Subgame‐perfect equilibrium in games with almost perfect information: Dispensing with public randomization. Issue 4 (11th November 2021)

• Record Type: Journal Article
• Authors: Barelli, Paulo; Duggan, John
• Is Part Of: Theoretical economics. Volume 16:Issue 4(2021)
• Page Start: 1221
• Page End: 1248
• Publication Date: 2021-11-11
• Subjects: Existence -- subgame‐perfect equilibrium -- infinite‐action games -- stochastic games -- public randomization; C72 -- C73; Economics -- Periodicals; 330.01
• DOI: 10.3982/TE3243
• Languages: English
• ISSNs: 1933-6837

Abstract

Abstract : 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.