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Systems Engineering

Quantum Analysis of "Hawk and Dove Game"

Bin Wang, Yinfeng Xu

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

In the classical and the Nash equilibrium is that one player adopts hawk strategy and the (other) adopts dove strategy. In this article, we study the and in (method) of quantum game, and (conclude) a new Nash equilibrium by means of quantum strategy, which is different from classical game, both game players adopt dove strategy to attain Pareto optimization.

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In the classical and the Nash equilibrium is that one player adopts hawk strategy and the (other) adopts dove strategy. In this article, we study the and in (method) of quantum game, and (conclude) a new Nash equilibrium by means of quantum strategy, which is different from classical game, both game players adopt dove strategy to attain Pareto optimization.
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.
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.
A game is said to be “quantized" when the expected payoff to the player(s) is computed via the higher order randomization notion of quantum superposition followed by measurement versus the randomization notion of probability distribution. A major motivation for quantizing a game is the potential manifestation of Nash equilibria that are superior to those already available in the game. Quantum superpositions are elements of a (projective) Hilbert space which, among other things, is an inner product space. The inner product of the Hilbert space of quantum superpositions is used here to give a geometric characterization of Nash equilibrium in quantized versions of Hawk-Dove games, a class of games to which the well known game Prisoners