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Chinese Physics Letters

Quantum Games of Continuous Distributed Incomplete Information

Chen Xi, Gan Qin, Zhou Xian-Yi, Du Jiang-Feng

Published Apr 14, 2005• 18 citations
Publisher

Abstract

We study two-player quantum games of incomplete information in which both the sides have partial information. The previous results of Du et al. [Phys. Rev. E 68 (2003) 016124] are incorporated in our more general formalism. Because of different roles played by the total information uncertainty and the information asymmetry, the game exhibits many interesting features.

DOI
10.1088/0256-307x/22/5/002

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We study two-player quantum games of incomplete information in which both the sides have partial information. The previous results of Du et al. [Phys. Rev. E 68 (2003) 016124] are incorporated in our more general formalism. Because of different roles played by the total information uncertainty and the information asymmetry, the game exhibits many interesting features.
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We investigate quantum games in which the information is asymmetrically distributed among the players and find that the possibility of the quantum game outperforming its classical counterpart depends strongly on not only the entanglement but also the informational asymmetry. What is more interesting, when the information distribution is asymmetric, is that the contradictive impact of the quantum entanglement on the profits is observed, which is not reported in quantum games of symmetric information.
Quantum games with incomplete information can be studied within a Bayesian framework. We analyze games quantized within the EWL framework [Eisert, Wilkens, and Lewenstein, Phys Rev. Lett. 83, 3077 (1999)]. We solve for the Nash equilibria of a variety of two-player quantum games and compare the results to the solutions of the corresponding classical games. We then analyze Bayesian games where there is uncertainty about the player types in two-player conflicting interest games. The solutions to the Bayesian games are found to have a phase diagram-like structure where different equilibria exist in different parameter regions, depending both on the amount of uncertainty and the degree of entanglement. We find that in games where a Pareto-optimal solution is not a Nash equilibrium, it is possible for the quantized game to have an advantage over the classical version. In addition, we analyze the behavior of the solutions as the strategy choices approach an unrestricted operation. We find that some games have a continuum of solutions, bounded by the solutions of a simpler restricted game. A deeper understanding of Bayesian quantum game theory could lead to novel quantum applications in a multi-agent setting.
Quantum entanglement has been recently demonstrated as a useful resource in conflicting-interest games of incomplete information between two players, Alice and Bob [Pappa et al., Phys. Rev. Lett. 114, 020401 (2015)]. The general setting for such games is that of correlated strategies where the correlation between competing players is established through a trusted common adviser; however, players need not reveal their input to the adviser. So far, the quantum advantage in such games has been revealed in a restricted sense. Given a quantum correlated equilibrium strategy, one of the players can still receive a higher than quantum average payoff with some classically correlated equilibrium strategy. In this work, by considering a class of asymmetric Bayesian games, we show the existence of games with quantum correlated equilibrium where the average payoff of both the players exceeds the respective individual maximum for each player over all classically correlated equilibriums.