An Efficient and Incentive Compatible Dynamic Auction for Multiple Complements

Abstract

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Why prices need algorithms

“…There are, however, natural valuation classes V that do not include all unit-demand valuations (many examples appear below). Research on such valuation classes, to which the non-existence results of Gul and Stacchetti [1999] and Milgrom [2000] do not apply, has progressed in a relatively ad hoc fashion, relying on explicit constructions to rule out the existence of Walrasian equilibria in various cases (see, e.g., [Candogan et al 2015;Ben-Zwi et al 2013;Sun and Yang 2014;Candogan and Pekec 2014]). Is a more systematic approach possible?…”

“…There is a large literature on understanding, for var-ious classes V of allowable valuations, what types of prices -item prices, anonymous bundle prices, etc. -are necessary and sufficient to guarantee the existence of pricing equilibria when all consumers have valuations in V (see, e.g., [Parkes and Ungar 2000;Sun and Yang 2006;Candogan et al 2015;Ben-Zwi et al 2013;Sun and Yang 2014;Candogan and Pekec 2014]). The goal of this paper is to formalize a general version of this question, show that the answer is inextricably linked to the computational complexity of well-studied problems (like demand oracles, revenuemaximization, or welfare-maximization), and derive from this connection a number of results for the (non-)existence of pricing equilibria.…”

Equilibrium, Auction, and Generalized Gross Substitutes and Complements

“…A related strand of the literature concerns auctions that apply to more general environments but have to use discriminatory and nonlinear pricing rules; see, e.g., [5,10,12,14,29]. In [50], an anonymous and nonlinear pricing rule is used. Another strand of the literature concerns auction design in the environment where bidders have interdependent values and the goods are multiple but homogeneous; see [2,40].…”

An Efficient and Strategy-Proof Double-Track Auction for Substitutes and Complements

“…Milgrom and Strulovici (2009) examine substitute goods in a more general setting. Sun and Yang (2014) investigate a related but different model in which all items for sale are complementary.…”

“…Although the seller has a reservation value function, she is assumed to reveal this function truthfully. This is a natural assumption from the well-known impossibility result of Myerson and Satterthwaite (1983), saying that it is impossible to design a trading mechanism even just for one buyer and one seller with one 12 The major differences between Sun and Yang (2014) and the current one are (1) while in the current model there are two sets of items, items of each set are substitutable and can be heterogeneous but are complementary to items in the other set, goods in the model of Sun and Yang (2014) are all complementary; (2) while the current model has a Walrasian equilibrium (Sun and Yang 2006) in which the pricing rule is anonymous and linear, the model of Sun and Yang (2014) can only guarantee the existence of a nonlinear pricing Walrasian equilibrium in which the pricing rule is anonymous but nonlinear; (3) while the current auction is a blend of ascending and descending formats where prices are specified on individual items, the auction of Sun and Yang (2014) is and must be a package auction in which prices are specified on bundles of items; (4) there does not exist any transformation between the current model and Sun and Yang (2014) and in fact the structure of equilibrium price vectors for the two models is inherently different; see Sun and Yang (2009, Theorem 3, p. 937;2014, Theorem 1, p. 432). These two models describe two typical, basic, and closely related yet intrinsically different economic environments.…”