We consider the problem of computing Nash equilibria in potential games where each player's strategy set is subject to private uncoupled constraints. This scenario is frequently encountered in real-world applications like road network congestion games where individual drivers adhere to personal budget and fuel limitations. Despite the plethora of algorithms that efficiently compute Nash equilibria (NE) in potential games, the domain of constrained potential games remains largely unexplored. We introduce an algorithm that leverages the Lagrangian formulation of NE. The algorithm is implemented independently by each player and runs in polynomial time with respect to the approximation error, the sum of the size of the action-spaces, and the game's inherent parameters.

翻译：我们考虑在每位玩家策略集受私有非耦合约束的势博弈中计算纳什均衡的问题。该场景常见于现实应用，例如在道路网络拥堵博弈中，个体驾驶员需遵守个人预算和燃油限制。尽管存在大量算法可高效计算势博弈中的纳什均衡（NE），但受约束势博弈领域仍鲜有探索。我们提出一种基于NE拉格朗日表述的算法。每位玩家独立运行该算法，其时间复杂度关于近似误差、行动空间规模之和以及博弈固有参数呈多项式级关系。