Full characterization of quantum correlated equilibria

Authors:
Zhaohui Wei;Shengyu Zhang
Affiliations:
Center for Quantum Technologies, National University of Singapore, Singapore;Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong
Venue:
Quantum Information & Computation
Year:
2013

Citing 5
Cited 0

Semidefinite programming

SIAM Review
Quantum computation and quantum information

Quantum computation and quantum information
Settling the complexity of computing two-player Nash equilibria

Journal of the ACM (JACM)
The Complexity of Computing a Nash Equilibrium

SIAM Journal on Computing
Quantum strategic game theory

Proceedings of the 3rd Innovations in Theoretical Computer Science Conference

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Abstract

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.