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Existence and Stability of Nash Equilibrium

Existence and Stability of Nash Equilibrium
Author: Guilherme Carmona
Publisher: World Scientific
Total Pages: 153
Release: 2013
Genre: Business & Economics
ISBN: 9814390658

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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.


Stability and Perfection of Nash Equilibria

Stability and Perfection of Nash Equilibria
Author: Eric van Damme
Publisher: Springer Science & Business Media
Total Pages: 354
Release: 2012-12-06
Genre: Mathematics
ISBN: 3642582427

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I have been pleased with the favourable reception of the first edition of this book and I am grateful to have the opportunity to prepare this second edition. In this revised and enlarged edition I corrected some misprints and errors that occurred in the first edition (fortunately I didn't find too many) and I added a large number of notes that give the reader an impression of what kind of results have been obtained since the first edition was printed and that give an indication of the direction the subject is taking. Many of the notes discuss (or refer to papers discussing) applications of the refinements that are considered. Of course, it is the quantity and the quality of the insights and the applications that lend the refinements their validity. Although the guide to the applications is far from complete, the notes certainly allow the reader to form a good judgement of which refinements have really yielded new insights. Hence, as in the first edition, I will refrain from speculating on which refinements of Nash equilibria will survive in the long run. To defend this position let me also cite Binmore [1990] who compares writing about refinements to the Herculean task of defeating the nine-headed Hydra which grew too heads for each that was struck off. It is a pleasure to have the opportunity to thank my secretary, Marjoleine de Wit, who skilfully and, as always, cheerfully typed the manuscript and did the proofreading.


Game Theory, Alive

Game Theory, Alive
Author: Anna R. Karlin
Publisher: American Mathematical Soc.
Total Pages: 400
Release: 2017-04-27
Genre: Mathematics
ISBN: 1470419823

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We live in a highly connected world with multiple self-interested agents interacting and myriad opportunities for conflict and cooperation. The goal of game theory is to understand these opportunities. This book presents a rigorous introduction to the mathematics of game theory without losing sight of the joy of the subject. This is done by focusing on theoretical highlights (e.g., at least six Nobel Prize winning results are developed from scratch) and by presenting exciting connections of game theory to other fields such as computer science (algorithmic game theory), economics (auctions and matching markets), social choice (voting theory), biology (signaling and evolutionary stability), and learning theory. Both classical topics, such as zero-sum games, and modern topics, such as sponsored search auctions, are covered. Along the way, beautiful mathematical tools used in game theory are introduced, including convexity, fixed-point theorems, and probabilistic arguments. The book is appropriate for a first course in game theory at either the undergraduate or graduate level, whether in mathematics, economics, computer science, or statistics. The importance of game-theoretic thinking transcends the academic setting—for every action we take, we must consider not only its direct effects, but also how it influences the incentives of others.


Algorithms - ESA 2007

Algorithms - ESA 2007
Author: Lars Arge
Publisher: Springer
Total Pages: 782
Release: 2007-09-17
Genre: Computers
ISBN: 3540755209

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This book constitutes the refereed proceedings of the 15th Annual European Symposium on Algorithms, ESA 2007, held in Eilat, Israel, in October 2007 in the context of the combined conference ALGO 2007. The 63 revised full papers presented together with abstracts of three invited lectures address all current subjects in algorithmics reaching from design and analysis issues of algorithms over to real-world applications and engineering of algorithms in various fields.


Twenty Lectures on Algorithmic Game Theory

Twenty Lectures on Algorithmic Game Theory
Author: Tim Roughgarden
Publisher: Cambridge University Press
Total Pages: 356
Release: 2016-08-30
Genre: Computers
ISBN: 1316781178

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Computer science and economics have engaged in a lively interaction over the past fifteen years, resulting in the new field of algorithmic game theory. Many problems that are central to modern computer science, ranging from resource allocation in large networks to online advertising, involve interactions between multiple self-interested parties. Economics and game theory offer a host of useful models and definitions to reason about such problems. The flow of ideas also travels in the other direction, and concepts from computer science are increasingly important in economics. This book grew out of the author's Stanford University course on algorithmic game theory, and aims to give students and other newcomers a quick and accessible introduction to many of the most important concepts in the field. The book also includes case studies on online advertising, wireless spectrum auctions, kidney exchange, and network management.


Pareto Optimality, Game Theory and Equilibria

Pareto Optimality, Game Theory and Equilibria
Author: Panos M. Pardalos
Publisher: Springer Science & Business Media
Total Pages: 872
Release: 2008-07-02
Genre: Mathematics
ISBN: 0387772472

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This comprehensive work examines important recent developments and modern applications in the fields of optimization, control, game theory and equilibrium programming. In particular, the concepts of equilibrium and optimality are of immense practical importance affecting decision-making problems regarding policy and strategies, and in understanding and predicting systems in different application domains, ranging from economics and engineering to military applications. The book consists of 29 survey chapters written by distinguished researchers in the above areas.


On the Existence of Pure Strategy Nash Equilibria in Two Person Discrete Games

On the Existence of Pure Strategy Nash Equilibria in Two Person Discrete Games
Author: Indrajit Mallick
Publisher:
Total Pages: 0
Release: 2011
Genre:
ISBN:

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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.