Investment Incentives in Truthful Approximation Mechanisms

36 Pages Posted: 13 Apr 2020 Last revised: 17 May 2022

See all articles by Mohammad Akbarpour

Mohammad Akbarpour

Stanford University

Scott Duke Kominers

Harvard University

Kevin Michael Li

affiliation not provided to SSRN

Shengwu Li

Harvard University - Society of Fellows

Paul R. Milgrom

Stanford University

Date Written: May 16, 2022

Abstract

We study investment incentives in truthful mechanisms that allocate resources using approximation algorithms instead of exact optimization. In such mechanisms, the price a bidder pays to acquire resources is generally not equal to the change in other bidders’ welfare—and these externalities skew investment incentives. Some approximation algorithms are arbitrarily close to efficient, but create such perverse investment incentives that their worst-case welfare guarantees fall to zero when bidders can invest before participating in the mechanism. We show that an algorithm’s guarantees in the allocation and investment problems coincide if and only if that algorithm’s “confirming” negative externalities are sufficiently small. Algorithms that exclude confirming negative externalities entirely (XCONE algorithms) thus have the same worst-case performance for the allocation and investment problems.

Keywords: Combinatorial optimization, Knapsack problem, Investment, Auctions, Approximation, Algorithms

JEL Classification: D44, D47, D82

Suggested Citation

Akbarpour, Mohammad and Kominers, Scott Duke and Li, Kevin Michael and Li, Shengwu and Milgrom, Paul R., Investment Incentives in Truthful Approximation Mechanisms (May 16, 2022). Available at SSRN: https://ssrn.com/abstract=3544100 or http://dx.doi.org/10.2139/ssrn.3544100

Mohammad Akbarpour

Stanford University ( email )

Scott Duke Kominers

Harvard University ( email )

Rock Center
Harvard Business School
Boston, MA 02163
United States

HOME PAGE: http://www.scottkom.com/

Kevin Michael Li

affiliation not provided to SSRN

Shengwu Li (Contact Author)

Harvard University - Society of Fellows ( email )

Cambridge, MA
United States

Paul R. Milgrom

Stanford University ( email )

Landau Economics Building
579 Serra Mall
Stanford, CA 94305-6072
United States
+1-650-723-3397 (Phone)
+1-419-791-8545 (Fax)

HOME PAGE: www.milgrom.net

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