Characterizing the Nash equilibria of a three-player Bayesian quantum game

Characterizing the Nash equilibria of a three-player Bayesian quantum game Quantum games with incomplete information can be studied within a Bayesian framework. We consider a version of prisoner’s dilemma (PD) in this framework with three players and characterize the Nash equilibria. A variation of the standard PD game is set up with two types of the second prisoner and the first prisoner plays with them with probability p and $$1-p$$ 1 - p , respectively. The Bayesian nature of the game manifests in the uncertainty that the first prisoner faces about his opponent’s type which is encoded either in a classical probability or in the amplitudes of a wave function. Here, we consider scenarios with asymmetric payoffs between the first and second prisoner for different values of the probability, p, and the entanglement. Our results indicate a class of Nash equilibria (NE) with rich structures, characterized by a phase relationship on the strategies of the players. The rich structure can be exploited by the referee to set up rules of the game to push the players toward a specific class of NE. These results provide a deeper insight into the quantum advantages of Bayesian games over their classical counterpart. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Characterizing the Nash equilibria of a three-player Bayesian quantum game

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media New York (outside the USA)
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-017-1593-z
Publisher site
See Article on Publisher Site

Abstract

Quantum games with incomplete information can be studied within a Bayesian framework. We consider a version of prisoner’s dilemma (PD) in this framework with three players and characterize the Nash equilibria. A variation of the standard PD game is set up with two types of the second prisoner and the first prisoner plays with them with probability p and $$1-p$$ 1 - p , respectively. The Bayesian nature of the game manifests in the uncertainty that the first prisoner faces about his opponent’s type which is encoded either in a classical probability or in the amplitudes of a wave function. Here, we consider scenarios with asymmetric payoffs between the first and second prisoner for different values of the probability, p, and the entanglement. Our results indicate a class of Nash equilibria (NE) with rich structures, characterized by a phase relationship on the strategies of the players. The rich structure can be exploited by the referee to set up rules of the game to push the players toward a specific class of NE. These results provide a deeper insight into the quantum advantages of Bayesian games over their classical counterpart.

Journal

Quantum Information ProcessingSpringer Journals

Published: Apr 21, 2017

References

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