Subgame‐perfect equilibrium in games with almost perfect information: Dispensing with public randomization
证明在自然状态无原子的几乎完美信息动态博弈中，公开随机化不扩大子博弈完美均衡的收益集合，任何通过公开随机化得到的均衡都可以去随机化为原博弈的等价均衡。
Harris, Reny, and Robson (1995) added a public randomization device to dynamic games with almost perfect information to ensure existence of subgame perfect equilibria (SPE). We show that when Nature's moves are atomless in the original game, public randomization does not enlarge the set of SPE payoffs: any SPE obtained using public randomization can be “decorrelated” to produce a payoff‐equivalent SPE of the original game. As a corollary, we provide an alternative route to a result of He and Sun (2020) on existence of SPE without public randomization, which in turn yields equilibrium existence for stochastic games with weakly continuous state transitions.