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 [22] 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.
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Christodoulou, G., Sgouritsa, A., Tang, B. (2015). On the Efficiency of All-Pay Mechanisms. In: Bansal, N., Finocchi, I. (eds) Algorithms - ESA 2015. Lecture Notes in Computer Science(), vol 9294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48350-3_30
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DOI: https://doi.org/10.1007/978-3-662-48350-3_30
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