On the Efficiency of All-Pay Mechanisms

TL;DR

This paper analyzes the inefficiency of all-pay auctions across different settings, providing improved bounds and a new mechanism that achieves high efficiency for multi-unit auctions.

Contribution

It offers new bounds on the price of anarchy for combinatorial and single-item all-pay auctions and introduces a novel randomized mechanism for multi-unit auctions with high efficiency.

Findings

Strengthened the upper bound on price of anarchy to 1.82 for combinatorial auctions.

Designed a multi-unit auction mechanism with 75% efficiency and unique pure Nash equilibrium.

Established tight bounds on price of anarchy for single-item all-pay auctions.

Abstract

We study the inefficiency of mixed equilibria, expressed as the price of anarchy, of all-pay auctions in three different environments: combinatorial, multi-unit and single-item auctions. First, we consider item-bidding combinatorial auctions where m all-pay auctions run in parallel, one for each good. For fractionally subadditive valuations, we strengthen the upper bound from 2 [Syrgkanis and Tardos STOC'13] to 1.82 by proving some structural properties that characterize the mixed Nash equilibria of the game. Next, we design an all-pay mechanism with a randomized allocation rule for the multi- unit auction. We show that, for bidders with submodular valuations, the mechanism admits a unique, 75% efficient, pure Nash equilibrium. The efficiency of this mechanism outperforms all the known bounds on the price of anarchy of mechanisms used for multi-unit auctions. Finally, we analyze single-item all-pay auctions motivated by their connection to contests and show tight bounds on the price of anarchy of social welfare, revenue and maximum bid.