Quantum two-players games, Entanglement and Nash equilibria

2014/02/17 by Katarzyna Bolonek-Lasoń, Bolonek-Lasoń, Katarzyna
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.1402.3932

openalex publication_date 2014/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The two-players N strategies games quantized according to the Eisert-Lewenstein-Wilkens scheme [1] are considered. It is shown that in the case of maximal entanglement no nontrivial pure Nash equilibrium exists. The proof relies on simple geometric properties of "chiral" group SU (N)× SU(N) and is based on considering the stability subgroup of the initial state of the game. The explicit forms of neither the gate operator nor the payoff matrix are necessary.

Citations

• The Generalized Quantization Schemes for Games and its Application to Quantum Information
• Werner-like States and Strategic Form of Quantum Games

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