Comparison of information structures in stochastic games with imperfect public monitoring

Abstract

This paper studies the impact of an improvement of information structure upon the perfect public equilibrium payoff set in discounted stochastic games with imperfect public monitoring. We first suggest three partial orders on information structures in stochastic games. Although each of them reduces to the notion of garbling in repeated games (Kandori in Rev Econ Stud 59:581-593, 1992), we find that an improvement of information in terms of our two garbling notions does not imply an expansion of the equilibrium payoff set for some games. We also show that more informativeness in terms of our third notion of garbling is sufficient for the expansion, thereby extending the well-known monotonicity result in Kandori (1992) to stochastic games. KeywordsStochastic game • Blackwell sufficiency • Information structure • Public monitoring • Perfect public equilibrium JEL Classification C72 • C73I owe many thanks to Ichiro Obara for his continuous guidance, encouragement, and invaluable advice. I am also grateful to a co-editor and two anonymous referees for insightful comments. All remaining errors are my own.

Maintaining Privacy in Cartels

“…This is a straightforward extension of proposition 1 of Kandori (1992) from repeated games to Markov games. It also follows immediately from corollary 1 of Kim (2016). QED Proposition 0 is one version of the standard result that transparency helps collusion.…”