Dynamic nonzero sum games are widely used to model multi agent decision making in control, economics, and related fields. Classical methods for computing Nash equilibria, especially in linear quadratic settings, rely on strong structural assumptions and become impractical for nonlinear dynamics, many players, or long horizons, where multiple local equilibria may exist. We show through examples that such methods can fail to reach the true global Nash equilibrium even in relatively small games. To address this, we propose two population based evolutionary algorithms for general dynamic games with linear or nonlinear dynamics and arbitrary objective functions: a co evolutionary genetic algorithm and a hybrid genetic algorithm particle swarm optimization scheme. Both approaches search directly over joint strategy spaces without restrictive assumptions and are less prone to getting trapped in local Nash equilibria, providing more reliable approximations to global Nash solutions.

翻译：动态非零和博弈被广泛应用于控制、经济学及相关领域的多智能体决策建模。计算纳什均衡的经典方法，特别是在线性二次型设定中，依赖于强结构假设，在处理非线性动态、多参与者或长时域（可能存在多个局部均衡）问题时变得不切实际。我们通过实例证明，即使在相对小规模的博弈中，此类方法也可能无法收敛至真实的全局纳什均衡。为此，我们针对具有线性/非线性动态及任意目标函数的一般动态博弈，提出两种基于种群的进化算法：一种协同进化遗传算法，以及一种遗传算法-粒子群优化的混合方案。这两种方法均能在无限制性假设的条件下直接搜索联合策略空间，更不易陷入局部纳什均衡，从而为全局纳什解提供更可靠的近似。