Fair and Truthful Mechanism with Limited Subsidy

37 Pages Posted: 5 May 2022

See all articles by Hiromichi Goko

Hiromichi Goko

Toyota Motor Corporation

Ayumi Igarashi

National Institute of Informatics

Yasushi Kawase

University of Tokyo

Kazuhisa Makino

Kyoto University

Hanna Sumita

Tokyo Institute of Technology

Akihisa Tamura

Keio University - Keio Economic Observatory

Yu Yokoi

National Institute of Informatics

Makoto Yokoo

Kyushu University

Abstract

The notion of envy-freeness is a natural and intuitive fairness requirement in resource allocation. With indivisible goods, such fair allocations are unfortunately not guaranteed to exist. Classical works have avoided this issue by introducing an additional divisible resource, i.e., money, to subsidize envious agents. In this paper, we aim to design a truthful allocation mechanism of indivisible goods to achieve both 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

Suggested Citation

Goko, Hiromichi and Igarashi, Ayumi and Kawase, Yasushi and Makino, Kazuhisa and Sumita, Hanna and Tamura, Akihisa and Yokoi, Yu and Yokoo, Makoto, Fair and Truthful Mechanism with Limited Subsidy. Available at SSRN: https://ssrn.com/abstract=4100937 or http://dx.doi.org/10.2139/ssrn.4100937

Hiromichi Goko

Toyota Motor Corporation ( email )

Japan

Ayumi Igarashi (Contact Author)

National Institute of Informatics ( email )

Yasushi Kawase

University of Tokyo ( email )

Kazuhisa Makino

Kyoto University ( email )

Hanna Sumita

Tokyo Institute of Technology ( email )

Akihisa Tamura

Keio University - Keio Economic Observatory ( email )

Yu Yokoi

National Institute of Informatics ( email )

Makoto Yokoo

Kyushu University ( email )

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