Demand Reduction and Inefficiency in Multi-Unit Auctions

Abstract

Auctions often involve the sale of many related goods: Treasury, spectrum and electricity auctions are examples. In multi-unit auctions, a bid for one unit may affect payments for other units won, giving rise to an incentive to shade bids differently across units. We establish that such differential bid shading results generically in ex post inefficient allocations in the uniform-price and pay-as-bid auctions. We also show that, in general, the efficiency and revenue rankings for the two formats are ambiguous. However, in settings with symmetric bidders, the pay-as-bid auction often outperforms. In particular, with diminishing marginal utility, symmetric information and linearity, it yields greater expected revenues. We explain the rankings through multi-unit effects, which have no counterparts in auctions with unit demands. We attribute the new incentives separately to multi-unit but constant marginal utility and diminishing marginal utility.JEL classification: D44, D82, D47, L13, L94

Bargaining in spectrum auctions: A review of the German auction in 2015

“…Instead, they bid on packages that could possibly form a feasible allocation under certain assumptions about the demands of competitors. This can also be considered a form of strategic demand reduction, a phenomenon that has received much attention in the literature on multi-unit auctions (Ausubel and Cramton, 2002;Weber, 1997).…”

“…Gul and Stacchetti (1999) showed that even if the substitutes condition is satisfied, then ascending and linear-price auctions such as the SMRA cannot implement the VCG outcome. In contrast, demand reduction has widely been observed in the field and analyzed game-theoretically (Ausubel and Cramton, 2002).…”

Centralizing Disconnected Markets? An Irrelevance Result

“…5 With n = 2 agents the non-existence of equilibria has long been recognized in the literature when marginal utility is decreasing (e.g. Kyle (1989) from Ausubel et al (2014), Du and Zhu (2016)). …”

“…This strategic behavior is commonly known as "demand-reduction" from standard multi-unit auctions that sell (here trade) one good, given agents have demand for multiple units (see Ausubel et al (2014)). It carries over to the case of multiple goods where the true demand is multi -(here two -) dimensional.…”

Putting Auction Theory to Work: The Simultaneous Ascending Auction

“…If, at round n ϩ 1, bidder j bids straightforwardly, then, regardless of the bids made by others, j 's assignment S ′ j at the end of round n ϩ 1 satisfies S ′ j ∈X j (p j ′), where p j ′ is j 's personalized price at the end of round n ϩ 1. Moreover, j 's tentative profit after any round-what it would earn if the auction were terminated after 9 Ausubel and Cramton (1996) argue that an incentive of this sort is unavoidable in a wide class of auctions, including all those that establish uniform prices for identical objects.…”