Investment Incentives in Truthful Approximation Mechanisms

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