Implementation Via Information Design in Binary-Action Supermodular Games

Abstract

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 played on the largest event where that action profile maximizes the average potential.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 44 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.