On the Inefficiency of the Uniform Price Auction

We present our results on Uniform Price Auctions, one of the standard sealed-bid multi-unit auction formats, for selling multiple identical units of a single good to multi-demand bidders. Contrary to the truthful and economically efficient multi-unit Vickrey auction, the Uniform Price Auction encourages strategic bidding and is socially inefficient in general. The uniform pricing rule is, however, widely popular by its appeal to the natural anticipation, that identical items should be identically priced. In this work we study equilibria of the Uniform Price Auction for bidders with (symmetric) submodular valuation functions, over the number of units that they win. We investigate pure Nash equilibria of the auction in undominated strategies; we produce a characterization of these equilibria that allows us to prove that a fraction 1-1/e of the optimum social welfare is always recovered in undominated pure Nash equilibrium -- and this bound is essentially tight. Subsequently, we study the auction under the incomplete information setting and prove a bound of 4-2/k on the economic inefficiency of (mixed) Bayes Nash equilibria that are supported by undominated strategies.Comment: Additions and Improvements upon SAGT 2012 results (and minor corrections on the previous version

Multi-Unit Auctions with Synergy

In this note we examine four standard multi-unit sealed-bid auctions in the presence of synergy. The structure of the equilibrium bidding strategy under each rule is quite intuitive. Whether the equilibrium involves "bundle-bidding" or "separating-bidding" strategy depends on the presence of the "exposure problem" and the pressure of "demand reduction" in each case. When the bidders can implicitly coordinate to avoid the "exposure problem" and the pressure of "demand reduction," the equilibrium strategy can be calculated using parallels with unit-demand auctions. However, in the presence of the "exposure problem" well-behaved symmetric equilibria that can be characterized by the first-order condition of bidders' maximization problem may not exist in at least some situations.Multi-Unit Auction

Bidding Behavior in Multi-Unit Auctions - An Experimental Investigation

We present laboratory experiments of five different multi-unit auction mechanisms. Two units of a homogeneous object were auctioned off among two bidders with flat demand for two units. We test whether expected demand reduction occurs in open and sealed-bid uniform-price auctions. Revenue equivalence is tested for these auctions as well as for the Ausubel, the Vickrey and the discriminatory sealed-bid auction. Furthermore, we compare the five mechanisms with respect to the efficient allocation of the units.Multi-Unit Auctions, Demand Reduction, Experimental Economics

Multi-Unit Auctions to Allocate Water Scarcity Simulating Bidding Behaviour with Agent Based Models

Multi-unit auctions are promising mechanisms for the reallocation of water. The main advantage of such auctions is to avoid the lumpy bid issue. However, there is great uncertainty about the best auction formats when multi-unit auctions are used. The theory can only supply the structural properties of equilibrium strategies and the multiplicity of equilibria makes comparisons across auction formats difficult. Empirical studies and experiments have improved our knowledge of multi- unit auctions but they remain scarce and most experiments are restricted to two bidders and two units. Moreover, they demonstrate that bidders have limited rationality and learn through experience. This paper constructs an agent-based model of bidders to compare the performance of alternative auction formats under circumstances where bidders submit continuous bid supply functions and learn over time to adjust their bids to improve their net incomes. We demonstrate that under the generalized Vickrey, simulated bids converge towards truthful bids as predicted by the theory and that bid shading is the rule for the uniform and discriminatory auctions. Our study allows us to assess the potential gains from agent-based modelling approaches in the assessment of the dynamic performance of multi-unit procurement auctions. Some recommendations on the desirable format of water auctions are provided.Multi-unit auctions, Learning, Multi-agent models, Water allocation

BIDDING BEHAVIOR IN MULTI-UNIT AUCTIONS - AN EXPERIMENTAL INVESTIGATION AND SOME THEORETICAL INSIGHTS

We present laboratory experiments of five different multi-unit auction mechanisms. Two units of a homogeneous object were auctioned off among two bidders with flat demand for two units. We test whether expected demand reduction occurs in open and sealed-bid uniform-price auctions. Revenue equivalence is tested for these auctions as well as for the Ausubel, the Vickrey and the discriminatory sealed-bid auction. Furthermore, we compare the five mechanisms with respect to the efficient allocation of the units. We also provide some theoretical insights concerning the equilibria of uniform-price auctions with incomplete information.Multi–Unit Auctions, Demand Reduction, Experimental Economics.

Bidding Behavior in Multi-Unit Auctions - An Experimental Investigation and some Theoretical Insights

We present laboratory experiments of five different multi-unit auction mechanisms. Two units of a homogeneous object were auctioned off among two bidders with at demand for two units. We test whether expected demand reduction occurs in open and sealed-bid uniform-price auctions. Revenue equivalence is tested for these auctions as well as for the Ausubel, the Vickrey and the discriminatory sealed-bid auction. Furthermore, we compare the five mechanisms with respect to the efficient allocation of the units. We also provide some theoretical insights concerning the equilibria of uniform-price auctions with incomplete information.Multi-Unit Auctions; Demand Reduction; Experimental Economics

Auctioning Securities

Treasury debt and other divisible securities are traditionally sold in either a pay-your-bid (discriminatory) auction or a uniform-price auction. We compare these auction formats with a Vickrey auction and also with two ascending-bid auctions. The Vickrey auction and the alternative ascending-bid auction (Ausubel 1996) have important theoretical advantages for sellers. In a setting without private information, these auctions achieve the maximal revenue as a unique equilibrium in dominant strategies. In contrast, the pay- your-bid, uniform-price, and standard ascending-bid auction admit a multiplicity of equilibria that yield low revenues for the seller. We show how these results extend to a setting where bidders have affiliated private information. Our results question the standard ways that securities are offered to the public.Auctions; Multi-Unit Auctions, Security Auctions, Treasury Auctions

Online Auctions

The economic literature on online auctions is rapidly growing because of the enormous amount of freely available field data. Moreover, numerous innovations in auction-design features on platforms such as eBay have created excellent research opportunities. In this article, we survey the theoretical, empirical, and experimental research on bidder strategies (including the timing of bids and winner's-curse effects) and seller strategies (including reserve-price policies and the use of buy-now options) in online auctions, as well as some of the literature dealing with online-auction design (including stopping rules and multi-object pricing rules).