An extension of quantal response equilibrium and determination of perfect equilibrium

Abstract As a strict refinement of Nash equilibrium, the concept of perfect equilibrium was formulated and extensively studied in the literature. To determine perfect equilibrium, this paper extends the logistic version of quantal response equilibrium (logit QRE) to a perturbed game. As a result of this extension, a smooth path is constructed for determining perfect equilibrium. The path starts from an arbitrary totally mixed strategy profile and leads to a perfect equilibrium. Numerical examples show that the extended QRE is comparable with the logit QRE and further confirm the effectiveness of the path.

[1]  B. O'Neill.  Nonmetric test of the minimax theory of two-person zerosum games. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[2]  Tilman Klumpp,et al.  Perfect equilibrium and lexicographic beliefs , 2003, Int. J. Game Theory.

[3]  Bernhard von Stengel,et al.  Computing Normal Form Perfect Equilibria for Extensive Two-Person Games , 2002 .

[4]  E. Damme.  Stability and perfection of Nash equilibria , 1987 .

[5]  Stuart D. McDonald,et al.  The Computation of Perfect and Proper Equilibrium for Finite Games via Simulated Annealing , 2010 .

[6]  R. Myerson.  Refinements of the Nash equilibrium concept , 1978 .

[7]  John C. Harsanyi,et al.  Общая теория выбора равновесия в играх / A General Theory of Equilibrium Selection in Games , 1989 .

[8]  R. Selten.  Reexamination of the perfectness concept for equilibrium points in extensive games , 1975, Classics in Game Theory.

[9]  Jean-François Mertens.  Stable Equilibria - A Reformulation: Part I. Definition and Basic Properties , 1989, Math. Oper. Res..

[10]  Kristoffer Arnsfelt Hansen,et al.  The Computational Complexity of Trembling Hand Perfection and Other Equilibrium Refinements , 2010, SAGT.

[11]  A.J.J. Talman,et al.  An algorithmic approach towards the tracing procedure of Harsanyi and Selten , 1995 .

[12]  R. McKelvey,et al.  Quantal Response Equilibria for Normal Form Games , 1995 .

[13]  Bernhardt Lieberman,et al.  Human behavior in a strictly determined 3 × 3 matrix game , 2007 .

[14]  Yoshitsugu Yamamoto,et al.  A path-following procedure to find a proper equilibrium of finite games , 1993 .

[15]  Dolf Talman,et al.  An Algorithmic Approach toward the Tracing Procedure for Bi-matrix Games , 1999 .