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A game-theoretic and dynamical-systems analysis of selection methods in coevolution

机译:协同进化中选择方法的博弈论与动力学系统分析

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We use evolutionary game theory (EGT) to investigate the dynamics and equilibria of selection methods in coevolutionary algorithms. The canonical selection method used in EGT is equivalent to the standard "fitness-proportional" selection method used in evolutionary algorithms. All attractors of the EGT dynamic are Nash equilibria; we focus on simple symmetric variable-sum games that have polymorphic Nash-equilibrium attractors. Against the dynamics of proportional selection, we contrast the behaviors of truncation selection, (/spl mu/,/spl lambda/),(/spl mu/+/spl lambda/), linear ranking, Boltzmann, and tournament selection. Except for Boltzmann selection, each of the methods we test unconditionally fail to achieve polymorphic Nash equilibrium. Instead, we find point attractors that lack game-theoretic justification, cyclic dynamics, or chaos. Boltzmann selection converges onto polymorphic Nash equilibrium only when selection pressure is sufficiently low; otherwise, we obtain attracting limit-cycles or chaos. Coevolutionary algorithms are often used to search for solutions (e.g., Nash equilibria) of games of strategy; our results show that many selection methods are inappropriate for finding polymorphic Nash solutions to variable-sum games. Another application of coevolution is to model other systems; our results emphasize the degree to which the model's behavior is sensitive to implementation details regarding selection-details that we might not otherwise believe to be critical.
机译:我们使用进化博弈论(EGT)来研究协同进化算法中选择方法的动力学和平衡性。 EGT中使用的规范选择方法等效于演化算法中使用的标准“适合度”选择方法。 EGT动态的所有吸引子都是纳什均衡。我们关注具有多态Nash平衡吸引子的简单对称可变和博弈。针对比例选择的动态,我们对比了截断选择,(/ spl mu /,/ spl lambda /),(/ spl mu / + / spl lambda /),线性排名,玻尔兹曼和锦标赛选择的行为。除Boltzmann选择外,我们无条件测试的每种方法均无法实现多态Nash平衡。相反,我们发现的点吸引子缺乏博弈论的论证,循环动力或混乱。仅当选择压力足够低时,玻尔兹曼选择才会收敛到多态Nash平衡。否则,我们将获得吸引人的极限周期或混乱。协同进化算法通常用于搜索战略博弈的解(例如,纳什均衡);我们的结果表明,许多选择方法都不适合为可变和博弈找到多态Nash解。协同进化的另一个应用是对其他系统建模。我们的结果强调了模型行为对有关选择细节的实现细节敏感的程度,否则我们可能认为这些细节并不重要。

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