Truthful and Competitive Double Auctions
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
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E-commerce web-sites such as Ebay as well as advertising exchanges (AdX) such as DoubleClick's, RightMedia, or AdECN work as intermediaries who sell items (e.g. page-views) on behalf of a seller (e.g. a publisher) to buyers on the opposite side of the market (e.g., advertisers). These platforms often use fixed-percentage sharing schemes, according to which (i) the platform runs an auction amongst buyers, and (ii) gives the seller a constant-fraction (e.g., 80%) of the auction proceeds. In these settings, the platform faces asymmetric information regarding both the valuations of buyers for the item (as in a standard auction environment) as well as about the seller's opportunity cost of selling the item. Moreover, platforms often face intense competition from similar market places, and such competition is likely to favor auction rules that secure high payoffs to sellers. In such an environment, what selling mechanism should platforms employ? Our goal in this paper is to study optimal mechanism design in settings plagued by competition and two-sided asymmetric information, and identify conditions under which the current practice of employing constant cuts is indeed optimal. In particular, we first show that for a large class of competition games, platforms behave in equilibrium as if they maximize a a convex combination of seller's payoffs and platform's revenue, with weight α on the seller's payoffs (which is proxy for the intensity of competition in the market). We generalize the analysis of Myerson and Satterthwaite (1983), and derive the optimal direct-revelation mechanism for each α. As expected, the optimal mechanism applies a reserve price which is decreasing in α. Next, we present an indirect implementation based on ``sharing schemes". We show that constant cuts are optimal if and only if the opportunity cost of the seller has a power-form distribution, and derive a simple formula for computing the optimal constant cut as a function of the sellers' distribution of opportunity costs, and the market competition proxy α. Finally, for completeness, we study the case of a seller's optimal auction with a fixed profit for the platform, and derive the optimal direct and indirect implementations in this setting.