论文标题
$ \ varepsilon $ -NASH在离散时间内多玩家非零和Dynkin游戏的平衡
$\varepsilon$-Nash Equilibria of a Multi-player Nonzero-sum Dynkin Game in Discrete Time
论文作者
论文摘要
我们以停止时间为策略（或纯粹的策略），研究无限的地平线离散时间n-player nonzero-sum dynkin游戏（$ n \ geq 2 $）。我们通过呈现建设性算法来证明游戏的存在$ \ varepsilon $ -NASH平衡点。主要特征之一是球员的回报取决于在终止阶段停止的球员集，这是至少一个球员停止的最小阶段。存在结果扩展到具有有限范围的非零和游戏的情况。最后，在有限地平线的特定情况下，通过两个显式示例来说明该算法。
We study the infinite horizon discrete time N-player nonzero-sum Dynkin game ($N \geq 2$) with stopping times as strategies (or pure strategies). We prove existence of an $\varepsilon$-Nash equilibrium point for the game by presenting a constructive algorithm. One of the main features is that the payoffs of the players depend on the set of players that stop at the termination stage which is the minimal stage in which at least one player stops. The existence result is extended to the case of a nonzero-sum game with finite horizon. Finally, the algorithm is illustrated by two explicit examples in the specific case of finite horizon.
