Ascending auctions: some impossibility results and their resolutions with final price discounts

When bidders are not substitutes, we show that there is no standard ascend-ing auction that implements a bidder-optimal competitive equilibrium under truthful bidding. Such an impossibility holds also in environments where the Vickrey payoff vector is a competitive equilibrium payoff and is thus stronger than de Vries, Schummer and Vohra s [On ascending Vickrey auctions for het-erogeneous objects, J. Econ. Theory, 132, 95-118] impossibility result with regards to the Vickrey payoff vector under general valuations. Similarly to Mishra and Parkes [Ascending price Vickrey auctions for general valuations, J. Econ. Theory, 132, 335-366], the impossibility can be circumvented by giving price discounts to the bidders from the final vector of prices. Nevertheless, the similarity is misleading: the solution we propose satisfies a minimality infor-mation revelation property that fails to be satisfied in any ascending auction that implements the Vickrey payoffs for general valuations. We investigate related issues when strictly positive increments have to be used under general continuous valuations.ascending auctions ; combinatorial auctions ; bidder-optimal competitive equilibrium ; non-linear pricing ; Vickrey payoffs ; increments

Ascending auctions: some impossibility results and their resolutions with final price discounts

When bidders are not substitutes, we show that there is no standard ascend-ing auction that implements a bidder-optimal competitive equilibrium under truthful bidding. Such an impossibility holds also in environments where the Vickrey payoff vector is a competitive equilibrium payoff and is thus stronger than de Vries, Schummer and Vohra s [On ascending Vickrey auctions for het-erogeneous objects, J. Econ. Theory, 132, 95-118] impossibility result with regards to the Vickrey payoff vector under general valuations. Similarly to Mishra and Parkes [Ascending price Vickrey auctions for general valuations, J. Econ. Theory, 132, 335-366], the impossibility can be circumvented by giving price discounts to the bidders from the final vector of prices. Nevertheless, the similarity is misleading: the solution we propose satisfies a minimality infor-mation revelation property that fails to be satisfied in any ascending auction that implements the Vickrey payoffs for general valuations. We investigate related issues when strictly positive increments have to be used under general continuous valuations.Lorsque les enchérisseurs ne sont pas substituts, nous montrons qu'il n'existe pas de mécanisme d'enchères ascendantes qui implémente un équilibre concurrentiel qui soit optimal pour les enchérisseurs. Un tel résultat d'impossibilité reste vrai dans les environnements où les payements de Vickrey sont concurrentiels et est donc plus fort que le résultat d'impossibilité de De Vries, Schummer et Vohra [On ascending Vickrey auctions for heterogeneous objects, J. Econ. Theory, 132, 95-118] relatif à l'implémentation des payements de Vickrey sans restrictions sur les valuations. De la même manière que dans Mishra et Parkes [Ascending price Vickrey auctions for general valuations, J. Econ. Theory, 132, 335-366], l'impossibilité est levée si l'on autorise une phase de réduction des prix à la fin de l'enchère. La similarité est trompeuse : la solution que l'on propose satisfait une propriété de "minimalité" relativement à la révélation des préférences des enchérisseurs, une propriété qui ne peut être satisfaite dans aucune des enchères qui implémente les payements de Vickrey. Nous analysons aussi la robustesse de tels mécanismes à la présence d'incréments

Ascending Price Vickrey Auctions for General Valuations

Ascending price auctions involving a single price path and buyers paying their final bid price cannot achieve the Vickrey–Clarke–Groves (VCG) outcome in the combinatorial auctions setting. Using a notion called universal competitive equilibrium prices, shown to be necessary and sufficient to achieve the VCG outcome using ascending price auctions, we define a class of ascending price auctions in which buyers bid on a single price path. Truthful bidding by buyers is an ex post Nash equilibrium in such auctions. By giving discounts to buyers from the final price, the VCG outcome is achieved for general valuations.Engineering and Applied Science

Auctions, Bidding and Exchange Design

The different auction types are outlined using a classification framework along six dimensions. The economic properties that are desired in the design of auction mechanisms and the complexities that arise in their implementation are discussed. Some of the most interesting designs from the literature are analyzed in detail to establish known results and to identify the emerging research directions.Engineering and Applied Science

An Iterative Generalized Vickrey Auction: Strategy-Proofness without Complete Revelation

