The uniqueness of the pivotal mechanisms without strategy-proofness
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The uniqueness of the pivotal mechanisms without strategy-proofness Yuta Nakamura1 Received: 14 September 2019 / Accepted: 15 July 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Moulin (J Public Econ 31:53–78, 1986; Theorem 4) characterizes the pivotal mechanisms without imposing strategy-proofness under the assumption of the full domain. In this paper, we provide a domain property that is necessary and sufficient for Moulin’s characterization without strategy-proofness to hold. We also provide examples of domains that do (not) satisfy our domain property. Keywords Pivotal mechanism · Domain restriction · No free ride · No disposal of utility · Distribution JEL Classification D82 · D47
1 Introduction In his Theorem 4, Moulin (1986) provides a characterization of Clarke’s (1971) pivotal mechanisms without imposing strategy-proofness. The theorem states that efficiency, feasibility, no free ride, and two mild monotonicity axioms characterize the pivotal mechanisms. Moulin’s (1986) characterization is important, because it shows the normative desirability of the pivotal mechanisms, while most of past studies have mainly focused on incentives of individuals given a mechanism. However, since all of Moulin’s (1986) results are shown under the assumption of the full domain, it is still unknown under which restricted domains his characterization is preserved. The model in the present study deals with public decision with a finite number of alternatives and money. Each individual has a quasi-linear preference over these decisions, and we examine the restricted domains of individuals’ private valuations. The special case in the present study includes single-object auction, multi-object auction
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Yuta Nakamura [email protected] School of Economics and Business Administration, Yokohama City University, Yokohama 236-0027, Japan
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Y. Nakamura
(Vickrey 1961), public goods provision (Clarke 1971), and so on. In this context, we present a domain property that is necessary and sufficient for Moulin’s characterization without strategy-proofness to hold. Finding such a domain property is useful for understanding the economic environments under which the use of the pivotal mechanisms is justified by Moulin’s characterization. We also provide examples of domains that do (not) satisfy our domain property. To the best of the author’s knowledge, this study is the first to examine a characterization of the pivotal mechanisms without strategy-proofness after Moulin (1986). However, past studies have identified the domain properties that are necessary and sufficient for characterizing a class of strategy-proof mechanisms. For example, Suijs (1996) and Carbajal (2010) expound the uniqueness of Groves mechanisms, and Chung and Olszewski (2007) and Heydenreich et al. (2009) examine those necessary and sufficient for the payoff equivalence property for strategy-proof mechanisms to hold. While the present study and Suijs (1996) deal with the finite set of alternatives, Heydenreich et al. (2009) and Ca
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