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Jilin Normal University Journal

Hawk-dove Game Model of Quantum under Asymmetric Information

Wang Mi-lin

Published Jan 1, 2011• 1 citation
OpenAlex

Abstract

In this paper,using the theory of Quantum game established a quantum model of the hawk-dove game under asymmetric information,find the quantum Nash equilibrium strategy with different values of entanglement.And comparison with the classical game theory.In conditions of the classic game,we come to several equilibrium strategies which associated with conflict costs.In conditions of the quantum game,when the entanglement is equal to we draw a only Nash equilibrium strategy which unrelated with conflict costs.Classical game equilibrium strategy is a special case of quantum,where the entanglement is equal to zero.So this promotes the Nash equilibrium strategy of hawk-dove game,also greatly simplifies the operation.

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In this paper,using the theory of Quantum game established a quantum model of the hawk-dove game under asymmetric information,find the quantum Nash equilibrium strategy with different values of entanglement.And comparison with the classical game theory.In conditions of the classic game,we come to several equilibrium strategies which associated with conflict costs.In conditions of the quantum game,when the entanglement is equal to we draw a only Nash equilibrium strategy which unrelated with conflict costs.Classical game equilibrium strategy is a special case of quantum,where the entanglement is equal to zero.So this promotes the Nash equilibrium strategy of hawk-dove game,also greatly simplifies the operation.
本文介绍量子博弈和量子演化博弈的基本概念，并分析鹰鸽博弈的量子策略和量子演化稳定策略。量子策略可以得到鹰鸽博弈的Pareto均衡，我们发现在资源利益比损失多情况下，鹰鹰策略不仅是Nash均衡还是量子演化稳定策略。 We introduce the basic concepts of quantum strategy and quantum evolution stable strategy and use them to analyze the Hawk-Dove game. We find that quantum strategy can realize the Pareto equilibrium by Dove-Dove strategy and the Hawk-Hawk strategy is not only a Nash equilibrium, but also a quantum evolution stable strategy when the re-source gain is larger than the loss in the Hawk-Dove game.
We study a quantum game played by two players with restricted multiple strategies. It is found that in quantum game Nash equilibrium does not always exist which is totally different from that in classical game. This happens only when the initial state is in entangled state. At the same time, we find that when Nash equilibrium exists the pay off function is usually different from that in the classical counterpart except in some special cases. This presents an explicit example where quantum game and classical game differ fundamentally.
We study a quantum game played by two players with restricted multiple strategies. It is found that in this restricted quantum game Nash equilibrium does not always exist when the initial state is entangled. At the same time, we find that when Nash equilibrium exists the payoff function is usually different from that in the classical counterpart except in some special cases. This presents an explicit example showing quantum game and classical game may differ. When designing a quantum game with limited strategies, the allowed strategy should be carefully chosen according to the type of initial state.