用神经算子近似求解动态斯塔克尔伯格博弈中的跟随者最优响应。
Neural Operators Can Play Dynamic Stackelberg Games
- 用基于注意力的神经算子逼近跟随者的最优响应策略。
- 近似策略下博弈价值与原问题接近，误差在紧凑集上可控制。
- 适用于需要建模复杂响应机制的博弈场景，如经济、交通调度。
动态斯塔克尔伯格博弈是一类两玩家博弈，领导者先行行动，跟随者则根据领导者的策略选择最优应对。然而，由于跟随者的最优响应算子（作为领导者控制的函数）通常解析不可解，只有简化的博弈能显式求解。本文证明，跟随者的最优响应算子可通过基于注意力的神经算子，在适应性开环控制的紧致子集上一致近似实现。进一步表明，当跟随者采用该近似响应时，博弈的价值逼近原始博弈的价值。主要结果基于我们关于平方可积适应随机过程间注意力神经算子的通用逼近定理，以及一类广义斯塔克尔伯格博弈的稳定性分析。
原文摘要 · Abstract (English)
Dynamic Stackelberg games are a broad class of two-player games in which the leader acts first, and the follower chooses a response strategy to the leader's strategy. Unfortunately, only stylized Stackelberg games are explicitly solvable since the follower's best-response operator (as a function of the control of the leader) is typically analytically intractable. This paper addresses this issue by showing that the \textit{follower's best-response operator} can be approximately implemented by an \textit{attention-based neural operator}, uniformly on compact subsets of adapted open-loop controls for the leader. We further show that the value of the Stackelberg game where the follower uses the approximate best-response operator approximates the value of the original Stackelberg game. Our main result is obtained using our universal approximation theorem for attention-based neural operators between spaces of square-integrable adapted stochastic processes, as well as stability results for a general class of Stackelberg games.
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