Random Perfect Information Games

• 成果类型: Article
• 署名作者: Flesch, Janos; Predtetchinski, Arkadi; Suomala, Ville
• 署名单位: Maastricht University; Maastricht University; University of Oulu
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.1277
• 发表日期: 2023
• 页码: 708-727
• 关键词: strategy nash equilibria; expected number; DYNAMICS

摘要

The paper proposes a natural measure space of zero-sum perfect information games with upper semicontinuous payoffs. Each game is specified by the game tree and by the assignment of the active player and the capacity to each node of the tree. The payoff in a game is defined as the infimum of the capacity over the nodes that have been visited during the play. The active player, the number of children, and the capacity are drawn from a given joint distribution independently across the nodes. We characterize the cumulative distribution function of the value v using the fixed points of the so-called value-generating function. The characterization leads to a necessary and sufficient condition for the event v >= k to occur with positive probability. We also study probabilistic properties of the set of player I's k-optimal strategies and the corresponding plays.