Multi-unit Object Allocation Problems with Money for (Non)Decreasing Incremental Valuations: Impossibility and Characterization Theorems

ISER DP No. 1097, August 2020

63 Pages Posted: 25 Sep 2020 Last revised: 26 Apr 2022

See all articles by Hiroki Shinozaki

Hiroki Shinozaki

Hitotsubashi University

Tomoya Kazumura

Graduate School of Economics, Kyoto University

Shigehiro Serizawa

Osaka University - Institute of Social and Economic Research (ISER)

Date Written: August 11, 2020

Abstract

We consider the problem of allocating multiple units of an object and collecting payments. Each agent can receive multiple units, and his (consumption) bundle is a pair consisting of the units he receives and his payment. An agent’s preference over bundles may not be quasi-linear. A class of preferences is rich if it includes all quasi-linear preferences with constant incremental valuations. We show that for an odd number of units, if a class of preferences is rich and includes at least one preference exhibiting both decreasing incremental valuations and either positive or negative income effects, then no rule satisfies efficiency, individual rationality, no subsidy for losers, and strategy-proofness. In contrast, for an even number of units, the existence of a rule satisfying the four properties depends on the size of the income effects. We further show that if a rich class of preferences includes only preferences that exhibit nondecreasing incremental valuations, then the generalized Vickrey rule (Saitoh and Serizawa, 2008; Sakai, 2008) is the only rule satisfying the four properties. Our results suggest that (i) there a rule satisfying the four properties “almost” only when preferences exhibit nondecreasing incremental valuations, and (ii) it depends not only on the properties of preferences such as nondecreasing incremental valuations, but also on other
characteristics of the environment such as the number of units.

Keywords: Efficiency, Strategy-Proofness, Non-Quasi-Linear Preferences, Non-Decreasing Marginal Valuations, Decreasing Marginal Valuations, Constant Marginal Valuations, Multi-Unit Auctions

JEL Classification: D44, D47, D71, D82

Suggested Citation

Shinozaki, Hiroki and Kazumura, Tomoya and Serizawa, Shigehiro, Multi-unit Object Allocation Problems with Money for (Non)Decreasing Incremental Valuations: Impossibility and Characterization Theorems (August 11, 2020). ISER DP No. 1097, August 2020, Available at SSRN: https://ssrn.com/abstract=3671180 or http://dx.doi.org/10.2139/ssrn.3671180

Hiroki Shinozaki

Hitotsubashi University ( email )

2-1
Naka
Kunitachi-shi, Tokyo 186-8601
Japan

Tomoya Kazumura

Graduate School of Economics, Kyoto University ( email )

Yoshida-Honmachi, Sakyo-ku, Kyoto
Kyoto, 606-8501
Japan

Shigehiro Serizawa (Contact Author)

Osaka University - Institute of Social and Economic Research (ISER) ( email )

6-1 Mihogaoka
Ibaraki, Osaka 567-0047
Japan
+81 6 6879 8558 (Phone)
+81 6 6878 2766 (Fax)

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
46
Abstract Views
482
PlumX Metrics