The generalized Vickrey auction (GVA) is a strategy-proof combinatorial auction, in which truthful bidding is the optimal strategy for an agent. In this paper we address a fundamental problem with the GVA, which is that it requires agents to compute and reveal their values for all combinations of items. This can be very difficult for bounded-rational agents with limited or costly computation. We propose an experimental design for an iterative combinatorial auction. We have a theoretical proof that the the auction implements the outcome of the Vickrey auction in special cases, and initial experimental results support our conjecture that the auction implements the outcome of the Vickrey auction in all cases. The auction has better information properties than the sealedbid GVA: in each round agents must only bid for the set of bundles that maximize their utility given current ask prices, which does not require agents to compute their exact values for every bundle.Engineering and Applied Science

Multi-item Vickrey-Dutch auctions

Descending price auctions are adopted for goods that must be sold quickly and in private values environments, for instance in flower, fish, and tobacco auctions. In this paper, we introduce ex post efficient descending auctions for two environments: multiple non-identical items and buyers with unit-demand valuations; and multiple identical items and buyers with non-increasing marginal values. Our auctions are designed using the notion of universal competitive equilibrium (UCE) prices and they terminate with UCE prices, from which the Vickrey payments can be determined. For the unit-demand setting, our auction maintains linear and anonymous prices. For the homogeneous items setting, our auction maintains a single price and adopts Ausubel's notion of "clinching" to compute the final payments dynamically. The auctions support truthful bidding in an ex post Nash equilibrium and terminate with an ex post efficient allocation. In simulation, we illustrate the speed and elicitation advantages of these auctions over their ascending price counterparts.

An Ascending-Price Generalized Vickrey Auction

A simple characterization of the equilibrium conditions required to compute Vickrey payments in the Combinatorial Allocation Problem leads to an ascending price Generalized Vickrey Auction. The ascending auc- tion, iBundle Extend & Adjust (iBEA), maintains non-linear and perhaps non-anonymous prices on bundles of items, and terminates with the ef- cient allocation and the Vickrey payments in ex post Nash equilibrium. Crucially, iBEA is able to implement the Vickrey outcome even when the Vickrey payments are not supported in a single competitive equilibrium. The auction closes with Universal competitive equilibrium prices, which provide enough information to compute individualized discounts to adjust the nal prices and implement Vickrey payments.Engineering and Applied Science

The Role of Auctions in Allocating Public Resources

This paper provides an economic framework within which to consider the effectiveness and limitations of auction markets. The paper looks at the use of auctions as a policy instrument and the effects of auction design on consumer interests, the efficient allocation of resources, and industry competitiveness.Australia; Research; Ascending-bid auction; Auctions; Bidders; Conservation funds; Descending-bid auction; Dutch auction; English auction; Environmental Management; First-price sealed-bid auction; Infrastructure; Markets; Oral auction; Outcry auction; Pollutant emission permits; Power supply contracts; Public resources; Radio- spectrum; Second-price sealed-bid auction Spectrum licences; Vickrey auction; Water rights;

Econometrics for Learning Agents

The main goal of this paper is to develop a theory of inference of player valuations from observed data in the generalized second price auction without relying on the Nash equilibrium assumption. Existing work in Economics on inferring agent values from data relies on the assumption that all participant strategies are best responses of the observed play of other players, i.e. they constitute a Nash equilibrium. In this paper, we show how to perform inference relying on a weaker assumption instead: assuming that players are using some form of no-regret learning. Learning outcomes emerged in recent years as an attractive alternative to Nash equilibrium in analyzing game outcomes, modeling players who haven't reached a stable equilibrium, but rather use algorithmic learning, aiming to learn the best way to play from previous observations. In this paper we show how to infer values of players who use algorithmic learning strategies. Such inference is an important first step before we move to testing any learning theoretic behavioral model on auction data. We apply our techniques to a dataset from Microsoft's sponsored search ad auction system

Multi-Item Vickrey-Dutch Auctions

Descending price auctions are adopted for goods that must be sold quickly and in private values environments, for instance in flower, fish, and tobacco auctions. In this paper, we introduce efficient descending auctions for two environments: multiple non-identical items and buyers with unit-demand valuations; and multiple identical items and buyers with non-increasing marginal values. Our auctions are designed using the notion of universal competitive equilibrium (UCE) prices and they terminate with UCE prices, from which the Vickrey payments can be determined. For the unit-demand setting, our auction maintains linear and anonymous prices. For the homogeneous items setting, our auction maintains a single price and adopts Ausubel's notion of “clinching” to compute the final payments dynamically. The auctions support truthful bidding in an ex post Nash equilibrium and terminate with an efficient allocation. In simulation, we illustrate the speed and elicitation advantages of these auctions over their ascending price counterparts.Engineering and Applied Science