Implementation via Information Design in Binary-Action Supermodular Games

52 Pages Posted: 12 Nov 2020

See all articles by Stephen Morris

Stephen Morris

MIT

Daisuke Oyama

University of Tokyo - Faculty of Economics

Satoru Takahashi

National University of Singapore (NUS) - Department of Economics

Date Written: November 12, 2020

Abstract

What outcomes can be implemented by the choice of an information structure in binary-action super-modular 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) and fully implementable (induced by all equilibria). 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. Full implementation requires sequential obedience in both directions. Our characterization of smallest equilibrium implementation can be used to solve the information design problem with adversarial equilibrium selection.

Keywords: Information design, supermodular game, smallest equilibrium implementation, sequential obedience, potential game

JEL Classification: C72, D72

Suggested Citation

Morris, Stephen Edward and Oyama, Daisuke and Takahashi, Satoru, Implementation via Information Design in Binary-Action Supermodular Games (November 12, 2020). Available at SSRN: https://ssrn.com/abstract=3697335 or http://dx.doi.org/10.2139/ssrn.3697335

Stephen Edward Morris (Contact Author)

MIT ( email )

77 Massachusetts Avenue
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Cambridge, MA 02139-4307
United States

HOME PAGE: http://https://economics.mit.edu/faculty/semorris

Daisuke Oyama

University of Tokyo - Faculty of Economics ( email )

7-3-1 Hongo, Bunkyo-ku
Tokyo 113-0033
Japan

Satoru Takahashi

National University of Singapore (NUS) - Department of Economics ( email )

1 Arts Link, AS2 #06-02
Singapore 117570, Singapore 119077
Singapore

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