mixed strategies of a player are identified (topologically) in a normal-form game, the resulting space may not be a simplex anymore but is a general polytope. We show that an index/degree theory of equilibria can be developed in full generality for games in which the strategy sets of the players are general polytopes and their payoff functions are multiaffine. Index and degree theories work as a tool that helps identify equilibria that are robust to payoff perturbations of the game. Because the strategy set of each player is the result of the identification of equivalent mixed strategies, the resulting polytope is of lower dimension than the original mixed strategy simplices. This, together with an index theory, has algorithmic applications for checking for the robustness of equilibria as well as finding equilibria in extensive-form games"--Pages viii-ix.
Author: Juan Escobar
Publisher:
ISBN:
Category :
Languages : en
Pages : 130
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Author: Reinhard Selten (Economist, Germany)
Publisher: Edward Elgar Publishing
ISBN: 9781781008294
Category :
Languages : en
Pages : 924
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Book Description
'These two volumes constitute an impressive collection of selected path-breaking works of Professor Selten. . . . Edward Elgar Publications deserve merit for bringing out most frequently-cited and prominent articles of Professor Selten in a conveniently available package.' - K. Ravikumar, Journal of Scientific and Industrial Research In 1994, the Nobel Prize was awarded to Reinhard Selten, John Nash and John Harsanyi, for pioneering analysis in game theory. Selten was the first to refine the Nash equilibrium concept of non-cooperative games for analysing dynamic strategic interaction and to apply these concepts to analyses of oligopoly.
