Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: May, 2024, Volume 92, Issue 3

Implementation via Information Design in Binary-Action Supermodular Games
p. 775-813

Stephen Morris, Daisuke Oyama, Satoru Takahashi

What outcomes can be implemented by the choice of an information structure in binary‐action supermodular games? An outcome is partially implementable if it satisfies obedience (Bergemann and Morris (2016)). We characterize when an outcome is smallest equilibrium implementable (induced by the smallest equilibrium). Smallest equilibrium implementation requires a stronger sequential obedience condition: there is a stochastic ordering of players under which players are prepared to switch to the high action even if they think only those before them will switch. We then characterize the optimal outcome induced by an information designer who prefers the high action to be played, but anticipates that the worst (hence smallest) equilibrium will be played. In a potential game, under convexity assumptions on the potential and the designer's objective, it is optimal to choose an outcome where actions are perfectly coordinated (all players choose the same action), with the high action profile played on the largest event where that action profile maximizes the average potential.

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Supplemental Material

Supplement to "Implementation via Information Design in Binary-Action Supermodular Games"

Stephen Morris, Daisuke Oyama, and Satoru Takahashi

This supplemental appendix contains material not found within the manuscript.