Efficiency in Games With Markovian Private Information


  • Juan F. Escobar,

    1. Center for Applied Economics, Dept. of Industrial Engineering, University of Chile, Santiago, Chile; jescobar@dii.uchile.cl
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  • Juuso Toikka

    1. Dept. of Economics, Massachusetts Institute of Technology, Cambridge, MA 02142, U.S.A.; toikka@mit.edu
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    • We thank Manuel Amador, Kyle Bagwell, Aaron Bodoh-Creed, Matt Elliot, Johannes Hörner, Matt Jackson, Carlos Lever, Jon Levin, Romans Pancs, Andy Skrzypacz, and, especially, Ilya Segal for useful discussions. We are grateful to a co-editor and four anonymous referees for comments. Escobar acknowledges the support of Fondecyt Project 11090166 and the Millennium Institute on Complex Engineering Systems. Toikka acknowledges financial support from the Yrjö Jahnsson Foundation. An earlier version of this work was circulated as “A Folk Theorem With Markovian Private Information.”


We study repeated Bayesian games with communication and observable actions in which the players' privately known payoffs evolve according to an irreducible Markov chain whose transitions are independent across players. Our main result implies that, generically, any Pareto-efficient payoff vector above a stationary minmax value can be approximated arbitrarily closely in a perfect Bayesian equilibrium as the discount factor goes to 1. As an intermediate step, we construct an approximately efficient dynamic mechanism for long finite horizons without assuming transferable utility.