Efficient and strategy-proof mechanism under general constraints

Kenzo Imamura () and Yasushi Kawase ()
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Kenzo Imamura: Department of Economics, University of Tokyo
Yasushi Kawase: Graduate School of Information Science and Technology, University of Tokyo

Theoretical Economics, Forthcoming

Abstract: This study investigates efficient and strategy-proof mechanisms for allocating indivisible goods under constraints. First, we examine a setting without endowments. In this setting, we introduce a class of constraints, ordered accessibility, for which the serial dictatorship mechanism is Pareto-efficient (PE), individually rational (IR), and group strategy-proof (GSP). Then, we prove that accessibility is a necessary condition for the existence of PE, IR, and GSP mechanisms. Moreover, we show that the SD mechanism with a dynamically constructed order satisfies PE, IR, and GSP if one school has an arbitrary accessible constraint and each of the other schools has a capacity constraint. Second, we examine a setting with endowments. We find that the \emph{generalized matroid} is a necessary and sufficient condition on the constraint structure for the existence of a mechanism that is PE, IR, and strategy-proof (SP). We also demonstrate that a top trading cycles mechanism satisfies PE, IR, and GSP under any generalized matroid constraint. Finally, we observe that any two out of the three properties---PE, IR, and GSP---can be achieved under general constraints.

Keywords: Matching with constraints; efficient matching; generalized matroid; strategy-proofness (search for similar items in EconPapers)
JEL-codes: C78 D47 D71 (search for similar items in EconPapers)
Date: 2024-09-24
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