Perfect and Proper Refinements of All Extreme Nash Equilibria for Bimatrix Games PDF Download
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Author: Charles Audet
Publisher:
ISBN:
Category :
Languages : en
Pages : 18
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Author: Charles Audet
Publisher:
ISBN:
Category :
Languages : en
Pages : 18
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Author: E. van Damme
Publisher: Springer Science & Business Media
ISBN: 3642499708
Category : Business & Economics
Languages : en
Pages : 161
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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.
Author: Eric van Damme
Publisher: Springer Science & Business Media
ISBN: 3642582427
Category : Mathematics
Languages : en
Pages : 354
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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.
Author: Slim Belhaiza
Publisher:
ISBN:
Category :
Languages : en
Pages : 11
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Author: Charles Audet
Publisher:
ISBN:
Category :
Languages : en
Pages : 15
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Author: Burkhard Monien
Publisher: Springer Science & Business Media
ISBN: 3540793089
Category : Computers
Languages : en
Pages : 371
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This book constitutes the refereed proceedings of the First International Symposium on Algorithmic Game Theory, SAGT 2008, held in Paderborn, Germany, in April/May 2008. The 28 revised full papes presented together with 3 invited lectures were carefully reviewed and selected from 60 submissions. The papers are organized in topical sections on routing and scheduling, markets, mechanism design, potpourri of games, solution concepts, and cost sharing.
Author:
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Category :
Languages : en
Pages :
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Author:
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ISBN:
Category :
Languages : en
Pages : 11
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Author: Julian Merschen
Publisher:
ISBN:
Category :
Languages : en
Pages :
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This thesis concerns the problem 2-NASH of finding a Nash equilibrium of a bimatrix game, for the special class of so-called "hard-to-solve" bimatrix games. The term "hardto-solve" relates to the exponential running time of the famous and often used Lemke- Howson algorithm for this class of games. The games are constructed with the help of dual cyclic polytopes, where the algorithm can be expressed combinatorially via labeled bitstrings defined by the "Gale evenness condition" that characterise the vertices of these polytopes. We define the combinatorial problem "Another completely labeled Gale string" whose solutions define the Nash equilibria of any game defined by cyclic polytopes, including the games where the Lemke-Howson algorithm takes exponential time. We show that "Another completely labeled Gale string" is solvable in polynomial time by a reduction to the "Perfect matching" problem in Euler graphs. We adapt the Lemke-Howson algorithm to pivot from one perfect matching to another and show that again for a certain class of graphs this leads to exponential behaviour. Furthermore, we prove that completely labeled Gale strings and perfect matchings in Euler graphs come in pairs and that the Lemke-Howson algorithm connects two strings or matchings of opposite signs. The equivalence between Nash Equilibria of bimatrix games derived from cyclic polytopes, completely labeled Gale strings, and perfect matchings in Euler Graphs implies that counting Nash equilibria is #P-complete. Although one Nash equilibrium can be computed in polynomial time, we have not succeeded in finding an algorithm that computes a Nash equilibrium of opposite sign. However, we solve this problem for certain special cases, for example planar graphs. We illustrate the difficulties concerning a general polynomial-time algorithm for this problem by means of negative results that demonstrate why a number of approaches towards such an algorithm are unlikely to be successful.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 464
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