A fair and truthful mechanism with limited subsidy

Hiromichi Goko, Ayumi Igarashi, Yasushi Kawase, Kazuhisa Makino, Hanna Sumita, Akihisa Tamura, Yu Yokoi and Makoto Yokoo

Games and Economic Behavior, 2024, vol. 144, issue C, 49-70

Abstract: The notion of envy-freeness is a natural and intuitive fairness requirement in resource allocation. With indivisible goods, such fair allocations are not guaranteed to exist. Classical works have avoided this issue by introducing an additional divisible resource, i.e., money. In this paper, we aim to design a truthful allocation mechanism of indivisible goods to achieve fairness and efficiency criteria with a limited amount of subsidy. Following the work of Halpern and Shah, our central question is as follows: to what extent do we need to rely on the power of money to accomplish these objectives? We show that, when agents have matroidal valuations, there is a truthful allocation mechanism that achieves envy-freeness and utilitarian optimality by subsidizing each agent with at most 1, the maximum marginal contribution of each item for each agent. The design of the mechanism rests crucially on the underlying matroidal M-convexity of the Lorenz dominating allocations.

Keywords: Mechanism design with money; Envy-freeness; Resource allocation; Algorithmic game theory (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:144:y:2024:i:c:p:49-70

DOI: 10.1016/j.geb.2023.12.006

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