Nonlocal correlations: Fair and Unfair Strategies in Bayesian Game

TL;DR

This paper demonstrates that quantum strategies can outperform both fair and unfair classical equilibrium strategies in Bayesian games, highlighting the advantage of nonlocal correlations in strategic decision-making.

Contribution

It provides an analytic characterization of nonlocal correlations that outperform classical equilibria, including unfair strategies, in a class of Bayesian games.

Findings

Quantum strategies outperform classical fair and unfair equilibria.

Nonlocal correlations provide an advantage in conflicting interest games.

The work includes a class of games with both fair and unfair classical equilibria.

Abstract

Interesting connection has been established between two apparently unrelated concepts, namely, quantum nonlocality and Bayesian game theory. It has been shown that nonlocal correlations in the form of advice can outperform classical equilibrium strategies in common interest Bayesian games and also in conflicting interest games. However, classical equilibrium strategies can be of two types, fair and unfair. Whereas in fair equilibrium payoffs of different players are same, in unfair case they differ. Advantage of nonlocal correlation has been demonstrated over fair strategies. In this work we show that quantum strategies can outperform even the unfair classical equilibrium strategies. For this purpose we consider a class of two players games which as a special case includes the conflicting game proposed in [Phys. Rev. Lett. 114, 020401 (2015)]. These games can have both fair and unfair classical equilibria and also can have only unfair ones. We provide a simple analytic characterization of the nonlocal correlations that are advantageous over the classical equilibrium strategies in these games.