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arXiv:quant-ph/0308034 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Quantum games of asymmetric information

Jiangfeng Du, Hui Li, Chenyong Ju

Published Jul 28, 2003• 42 citations
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Abstract

We investigate quantum games in which the information is asymmetrically distributed among the players and find that the possibility of the quantum game outperforming its classical counterpart depends strongly on not only the entanglement but also the informational asymmetry. What is more interesting, when the information distribution is asymmetric, is that the contradictive impact of the quantum entanglement on the profits is observed, which is not reported in quantum games of symmetric information.

DOI
10.1103/physreve.68.016124

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We investigate quantum games in which the information is asymmetrically distributed among the players and find that the possibility of the quantum game outperforming its classical counterpart depends strongly on not only the entanglement but also the informational asymmetry. What is more interesting, when the information distribution is asymmetric, is that the contradictive impact of the quantum entanglement on the profits is observed, which is not reported in quantum games of symmetric information.
We study a general 2 × 2 symmetric entangled quantum game. When one player has access only to classical strategies, while the other can use the full range of quantum strategies, there are ‘miracle’ moves available to the quantum player that can direct the game towards the quantum player's preferred result regardless of the classical player's strategy. The advantage pertaining to the quantum player is dependent on the degree of entanglement. Below a critical level, dependent on the pay–offs in the game, the miracle move is of no advantage.
Quantum entanglement has been recently demonstrated as a useful resource in conflicting-interest games of incomplete information between two players, Alice and Bob [Pappa et al., Phys. Rev. Lett. 114, 020401 (2015)]. The general setting for such games is that of correlated strategies where the correlation between competing players is established through a trusted common adviser; however, players need not reveal their input to the adviser. So far, the quantum advantage in such games has been revealed in a restricted sense. Given a quantum correlated equilibrium strategy, one of the players can still receive a higher than quantum average payoff with some classically correlated equilibrium strategy. In this work, by considering a class of asymmetric Bayesian games, we show the existence of games with quantum correlated equilibrium where the average payoff of both the players exceeds the respective individual maximum for each player over all classically correlated equilibriums.