论文标题
具有唯一数量响应平衡的逆矩阵游戏
Inverse Matrix Games with Unique Quantal Response Equilibrium
论文作者
论文摘要
在逆游戏问题中，需要在游戏中推断玩家的成本功能，以使所需的联合策略是NASH平衡。我们研究一类多人矩阵游戏的逆游戏问题，每个玩家所感知的成本都被随机噪声损坏。我们为玩家的量子响应平衡提供了足够的条件 - 纳什均衡对具有感知噪声的游戏的概括 - 是独一无二的。我们开发了有效的优化算法，用于根据半决赛程序和双层优化推断成本矩阵。我们证明了这些方法在鼓励避免碰撞和公平资源分配中的应用。
In an inverse game problem, one needs to infer the cost function of the players in a game such that a desired joint strategy is a Nash equilibrium. We study the inverse game problem for a class of multiplayer matrix games, where the cost perceived by each player is corrupted by random noise. We provide sufficient conditions for the players' quantal response equilibrium -- a generalization of the Nash equilibrium to games with perception noise -- to be unique. We develop efficient optimization algorithms for inferring the cost matrix based on semidefinite programs and bilevel optimization. We demonstrate the application of these methods in encouraging collision avoidance and fair resource allocation.
