Bayesian Nash Equilibria and Bell Inequalities
Taksu Cheon, Azhar Iqbal
TL;DR
This paper explores the connection between quantum strategies in games with incomplete information and Bell inequalities, revealing how quantum advantages relate to nonlocal correlations.
Contribution
It introduces a multi-sector probability matrix formalism that unifies classical and quantum strategies in game theory, clarifying the role of nonlocality.
Findings
Quantum strategies can outperform classical ones in the extended Battle of Sexes game.
Breaking Bell inequalities correlates with quantum advantage in game payoffs.
The formalism links quantum game theory with foundational quantum physics concepts.
Abstract
Games with incomplete information are formulated in a multi-sector probability matrix formalism that can cope with quantum as well as classical strategies. An analysis of classical and quantum strategy in a multi-sector extension of the game of Battle of Sexes clarifies the two distinct roles of nonlocal strategies, and establish the direct link between the true quantum gain of game's payoff and the breaking of Bell inequalities.
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