Subgame-perfection in quitting games with perfect information and differential equations

• 成果类型: Article
• 署名作者: Solan, E
• 署名单位: Tel Aviv University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1040.0108
• 发表日期: 2005
• 页码: 51-72
• 关键词: 2-player stochastic games; Stopping games; equilibria; THEOREM; maxmin

摘要

We introduce a new approach to studying subgame-perfect equilibrium payoffs in stochastic games: the differential equations approach. We apply our approach to quitting games with perfect information. Those are sequential games in which at every stage one of n players is chosen; each player is chosen with probability 1/n. The chosen player i decides whether to quit, in which case the game terminates and the terminal payoff is some vector a(i) is an element of R-n, or whether to continue, in which case the game continues to the next stage. If no player ever quits, the payoff is some vector a(*) is an element of R-n. We define a certain differential inclusion, prove that it has at least one solution, and prove that every vector on a solution of this differential inclusion is a subgame-perfect equilibrium payoff.