论文标题
多人游戏上校游戏
The Multiplayer Colonel Blotto Game
论文作者
论文摘要
我们启动了经典连续上校障碍游戏的自然多人游戏概括的研究。由Borel引入的两人模板游戏作为跨$ n $同时阵线的资源竞争模型，已广泛研究了一个世纪，并在整个社会科学中看到了许多应用。我们的作品定义了多人上校的障碍游戏，并在各种$ k $（玩家数量）和$ n $的情况下得出了Nash Equilibria。我们还介绍了一个“布尔”版本的“布洛”版本，该版本在多人游戏设置中变得有趣。与两人理论文献一样，我们工作的主要技术困难是将各种边际分布耦合到满足严格总和约束的联合分布中的挑战。与在连续环境中以前的工作相反，我们以有效的采样算法的形式得出耦合算法。
We initiate the study of the natural multiplayer generalization of the classic continuous Colonel Blotto game. The two-player Blotto game, introduced by Borel as a model of resource competition across $n$ simultaneous fronts, has been studied extensively for a century and seen numerous applications throughout the social sciences. Our work defines the multiplayer Colonel Blotto game and derives Nash equilibria for various settings of $k$ (number of players) and $n$. We also introduce a "Boolean" version of Blotto that becomes interesting in the multiplayer setting. The main technical difficulty of our work, as in the two-player theoretical literature, is the challenge of coupling various marginal distributions into a joint distribution satisfying a strict sum constraint. In contrast to previous works in the continuous setting, we derive our couplings algorithmically in the form of efficient sampling algorithms.
