Abstract
We study the inefficiency of mixed Nash 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 in Proceedings of the 45th symposium on theory of computing (STOC ’13), 2013) 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 mixed Nash equilibria in 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 with respect to social welfare, revenue and maximum bid.
Highlights
It is a common economic phenomenon in competitions that agents make irreversible investments without knowing the outcome
We study the efficiency of mixed Nash equilibria in all-pay auctions with complete information, from a worst-case analysis perspective, using the price of anarchy [16] as a measure
We study the equilibria induced from allpay mechanisms in three fundamental resource allocation scenarios; combinatorial auctions, multi-unit auctions and single-item auctions
Summary
It is a common economic phenomenon in competitions that agents make irreversible investments without knowing the outcome. The all-pay auction can be viewed as a single-prize contest, where the payments correspond to the effort that players make in order to win the competition. We study the equilibria induced from allpay mechanisms in three fundamental resource allocation scenarios; combinatorial auctions, multi-unit auctions and single-item auctions. Each player has different preferences for different subsets of the items and this is expressed via a valuation set function. A multi-unit auction can be considered as an important special case, where there are multiple copies of a single good. The valuations of the players are not set functions, but depend only on the number of copies received. All-pay auctions have received a lot of attention for the case of a single item, as they model all-pay contests and procurements via contests
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