Chess-Like Games May Have No Uniform Nash Equilibria Even in Mixed Strategies. (22nd May 2013)

• Record Type: Journal Article
• Authors: Boros, Endre; Gurvich, Vladimir; Yamangil, Emre
• Other Names: Briec Walter Academic Editor.
• Is Part Of: Game theory. Volume 2013(2013)
• Publication Date: 2013-05-22
• Subjects: Game theory -- Periodicals; Game theory; Periodicals; 519.3
• DOI: 10.1155/2013/534875
• Languages: English
• ISSNs: 2314-6559

Abstract

Abstract : 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.