Strategy-proof and anonymous allocation rules of indivisible goods: A new characterization of Vickrey allocation rule

We consider situations where a society allocates a finite units of an indivisible good among agents, and each agent receives at most one unit of the good. For example, imagine that a government allocates a fixed number of licences to private firms, or imagine that a government distributes equally divided lands to households. We show that the Vickrey allocation rule is the unique allocation rule satisfying strategy-proofness, anonymity and individual rationality. 1. Introduction We consider situations where a society allocates a finite units of an indivisible good among agents, and each agent receives at most one unit of the good. For example, imagine that a government allocates a fixed number of licences to private firms, or imagine that a government distributes equally divided lands to households. 1 A number of allocation rules, including several forms of auction, are proposed for various social purposes such as efficiency , revenue maximization, etc. For the purpose of efficiency, one rule has a remarkable feature. It is " the Vickrey allocation rule ". First, the Vickrey allocation rule allocates the goods to agents evaluating the good highest. (" Efficiency ") Second, the Vickrey allocation rule extracts true information on agents' valuations from them. (" Strategy-Proofness ") Thirdly, the Vickrey allocation rule induces agents' voluntary participation. (" Individual Rationality ") And most importantly, as proved by Holmstrom (1979), the Vickrey allocation rule is the unique rule satisfying these three properties. It is well known that the Vickrey allocation rule also satisfies a property of impartiality called " anonymity ". In this paper, we characterize the Vickrey allocation rule by focusing on anonymity instead of efficiency. Our characterization emphasizes that the Vickrey allocation rule also has a remarkable feature for the purpose of impartiality. An allocation rule is generally formulated as a function from the set of agents' valuations on the good to the feasible set. An allocation rule is efficient if it allocates the goods to agents evaluating the good highest. Given an allocation rule, since agents' private valuations are not known to the others, there may be incentives for agents to misrepresent their values in order to manipulate the final outcomes to their favor. As a result, the actual outcomes may not constitute a socially desirable allocation relative to agents' true valuations. Therefore, allocation rules need to be immune to such strategic misrepresen-tation in order to securely attain a desirable allocation for agents' true …