Subgame-Perfect Equilibrium in Games with Almost Perfect Information : Dispensing with Public Randomization

Harris, Reny, and Robson (Econometrica, 1995) add 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, SPE obtained via this channel can be "de-correlated" to produce a payoff-equivalent SPE of the original game; thus, public randomization is in a sense without loss of generality. As a corollary, we provide an alternative route to a result of He and Sun (2016) on existence of SPE without public randomization, which in turn yields an equilibrium existence result for stochastic games with weakly continuous state transitions