Towards a Characterization of Worst Case Equilibria in the Discriminatory Price Auction

Markakis, Evangelos, Sgouritsa, Alkmini and Tsikiridis, Artem (2022) Towards a Characterization of Worst Case Equilibria in the Discriminatory Price Auction. In: Conference on Web and Internet Economics (WINE) 2021, 2021-12-14 - 2021-12-17, Potsdam, Germany.

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Abstract

We study the performance of the discriminatory price auction under the uniform bidding interface, which is one of the popular formats for running multi-unit auctions in practice. We undertake an equilibrium analysis with the goal of characterizing the inefficient mixed equilibria that may arise in such auctions. We consider bidders with capped-additive valuations, which is in line with the bidding format, and we first establish a series of properties that help us understand the sources of inefficiency. Moving on, we then use these results to derive new lower and upper bounds on the Price of Anarchy of mixed equilibria. For the case of two bidders, we arrive at a complete characterization of inefficient equilibria and show an upper bound of 1.1095, which is also tight. For multiple bidders, we show that the Price of Anarchy is strictly worse, improving the best known lower bound for submodular valuations. We further present an improved upper bound of 4/3 for the special case where there exists a “high” demand bidder. Finally, we also study Bayes-Nash equilibria, and exhibit a separation result that had been elusive so far. Namely, already with two bidders, the Price of Anarchy for Bayes-Nash equilibria is strictly worse than that for mixed equilibria. Such separation results are not always true (e.g., the opposite is known for simultaneous second price auctions) and reveal that the Bayesian model here introduces further inefficiency.

Item Type:	Conference or Workshop Item (Unspecified)
Divisions:	Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User:	Symplectic Admin
Date Deposited:	25 Oct 2021 08:23
Last Modified:	29 Nov 2023 04:18
DOI:	10.1007/978-3-030-94676-0_11
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3141295

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• Towards a Characterization of Worst Case Equilibria in the Discriminatory Price Auction. (deposited 22 Oct 2021 08:04)
  • Towards a Characterization of Worst Case Equilibria in the Discriminatory Price Auction. (deposited 25 Oct 2021 08:23) [Currently Displayed]