On Low-Envy Truthful Allocations

Authors:
Ioannis Caragiannis;Christos Kaklamanis;Panagiotis Kanellopoulos;Maria Kyropoulou
Affiliations:
Research Academic Computer Technology Institute and Department of Computer Engineering and Informatics, University of Patras, Rio, Greece 26500;Research Academic Computer Technology Institute and Department of Computer Engineering and Informatics, University of Patras, Rio, Greece 26500;Research Academic Computer Technology Institute and Department of Computer Engineering and Informatics, University of Patras, Rio, Greece 26500;Research Academic Computer Technology Institute and Department of Computer Engineering and Informatics, University of Patras, Rio, Greece 26500
Venue:
ADT '09 Proceedings of the 1st International Conference on Algorithmic Decision Theory
Year:
2009

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Abstract

We study the problem of allocating a set of indivisible items to players having additive utility functions over the items. We consider allocations in which no player envies the bundle of items allocated to the other players too much. We present a simple proof that deterministic truthful allocations do not minimize envy by characterizing the truthful mechanisms for two players and two items. Also, we present an analysis for uniformly random allocations which are naturally truthful in expectation. These results simplify or improve previous results of Lipton et al.