# Mechanism design with two alternatives in quasi-linear environments

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## Abstract

We study mechanism design in quasi-linear private values environments when there are two alternatives. We show that under a mild range condition, every implementable allocation rule is a *generalized utility function maximizer*. In unbounded domains, if we replace our range condition by an *independence* condition, then every implementable allocation rule is an affine maximizer. Our results extend Roberts’ affine maximizer theorem (Roberts, In: Laffont J-J (ed) The characterization of implementable choice rules, 1979) to the case of two alternatives.

## Notes

### Acknowledgments

We are extremely grateful to Marc Fleurbaey, Benny Moldovanu, Anup Pramanik, Souvik Roy, Arunava Sen, and Dries Vermulen, and two anonymous referees for useful comments and discussions.

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