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Proceedings Paper

Characterizing the Nash equilibria of three-player Bayesian quantum games
Author(s): Neal Solmeyer; Radhakrishnan Balu
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Paper Abstract

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.

Paper Details

Date Published: 5 May 2017
PDF: 12 pages
Proc. SPIE 10212, Advanced Photon Counting Techniques XI, 102120T (5 May 2017); doi: 10.1117/12.2262518
Show Author Affiliations
Neal Solmeyer, U.S. Army Research Lab. (United States)
Radhakrishnan Balu, U.S. Army Research Lab. (United States)

Published in SPIE Proceedings Vol. 10212:
Advanced Photon Counting Techniques XI
Mark A. Itzler; Joe C. Campbell, Editor(s)

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