论文标题
零和连续时间马尔可夫游戏，一侧停止
Zero-sum continuous-time Markov games with one-side stopping
论文作者
论文摘要
该论文关注的是连续时间有限状态马尔可夫控制游戏的变体，并在两个玩家都能影响过渡率的情况下停止，而只有一个玩家可以选择停止时间。我们使用动态编程原理，并将此问题减少到具有单方面约束的ODE系统。该系统扮演着钟声方程的角色。我们证明其解决方案提供了玩家的最佳策略。此外，我们证明了具有单方面约束的ODES系统的存在和唯一定理。
The paper is concerned with a variant of the continuous-time finite state Markov game of control and stopping where both players can affect transition rates, while only one player can choose a stopping time. We use the dynamic programming principle and reduce this problem to a system of ODEs with unilateral constraints. This system plays the role of the Bellman equation. We show that its solution provides the optimal strategies of the players. Additionally, we prove the existence and uniqueness theorem for the deduced system of ODEs with unilateral constraints.
