2006/02/28 by Tsubasa Ichikawa, Izumi Tsutsui · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Duality (order theory) #Game theory #Hilbert space #Mathematical economics #Mathematics #Normal-form game #Physics #Pure mathematics #Quantization (signal processing) #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Qubit #Repeated game #Symmetric game #Theoretical physics #quant-ph
paper · pdf · doi:10.1016/j.aop.2006.05.001
published as Ann. Phys. 322 (2007) 531. · 12 pages, 14 figures
arxiv created 2006/05/17 · openalex publication_date 2006/06/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Symmetric quantum games for 2-player, 2-qubit strategies are analyzed in detail by using a scheme in which all pure states in the 2-qubit Hilbert space are utilized for strategies. We consider two different types of symmetric games exemplified by the familiar games, the Battle of the Sexes (BoS) and the Prisoners' Dilemma (PD). These two types of symmetric games are shown to be related by a duality map, which ensures that they share common phase structures with respect to the equilibria of the strategies. We find eight distinct phase structures possible for the symmetric games, which are determined by the classical payoff matrices from which the quantum games are defined. We also discuss the possibility of resolving the dilemmas in the classical BoS, PD and the Stag Hunt (SH) game based on the phase structures obtained in the quantum games. It is observed that quantization cannot resolve the dilemma fully for the BoS, while it generically can for the PD and SH if appropriate correlations for the strategies of the players are provided.