Abstract
We revisit the inefficiency of the uniform price auction, one of the standard multi-unit auction formats, for allocating multiple units of a single good. In the uniform price auction, each bidder submits a sequence of non-increasing marginal bids, one for each additional unit. The per unit price is then set to be the highest losing bid. We focus on the pure Nash equilibria of such auctions, for bidders with submodular valuation functions. Our result is a tight upper and lower bound on the inefficiency of equilibria, showing that the Price of Anarchy is bounded by 2.188. This resolves one of the open questions posed in previous works on multi-unit auctions.
This work has been partly supported by the University of Piraeus Research Center, and by a research program of the Athens University of Economics and Business.
Notes
- 1.
We note that Theorem 2 holds for any deterministic tie-breaking rule.
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Birmpas, G., Markakis, E., Telelis, O., Tsikiridis, A. (2017). Tight Welfare Guarantees for Pure Nash Equilibria of the Uniform Price Auction. In: Bilò, V., Flammini, M. (eds) Algorithmic Game Theory. SAGT 2017. Lecture Notes in Computer Science(), vol 10504. Springer, Cham. https://doi.org/10.1007/978-3-319-66700-3_2
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