Supermodular Mechanism Design
Theoretical Economics 5(2010),403–443 1555-7561/20100403 Supermodular mechanism design L M Department of Economics, University of Texas This paper introduces a mechanism design approach that allows dealing with the multiple equilibrium problem, using mechanisms that are robust to bounded ra- tionality. 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 strate- gic complementarities—then this mechanism can be converted into a supermod- ular 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 equilib- rium. Finally, I provide a revelation principle for supermodular implementation in environments with general preferences. K.Implementation,mechanisms,multipleequilibriumproblem,learn- ing, strategic complementarities, supermodular games. JEL .C72,D78,D83. 1. I For the economist designing contracts, taxes, or other institutions, there is a dilemma between the simplicity of a mechanism and the multiple equilibrium problem. On the one hand, simple mechanisms often restrict attention to the “right” equilibria. In public good contexts, for example, most tax schemes overlook inefficient equilibrium situa- tions, provided that one equilibrium outcome is a social optimum.
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