AI 中文总结
研究连续博弈中战略行为演化，针对PWGF框架局限，推广参数化前推映射框架到非梯度流用于博弈动力学，通过数值实验证明新框架在瓦瑟斯坦度量下有可证明误差界且有效。
AI 中文摘要
我们为连续博弈中战略行为的演化引入了一个参数化计算框架。通过策略空间上随时间变化的概率密度来考虑玩家的集体动态，该密度表示在任何给定时间选择每种策略的可能性。我们不是直接求解控制这种演化的高维福克 - 普朗克方程，而是将概率密度表示为具有参数化前推映射的参考分布的前推，并考虑参数化方程的演化。这项工作的动机源于参数化瓦瑟斯坦梯度流（PWGF）框架应用于博弈动力学时的局限性。PWGF为可表述为瓦瑟斯坦梯度流的概率密度演化方程提供了参数化方法，但并非所有博弈动力学都允许这样的梯度流表述。我们将参数化前推映射框架推广到非梯度流，并将其应用于具有瓦瑟斯坦度量中可证明误差界的博弈动力学。提供了几个经济学中非梯度系统的数值实验来证明这个新框架的有效性。
英文摘要
We introduce a parameterized computational framework for the evolution of strategic behavior in continuous games. We consider the collective dynamics of players through a time-dependent probability density over the strategy space, representing the likelihood of each strategy being chosen at any given time. Instead of directly solving the high-dimensional Fokker-Planck equation that governs this evolution, we represent the probability density as the pushforward of a reference distribution with parameterized pushforward maps and consider the evolution of the parameterized equations. The motivation for this work comes from a limitation of the parameterized Wasserstein gradient flow (PWGF) framework when it is applied to game dynamics. PWGF provides a parameterized approach for evolution equations of probability density that can be formulated as Wasserstein gradient flows. However, not all game dynamics admit such a gradient flow formulation. We generalize the parameterized pushforward map framework to the non-gradient flows and apply it to the game dynamics with provable error bound in Wasserstein metric. Numerical experiments with several non-gradient systems in economics are provided to demonstrate the effectiveness of this new framework.
