A New Sequence Form Approach for the Enumeration and Refinement of All Extreme Nash Equilibria for Extensive Form Games PDF Download
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Author: Charles Audet
Publisher:
ISBN:
Category :
Languages : en
Pages : 15
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Author: Charles Audet
Publisher:
ISBN:
Category :
Languages : en
Pages : 15
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Book Description
Author: Audet, Charles
Publisher: Montréal : Groupe d'études et de recherche en analyse des décisions
ISBN:
Category :
Languages : en
Pages : 14
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Book Description
Author: Eric van Damme
Publisher: Springer
ISBN:
Category : Equilibrium (Economics).
Languages : en
Pages : 164
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Book Description
Author: John H. Aldrich
Publisher: University of Michigan Press
ISBN: 9780472069866
Category : Political Science
Languages : en
Pages : 516
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Book Description
Richard McKelvey's classic papers, accompanied by original essays by leading names in the field
Author: Tamer Basar
Publisher: SIAM
ISBN: 9781611971132
Category : Mathematics
Languages : en
Pages : 534
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Book Description
Recent interest in biological games and mathematical finance make this classic 1982 text a necessity once again. Unlike other books in the field, this text provides an overview of the analysis of dynamic/differential zero-sum and nonzero-sum games and simultaneously stresses the role of different information patterns. The first edition was fully revised in 1995, adding new topics such as randomized strategies, finite games with integrated decisions, and refinements of Nash equilibrium. Readers can now look forward to even more recent results in this unabridged, revised SIAM Classics edition. Topics covered include static and dynamic noncooperative game theory, with an emphasis on the interplay between dynamic information patterns and structural properties of several different types of equilibria; Nash and Stackelberg solution concepts; multi-act games; Braess paradox; differential games; the relationship between the existence of solutions of Riccati equations and the existence of Nash equilibrium solutions; and infinite-horizon differential games.
Author: Guilherme Carmona
Publisher: World Scientific
ISBN: 9814390666
Category : Business & Economics
Languages : en
Pages : 153
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Book Description
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.
Author: Noah Daniel Stein
Publisher:
ISBN:
Category :
Languages : en
Pages : 191
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Book Description
The main contribution of this thesis is a new solution concept for symmetric games (of complete information in strategic form), the exchangeable equilibrium. This is an intermediate notion between symmetric Nash and symmetric correlated equilibrium. While a variety of weaker solution concepts than correlated equilibrium and a variety of refinements of Nash equilibrium are known, there is little previous work on "interpolating" between Nash and correlated equilibrium. Several game-theoretic interpretations suggest that exchangeable equilibria are natural objects to study. Moreover, these show that the notion of symmetric correlated equilibrium is too weak and exchangeable equilibrium is a more natural analog of correlated equilibrium for symmetric games. The geometric properties of exchangeable equilibria are a mix of those of Nash and correlated equilibria. The set of exchangeable equilibria is convex, compact, and semi-algebraic, but not necessarily a polytope. A variety of examples illustrate how it relates to the Nash and correlated equilibria. The same ideas which lead to the notion of exchangeable equilibria can be used to construct tighter convex relaxations of the symmetric Nash equilibria as well as convex relaxations of the set of all Nash equilibria in asymmetric games. These have similar mathematical properties to the exchangeable equilibria. An example game reveals an algebraic obstruction to computing exact exchangeable equilibria, but these can be approximated to any degree of accuracy in polynomial time. On the other hand, optimizing a linear function over the exchangeable equilibria is NP-hard. There are practical linear and semidefinite programming heuristics for both problems. A secondary contribution of this thesis is the computation of extreme points of the set of correlated equilibria in a simple family of games. These examples illustrate that in finite games there can be factorially many more extreme correlated equilibria than extreme Nash equilibria, so enumerating extreme correlated equilibria is not an effective method for enumerating extreme Nash equilibria. In the case of games with a continuum of strategies and polynomial utilities, the examples illustrate that while the set of Nash equilibria has a known finite-dimensional description in terms of moments, the set of correlated equilibria admits no such finite-dimensional characterization.
Author: Charles Audet
Publisher:
ISBN:
Category :
Languages : en
Pages : 18
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Book Description
Author: Drew Fudenberg
Publisher:
ISBN:
Category :
Languages : en
Pages : 57
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Book Description
Author: Nicola Gatti
Publisher:
ISBN:
Category :
Languages : en
Pages : 38
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Book Description
Van Damme [1984] introduces the concept of quasi-perfect equilibrium, which re-fines sequential equilibrium as well as normal-form perfect equilibrium. It has been argued by Mertens [1995] that quasi-perfection is conceptually superior to extensive-form perfection, since quasi-perfection guarantees normal-form perfection, which for two-player games is equivalent to admissibility. On the other hand, while extensive-form perfect equilibria are defined as limit points of sequences of Nash equilibria of a general class of perturbed games in extensive form, till now, to the best of our knowledge, there is no characterization of quasi-perfect equilibria in terms of limit points of equilibria of perturbed games. The only known result is Lemma 1 by Miltersen and Sørensen [2010], showing that limit points of sequences of Nash equilibria of a particular class of perturbed games in sequence form are quasi-perfect equilibria of the original, unperturbed game in extensive form. However, as the authors point out, their main result only proves that a subset of the quasi-perfect equilibria can be obtained as limit points of equilibria of their class of perturbed games, and, thus, their paper provides no characterization of quasi-perfect equilibria in terms of perturbed games. The present paper fills this gap providing such characterization, showing that any quasi-perfect equilibrium can be obtained as limit point of a sequence of Nash equilibria of a certain class of perturbed games in sequence form, at least for the case of two-player games with nature. This result shows that the sequence form is not merely a computationally efficient representation, but it also captures game features that other forms are not able to effectively express.
