Duality, Phase Structures and Dilemmas in Symmetric Quantum Games

Abstract

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.

12 pages, 14 figures

References in corpus (12)

• Quantum Games and Quantum Strategies
• Experimental realization of quantum games on a quantum computer
• A Quantum Approach To Static Games Of Complete Information
• Quantum Games
• Comment on `Quantum Games and Quantum Strategies'
• Advantage of a quantum player over a classical one in 2x2 quantum games
• Efficiency and formalism of quantum games
• Classical and Quantum Contents of Solvable Game Theory on Hilbert Space
• Dilemma and Quantum Battle of Sexes
• Generalized Quantization Scheme for Two-Person Non-Zero-Sum Games
• Comment on: "A quantum approach to static games of complete information''
• Reply to "Comment on: A Quantum Approach to Static Games of Complete Information"

Cited by in corpus (17)

• Quantum Game Theory Based on the Schmidt Decomposition
• Uniqueness of Nash equilibria in quantum Cournot duopoly game
• Quantum Stackelberg duopoly in the presence of correlated noise
• Constructing quantum games from a system of Bell's inequalities
• N-player quantum games in an EPR setting
• An Analysis of the Quantum Penny Flip Game using Geometric Algebra
• Quantum Matching Pennies Game
• Analyzing three-player quantum games in an EPR type setup
• Constructing quantum games from symmetric non-factorizable joint probabilities
• Analysis of two-player quantum games in an EPR setting using geometric algebra
• Quantum Stackelberg duopoly in noninertial frame
• Non-factorizable Joint Probabilities and Evolutionarily Stable Strategies in the Quantum Prisoner's Dilemma Game
• General quantum two-players games, their gate operators and Nash equilibria
• Note on maximally entangled Eisert-Lewenstein-Wilkens quantum games
• Quantization of Blackjack: Quantum Basic Strategy and Advantage
• Quantum Cournot model based on general entanglement operator
• On the equivalence between non-factorizable mixed-strategy classical games and quantum games