Full characterization of quantum correlated equilibria

Abstract

Quantum game theory aims to study interactions of people (or other agents) using quan- tum devices with possibly conflicting interests. Recently Zhang studied some quantita- tive questions in general quantum strategic games of growing sizes [19]. However, a fundamental question not addressed there is the characterization of quantum correlated equilibria (QCE). In this paper, we answer this question by giving a sufficient and nec- essary condition for an arbitrary state ρ being a QCE. In addition, when the condition fails to hold for some player i, we give an explicit positive-operator valued measurement (POVM) for that player to achieve a strictly positive gain of payoff. Finally, we give some upper bounds for the maximum gain by playing quantum strategies over classical ones, and the bounds are tight for some games. © Rinton Press.