Second-best efficiency of allocation rules: strategy-proofness and single-peaked preferences with multiple commodities
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Second-best efficiency of allocation rules: strategy-proofness and single-peaked preferences with multiple commodities Hidekazu Anno · Hiroo Sasaki
Received: 23 May 2012 / Accepted: 17 November 2012 © Springer-Verlag Berlin Heidelberg 2012
Abstract We study strategy-proof allocation rules in economies with perfectly divisible multiple commodities and single-peaked preferences. In this setup, it is known that the incompatibility among strategy-proofness, Pareto efficiency and nondictatorship arises in contrast with the Sprumont (Econometrica 59:509–519, 1991) one commodity model. We first investigate the existence problem of strategy-proof and second-best efficient rules, where a strategy-proof rule is second-best efficient if it is not Pareto-dominated by any other strategy-proof rules. We show that there exists an egalitarian rational (consequently, non-dictatorial) strategy-proof rule satisfying second-best efficiency. Second, we give a new characterization of the generalized uniform rule with the second-best efficiency in two-agent case. Keywords Strategy-proofness · Single-peaked preference · Second-best efficiency · Generalized uniform rule JEL Classification
D63 · D71 · D78
1 Introduction Ever since Sprumont (1991), resource allocation problems in economies with singlepeaked preferences have been studied by many authors. As is pointed out in Sprumont
H. Anno (B) Graduate School of Fundamental Science and Engineering, Waseda university, 3-4-1 Okubo, Shinjuku-ku, Tokyo, Japan e-mail: [email protected] H. Sasaki School of Commerce, Waseda university, 1-6-1 Nishiwaseda, Shinjuku-ku, Tokyo, Japan e-mail: [email protected]
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(1991), a single-peaked preference model may have several important interpretations. One possible interpretation is the “fixed-price economy” interpretation. In this interpretation, the peak of a preference is interpreted as a “Walrasian demand” under a fixed price. Another possible interpretation is a “task-sharing problem”. Suppose that there is a group of agents that is involved in a production process. To complete the task, a fixed amount of (homogeneous) work is needed. Finally, each agent receives a piece of output according to his contribution. In this circumstance, it is natural to assume that each agent has a single-peaked preference over the space of quantity of work (the real line).1 In this paper, we call a mapping that associates each list of preferences with an allocation of resource a resource allocation rule, or simply a rule. If there is only one commodity, Sprumont (1991) presents a characterization of a resource allocation rule called the uniform rule.2 Under the uniform rule, the same amount of the commodity is allotted to everyone except people whose peaks are small enough if excess demand exists or large enough if excess supply exists. He proves that the uniform rule is the only rule that satisfies three axioms: strategy-proofness, Pareto efficiency, and anonymity. Strategy-proofness means that announcing their true preferences is a dominant
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