Table of Contents
Game Theory
Volume 2013, Article ID 534875, 10 pages
Research Article

Chess-Like Games May Have No Uniform Nash Equilibria Even in Mixed Strategies

RUTCOR, Rutgers University, 640 Bartholomew Road, Piscataway, NJ 08854-8003, USA

Received 2 February 2013; Accepted 22 April 2013

Academic Editor: Walter Briec

Copyright © 2013 Endre Boros et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Recently, it was shown that Chess-like games may have no uniform (subgame perfect) Nash equilibria in pure positional strategies. Moreover, Nash equilibria may fail to exist already in two-person games in which all infinite plays are equivalent and ranked as the worst outcome by both players. In this paper, we extend this negative result further, providing examples that are uniform Nash equilibria free, even in mixed or independently mixed strategies. Additionally, in case of independently mixed strategies we consider two different definitions for effective payoff: the Markovian and the a priori realization.