Random Perfect Information Games
该论文构建了一个零和完美信息博弈的自然测度空间，其中每个博弈由博弈树、活跃玩家和节点容量定义，并利用值生成函数的不动点刻画了博弈值的累积分布函数。
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 [Formula: see text] to occur with positive probability. We also study probabilistic properties of the set of player I’s k-optimal strategies and the corresponding plays.