We introduce a regret-based fitness assignment strategy for evolutionary algorithms to find Nash equilibria in noncooperative simultaneous combinatorial game theory problems where it is computationally intractable to enumerate all decision options of the players involved in the game. Applications of evolutionary algorithms to non-cooperative simultaneous games have been limited due to challenges in guiding the evolutionary search toward equilibria, which are usually inferior points in the objective space. We propose a regret-based approach to select candidate decision options of the players for the next generation in a multipopulation genetic algorithm called Regret-Based Nash Equilibrium Sorting Genetic Algorithm (RNESGA). We show that RNESGA can converge to multiple Nash equilibria in a single run using two- and three- player competitive knapsack games and other games from the literature. We also show that pure payoff-based fitness assignment strategies perform poorly in three-player games.

中文翻译：

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多玩家组合博弈论问题的基于遗憾的纳什均衡排序遗传算法。

我们为进化算法引入了一种基于遗憾的适应度分配策略，以在非合作同时组合博弈论问题中找到纳什均衡，其中枚举参与博弈的玩家的所有决策选项在计算上是困难的。进化算法在非合作同步博弈中的应用受到限制，因为在引导进化搜索走向平衡方面存在挑战，平衡通常是目标空间中的劣势点。我们提出了一种基于遗憾的方法，在称为基于遗憾的纳什均衡排序遗传算法 (RNESGA) 的多种群遗传算法中为下一代选择玩家的候选决策选项。我们表明，RNESGA 可以使用两人和三人竞技背包游戏和文献中的其他游戏在一次运行中收敛到多个纳什均衡。我们还表明，纯基于收益的健身分配策略在三人游戏中表现不佳。