论文标题
连续游戏中用于计算平衡的双Oracle算法
Double Oracle Algorithm for Computing Equilibria in Continuous Games
论文作者
论文摘要
许多有效的算法旨在恢复各种有限游戏的NASH平衡。具有无限策略空间（例如多项式游戏）的连续游戏的特殊类别可以通过半决赛编程来解决。但是，总的来说，连续游戏并不直接适合计算程序。在这项贡献中，我们开发了一种迭代策略生成技术，用于在整个连续的两人零和紧凑策略集中找到NASH平衡。过去，该过程称为双Oracle算法，过去已成功地应用于大型有限游戏。我们证明了双甲骨文算法与NASH平衡的收敛性。此外，保证该算法可以在有限的步骤中恢复近似平衡。我们的数值实验表明，在文献中出现的几个游戏示例上，它表现出色。特别是，我们通过连续上校模板游戏的版本对实验进行了详细的分析。
Many efficient algorithms have been designed to recover Nash equilibria of various classes of finite games. Special classes of continuous games with infinite strategy spaces, such as polynomial games, can be solved by semidefinite programming. In general, however, continuous games are not directly amenable to computational procedures. In this contribution, we develop an iterative strategy generation technique for finding a Nash equilibrium in a whole class of continuous two-person zero-sum games with compact strategy sets. The procedure, which is called the double oracle algorithm, has been successfully applied to large finite games in the past. We prove the convergence of the double oracle algorithm to a Nash equilibrium. Moreover, the algorithm is guaranteed to recover an approximate equilibrium in finitely-many steps. Our numerical experiments show that it outperforms fictitious play on several examples of games appearing in the literature. In particular, we provide a detailed analysis of experiments with a version of the continuous Colonel Blotto game.
