OPTIMALITY AND STABILITY OF SYMMETRIC EVOLUTIONARY GAMES WITH APPLICATIONS IN GENETIC SELECTION
OPTIMALITY AND STABILITY OF SYMMETRIC EVOLUTIONARY GAMES WITH APPLICATIONS IN GENETIC SELECTION
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DOI：
10.3934/mbe.2015.12.503
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发表时间：
2015-06-01
影响因子：
2.6
通讯作者：
Wu, Zhijun
中科院分区：
文献类型：
--
作者：
Huang, Yuanyuan;Hao, Yiping;Wu, Zhijun
对称进化博弈，即具有对称适应度矩阵的进化博弈，在群体遗传学中具有重要的应用，它们可以用于建模，例如给定群体的基因型的选择和进化。在本文中，我们回顾了获得对称进化博弈最优且稳定策略的理论，并提供了一些新的证明和计算方法。特别是，我们回顾了对称进化博弈与广义背包问题之间的关系，并讨论了从该关系导出的用于测试策略的最优性和稳定性的一阶和二阶充要条件。有些条件的给出形式与以前的工作不同，可以更有效地进行验证。我们还推导出比传统方法更有效的计算方法来评估条件。我们展示了如何应用这些条件来证明一类特殊遗传选择游戏（包括遗传性疾病研究中的一些游戏）的策略及其稳定性。
Symmetric evolutionary games, i.e., evolutionary games with symmetric fitness matrices, have important applications in population genetics, where they can be used to model for example the selection and evolution of the genotypes of a given population. In this paper, we review the theory for obtaining optimal and stable strategies for symmetric evolutionary games, and provide some new proofs and computational methods. In particular, we review the relationship between the symmetric evolutionary game and the generalized knapsack problem, and discuss the first and second order necessary and sufficient conditions that can be derived from this relationship for testing the optimality and stability of the strategies. Some of the conditions are given in different forms from those in previous work and can be verified more efficiently. We also derive more efficient computational methods for the evaluation of the conditions than conventional approaches. We demonstrate how these conditions can be applied to justifying the strategies and their stabilities for a special class of genetic selection games including some in the study of genetic disorders.