• Open Access

Supermodular mechanism design

Authors

  • Laurent Mathevet

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    • I am profoundly grateful to Federico Echenique, Matt Jackson, Preston McAfee, and Leeat Yariv for their help and encouragement. Special thanks are due to Rabah Amir for his insightful comments as a discussant at the IESE Conference on Complementarities, and to Morgan Kousser, John Ledyard, Thomas Palfrey, Eran Shmaya, and David Young for helpful advice and conversations. I also wish to thank anonymous referees for thoughtful suggestions as well as Kim Border, Chris Chambers, Paul J. Healy, Bong Chan Koh, Serkan Kucuksenel, Paul Milgrom, and seminar/conference participants at Caltech, Stanford GSB, IESE, UBC, UC Irvine, UT Austin, Carnegie Mellon, Oxford, INSEAD, Autonoma de Barcelona, Pompeu Fabra, LBS, the 5th LGS Conference, and the Game Theory Conference at Stony Brook. The HSS Division at Caltech, Matt Jackson, and Andrea Mattozzi are gratefully acknowledged for financial support. Part of this paper was written while I was visiting Stanford Economics Department, and I am grateful for their hospitality.


Abstract

This paper introduces a mechanism design approach that allows dealing with the multiple equilibrium problem, using mechanisms that are robust to bounded rationality. This approach is a tool for constructing supermodular mechanisms, i.e., mechanisms that induce games with strategic complementarities. In quasilinear environments, I prove that if a social choice function can be implemented by a mechanism that generates bounded strategic substitutes—as opposed to strategic complementarities—then this mechanism can be converted into a supermodular mechanism that implements the social choice function. If the social choice function also satisfies some efficiency criterion, then it admits a supermodular mechanism that balances the budget. Building on these results, I address the multiple equilibrium problem. I provide sufficient conditions for a social choice function to be implementable with a supermodular mechanism whose equilibria are contained in the smallest interval among all supermodular mechanisms. This is followed by conditions for supermodular implementability in unique equilibrium. Finally, I provide a revelation principle for supermodular implementation in environments with general preferences.

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