Correlated Equilibria of Classical Strategic Games with Quantum Signals
Pierfrancesco La Mura
TL;DR
The paper asks whether quantum signals can improve coordination beyond all classical correlated equilibria in fixed classical games, and answers affirmatively by introducing quantum correlated equilibria where measurements on entangled states influence players' information. It provides a formal framework that generalizes classical correlated equilibrium to include quantum measurements and proves existence, illustrating strict payoff gains with a concrete example that leverages entanglement. This work links game theory with quantum information, showing that Bell-inequality-violating correlations can yield more efficient outcomes and prompting reevaluation of related impossibility results. The results extend Aumann's signaling paradigm to the quantum domain and suggest new avenues for coordination in strategic settings.
Abstract
Correlated equilibria are sometimes more efficient than the Nash equilibria of a game without signals. We investigate whether the availability of quantum signals in the context of a classical strategic game may allow the players to achieve even better efficiency than in any correlated equilibrium with classical signals, and find the answer to be positive.