Continuous selections from the Pareto correspondence and non-manipulability in exchange economies

Abstract

In n-agent exchange economies, we show that all efficient and continuous rules are "diagonally dictatorial" over the restricted domain of linear preferences and, in the 2-good case, over the domain of homothetic preferences. The diagonal dictator receives the entire endowment whenever all agents have an identical preference. We show that (fully) dictatorial rules are the only rules satisfying, in addition, veto-proofness, the requirement that if truth-telling ever leads to the worst outcome for an agent, he should not be able to escape it, by rnisrepresenting his preference. The same conclusion holds replacing veto-proofness with stronger notions of non-manipulability, veto-proofness* (no one can escape from the worst outcome or switch to the best outcome), weak strategy-proofness (no one can increase his bundle), and strategy-proofness. We extend these results to any larger domain imposing non-bossiness (no one can affect others' bundles without affecting his own). (C) 2003 Elsevier B.V. All rights reserved.