Duality, phase structures, and dilemmas in symmetric quantum games

Journal Article · Thu Mar 15 00:00:00 EDT 2007 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2006.05.001· OSTI ID:20976734

Ichikawa, Tsubasa ^[1]; Tsutsui, Izumi ^[1]

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1. High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801 (Japan)

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.

• OSTI ID: 20976734
• Journal Information: Annals of Physics (New York), Vol. 322, Issue 3; Other Information: DOI: 10.1016/j.aop.2006.05.001; PII: S0003-4916(06)00110-2; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DUALITY
GAME THEORY
HILBERT SPACE
MATRICES
QUANTIZATION
QUANTUM ENTANGLEMENT
QUANTUM MECHANICS
QUBITS