Investment Incentives in Near-Optimal Mechanisms

Abstract

In a Vickrey auction, if one bidder can invest to increase his value, the combined mechanism including investments is still fully optimal. By contrast, for any β < 1, there exist monotone allocation rules that guarantee a fraction β of the allocative optimum in the worst case, but such that the associated mechanism with investments by one bidder can lead to arbitrarily small fractions of the full optimum being achieved. We show that if a monotone allocation rule “excludes bossy negative externalities” and guarantees a fraction β in the worst case, then that guarantee persists when investment is possible.

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

JEL Classification: D44, D47, D82