论文标题
确定性的N-Per人最短路径和对称挖掘的终端游戏具有纯平稳策略的NASH平衡
Deterministic n-person shortest path and terminal games on symmetric digraphs have Nash equilibria in pure stationary strategies
论文作者
论文摘要
我们证明，确定性的n-perion最短路径游戏具有纯净和固定策略的NASH equlibrium，如果它是边缘对称性的（即（u，v），每当（v，v，u）（v，u）是移动（v，u），除了进入终端顶点的移动），每个运动的长度对每个球员都是积极的。这两种情况都是必不可少的，尽管如果存在一个没有NE的2人非对称游戏，则仍然是一个空旷的问题。我们提供了不积极的2人NE 2人边缘对称游戏的示例。我们还考虑了终端游戏的特殊情况（最短的路径游戏，其中只有终端移动的长度非零，可能为负），并证明边缘对称的N-per-ser-terminal游戏总是在纯粹和平稳的策略中具有NASH Equilibria。此外，我们证明了边缘对称的2人终端游戏具有统一（子游戏）NASH平衡，只要任何无限的比赛都比两个玩家的任何终端都要差。
We prove that a deterministic n-person shortest path game has a Nash equlibrium in pure and stationary strategies if it is edge-symmetric (that is (u,v) is a move whenever (v,u) is, apart from moves entering terminal vertices) and the length of every move is positive for each player. Both conditions are essential, though it remains an open problem whether there exists a NE-free 2-person non-edge-symmetric game with positive lengths. We provide examples for NE-free 2-person edge-symmetric games that are not positive. We also consider the special case of terminal games (shortest path games in which only terminal moves have nonzero length, possibly negative) and prove that edge-symmetric n-person terminal games always have Nash equilibria in pure and stationary strategies. Furthermore, we prove that an edge-symmetric 2-person terminal game has a uniform (subgame perfect) Nash equilibrium, provided any infinite play is worse than any of the terminals for both players.
