Quantum minority game utilizing various forms of entanglement

摘要

The quantum Minority game provides a means of studying the effect of multi-partite entanglement in a game theoretic setting. We study symmetric Nash equilibria and symmetric Pareto optimal strategies arising in a four-player quantum Minority game that uses an initial state that is a superposition of a GHZ state and products of EPR pairs. We find that the payoff curve for the symmetric Pareto optimal strategy is the same as that for the maximal violation of the Mermin-Ardehali-Belinskii-Klyshko inequality for the initial state, indicating a correspondence between quantum game theory and Bell inequalities. We also show that no advantage over the classical Minority game can be obtained when the initial state has only two party entanglement.