Mixed-strategy Nash equilibrium for a discontinuous symmetric N -player game - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2018

Mixed-strategy Nash equilibrium for a discontinuous symmetric N -player game

Résumé

We consider a game in which each player must find a compromise between more daring strategies that carry a high risk for him to be eliminated, and more cautious ones that, however, reduce his final score. For two symmetric players this game was originally formulated in 1961 by Dresher, who modeled a duel between two opponents. The game has also been of interest in the description of athletic competitions. We extend here the two-player game to an arbitrary number N of symmetric players. We show that there is a mixed-strategy Nash equilibrium and find its exact analytic expression, which we analyze in particular in the limit of large N, where mean-field behavior occurs. The original game with N  =  2 arises as a singular limit of the general case.

Dates et versions

hal-02138332 , version 1 (23-05-2019)

Identifiants

Citer

Hendrik-Jan Hilhorst, Cécile Appert-Rolland. Mixed-strategy Nash equilibrium for a discontinuous symmetric N -player game. Journal of Physics A: Mathematical and Theoretical, 2018, 51 (9), pp.095001. ⟨10.1088/1751-8121/aaa883⟩. ⟨hal-02138332⟩
25 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More