Quantum Inf Process (2016) 15:4337–4346
Bayesian Nash equilibria using extended Werner-like
· M. E. Soto
Received: 30 October 2015 / Accepted: 2 July 2016 / Published online: 11 July 2016
© Springer Science+Business Media New York 2016
Abstract We study quantum strategies in games of incomplete information using a
formalism of game theory based on multi-sector probability matrix. We analyze an
extension of the well-known game of Battle of Sexes using an extended Werner-like
state focusing in how its mixedness and entanglement affect the Bayesian Nash payoffs
of the player. It is shown that entanglement is needed to outperform classical payoffs
but not all entangled states are useful due to the presence of mixedness. A threshold
for the mixedness parameter and the minimum entanglement value were found.
Keywords Quantum games · Bayesian Nash equilibria · Extended Werner-like states
The study of games has inspired the development of mathematical theories and models.
One of these is game theory, developed by John Von Neumann and Oskar Morgenstern
. Its objective is not the analysis of the hazard or randomness but the strategic
behavior of players, i.e., to tell us what strategies rational players will follow and
what expectations they can rationally entertain about other rational player’s strategies.
Game theory has reached a high level of mathematical sophistication and has shown a
great versatility in solving many economical, social and evolutive problems, becoming
the universal language for the uniﬁcation of the behavioral sciences.
This work was supported by FONDECyT No. 3130443.
Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción, Chile
Departamento de Física, Universidad del Bío-Bío, Casilla 5-C, Concepción, Chile