Full characterization of quantum correlated equilibria (pp0846-0860)
          Zhaohui Wei and Shengyu Zhang
          doi: https://doi.org/10.26421/QIC13.9-10-7
Abstracts: Quantum game theory aims to study interactions of people (or other agents) using quantum devices with possibly conflicting interests. Recently Zhang studied some quantitative 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 necessary 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.
Key words: game theory, quantum correlated equilibria, maximum gain