The equivalence of Bell's inequality and the Nash inequality in a quantum game-theoretic setting

Azhar Iqbal, James M. Chappell, Derek Abbott

Published 2015-07-27Version 1

Are there two-player games in which a strategy pair can exist as a Nash equilibrium only when the game is played quantum mechanically? To find an answer to this question, we study two-player games that are played in generalized Einstein-Podolsky-Rosen setting. Considering particular strategy pairs, we identify sets of games for which the pair can exist as a Nash equilibrium when Bell's inequality is violated. We thus identify games and players' strategies for which the Nash inequality becomes equivalent to Bell's inequality. As the violation of Bell's inequality is regarded as being quantum in nature, this paper thus addresses the earliest criticisms of quantum games that questioned if they were truly quantum.