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Modern Physics

Quantum Evolution Strategy of Hawk-Dove Game

Aiwen Kuang

Published Jan 1, 2013• 0 citations
Publisher

Abstract

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.

DOI
10.12677/mp.2013.32013

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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.
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.
We quantize the Hawk–Dove game by using the most general form of a pure initial state to investigate the existence of pure and mixed evolutionarily stable strategies (ESS). An example is considered to draw a comparison between the classical and quantum version of the game. Our choice of the most general initial quantum state enables us to make the game symmetric or asymmetric. We show that for a particular set of game parameters where there exists only mixed ESS in the classical version of the game, quantization allows even a pure strategy to be an ESS for the symmetric game in addition to mixed ESS. On the other hand only pure strategy ESS can exist for the asymmetric quantum version of the Hawk–Dove game.
S. J. van Enk and R. Pike in PRA 66, 024306 (2002), argue that the equilibrium solution to a quantum game isn't unique but is already present in the classical game itself. In this work, we debunk this assertion by showing that a random strategy in a particular quantum (Hawk-Dove) game is unique to the quantum game. In other words the equilibrium solution of the quantum Hawk-Dove game can not be obtained in the classical Hawk-Dove game. Moreover, we provide an analytical solution to the quantum 2×22\times22×2 strategic form Hawk-Dove game using random mixed strategies. The random strategies which we describe are evolutionary stable implying both Pareto optimality and Nash equilibrium with their payoff's classically unobtainable.