# Strategy-proofness versus symmetry in economies with an indivisible good and money

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## Abstract

We consider the problem of allocating a single indivisible good among \(n\) agents when monetary transfers are allowed. We study the possibility of constructing strategy-proof, symmetric, and budget balanced mechanisms. We show that there is no strategy-proof, symmetric, and budget balanced mechanism (under the weak domain condition that the set of agent’s possible valuations includes at least \(n+1\) common valuations). Moreover, this result implies that there is no strategy-proof, symmetric, and budget balanced mechanism (i) in the model where agents may have non-quasilinear preferences, and/or (ii) in the unit-demand model with \(n\) heterogeneous indivisible goods.

## Keywords

Strategy-proofness Symmetry Budget balance Indivisible good Monetary transfer## JEL Classification

C72 D63 D71 D82## Notes

### Acknowledgments

We would like to thank Kazutoshi Ando, an associate editor, and two anonymous referees for helpful suggestions and comments. This research was partially supported by Grant-in-Aid for Scientific Research from Japan Society for the Promotion of Science.

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