Quantum game theory and decision optimization

Abstract

In this presentation, we consider Nash equilibria and correlated equilibria of classical and quantum games in the context of their Pareto efficiency. The examples of the prisoner’s dilemma, battle of the sexes and the game of chicken are studied. Correlated equilibria usually improve Nash equilibria of games but require a trusted correlation device susceptible to manipulation. The quantum extension of these games in the Eisert–Wilkens–Lewenstein formalism and the Frąckiewicz–Pykacz parameterization is analyzed. It is shown that the Nash equilibria of these games in quantum mixed Pauli strategies are closer to Pareto optimal results than their classical counterparts. The relationship of mixed Pauli strategies equilibria and correlated equilibria is also studied [1]. We also consider the quantum version of the absentminded driver problem and show that through appropriately chosen initial quantum state, the unitary strategies enable the decision maker to obtain the maximum possible payoff [2].

References

[1] Szopa M.: Efficiency of Classical and Quantum Games Equilibria. Entropy 2021, 23, 506, https://doi.org/10.3390/e23050506

[2] Frąckiewicz P., Rycerz K., and Szopa M.: Quantum absentminded driver problem revisited. Quantum Information Processing (2022) 21:34, https://doi.org/10.1007/s11128-021-03377-6 .

Bio: Marek Szopa is a professor of physical sciences, graduate of the University of Silesia. Szopa is currently working in quantum game theory and its application to negotiations and decision making.