Successful algorithms have been developed for computing Nash equilibrium in a variety of finite game classes. However, solving continuous games---in which the pure strategy space is (potentially uncountably) infinite---is far more challenging. Nonetheless, many real-world domains have continuous action spaces, e.g., where actions refer to an amount of time, money, or other resource that is naturally modeled as being real-valued as opposed to integral. We present a new algorithm for computing Nash equilibrium strategies in continuous games. In addition to two-player zero-sum games, our algorithm also applies to multiplayer games and games of imperfect information. We experiment with our algorithm on a continuous imperfect-information Blotto game, in which two players distribute resources over multiple battlefields. Blotto games have frequently been used to model national security scenarios and have also been applied to electoral competition and auction theory. Experiments show that our algorithm is able to quickly compute close approximations of Nash equilibrium strategies for this game.

中文翻译：

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在连续博弈中计算近似纳什均衡的算法应用于连续 Blotto

已经开发出成功的算法来计算各种有限博弈类中的纳什均衡。然而，解决连续博弈——其中纯策略空间是（可能是不可数的）无限的——更具挑战性。尽管如此，许多现实世界的领域都有连续的动作空间，例如，动作指的是时间、金钱或其他资源的数量，这些资源自然建模为实值而不是积分。我们提出了一种在连续博弈中计算纳什均衡策略的新算法。除了两人零和博弈，我们的算法也适用于多人博弈和不完美信息博弈。我们在连续不完美信息 Blotto 游戏中试验我们的算法，其中两个玩家在多个战场上分配资源。Blotto 游戏经常被用于模拟国家安全场景，也被应用于选举竞争和拍卖理论。实验表明，我们的算法能够快速计算该博弈的纳什均衡策略的近似值。