Quantum game theory and the complexity of approximating quantum Nash equilibria

John Bostanci1 and John Watrous2

1Computer Science Department, Columbia University
2Institute for Quantum Computing and School of Computer Science, University of Waterloo

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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.

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Cited by

[1] Wayne Lin, Georgios Piliouras, Ryann Sim, and Antonios Varvitsiotis, "Quantum Potential Games, Replicator Dynamics, and the Separability Problem", arXiv:2302.04789, (2023).

[2] Constantin Ickstadt, Thorsten Theobald, and Elias Tsigaridas, "Semidefinite games", arXiv:2202.12035, (2022).

[3] Rahul Jain, Georgios Piliouras, and Ryann Sim, "Matrix Multiplicative Weights Updates in Quantum Zero-Sum Games: Conservation Laws & Recurrence", arXiv:2211.01681, (2022).

[4] Rafael Frongillo, "Quantum Information Elicitation", arXiv:2203.07469, (2022).

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