Open AccessSubgame‐perfect equilibrium in games with almost perfect information: Dispensing with public randomization
Author(s) -
Barelli Paulo,
Duggan John
Publication year - 2021
Publication title -
theoretical economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.404
H-Index - 32
eISSN - 1555-7561
pISSN - 1933-6837
DOI - 10.3982/te3243
Subject(s) - subgame perfect equilibrium , corollary , mathematical economics , stochastic game , sequential equilibrium , randomization , mathematics , computer science , repeated game , game theory , equilibrium selection , combinatorics , medicine , randomized controlled trial , surgery
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.