Quantum game theory and the complexity of approximating quantum Nash equilibria

TL;DR

This paper explores the computational complexity of finding approximate Nash equilibria in quantum games, establishing that the problem is PPAD-complete, similar to classical game theory, and extends existing methods to quantum strategy spaces.

Contribution

It proves that computing approximate Nash equilibria in quantum games is PPAD-complete and develops new techniques for strategy spaces defined by semidefinite programs.

Findings

Quantum Nash equilibrium computation is PPAD-complete.

Extended computational methods to quantum strategy spaces.

Bridged classical and quantum game theory complexity.

Abstract

This paper is concerned with complexity theoretic aspects of a general formulation of quantum game theory that models strategic interactions among rational agents that process and exchange quantum information. In particular, we prove that the computational problem of finding an approximate Nash equilibrium in a broad class of quantum games is, like the analogous problem for classical games, included in (and therefore complete for) the complexity class PPAD. Our main technical contribution, which facilitates this inclusion, is an extension of prior methods in computational game theory to strategy spaces that are characterized by semidefinite programs.