论文标题
Cox Process Hotelling游戏的NASH平衡结构
Nash equilibrium structure of Cox process Hotelling games
论文作者
论文摘要
我们研究了一个N-玩家游戏，其中每个玩家的纯粹动作是在波兰空间上选择一个非负功能，该功能支持有限的扩散度量，但要受到该功能积分的有限限制。此功能用于定义波兰空间上泊松点过程的强度。这些过程与播放器独立，并且对玩家的价值是其在叠加点过程中其开放voronoi单元格的量度。在随机策略下，球员的点过程是一个COX过程，玩家之间的竞争性质类似于Hotelling竞争游戏中的过程。我们描述了这样的游戏承认NASH均衡并证明存在NASH平衡时，它是独一无二的，并且由纯策略组成，这些策略与总强度相同的比例成比例。我们举例说明了不存在纳什均衡的游戏。更好地理解纳什平衡存在的标准仍然是一个有趣的开放问题。
We study an N-player game where a pure action of each player is to select a non-negative function on a Polish space supporting a finite diffuse measure, subject to a finite constraint on the integral of the function. This function is used to define the intensity of a Poisson point process on the Polish space. The processes are independent over the players, and the value to a player is the measure of the union of its open Voronoi cells in the superposition point process. Under randomized strategies, the process of points of a player is thus a Cox process, and the nature of competition between the players is akin to that in Hotelling competition games. We characterize when such a game admits Nash equilibria and prove that when a Nash equilibrium exists, it is unique and comprised of pure strategies that are proportional in the same proportions as the total intensities. We give examples of such games where Nash equilibria do not exist. A better understanding of the criterion for the existence of Nash equilibria remains an intriguing open problem.
