Multi-Item Auctions

Demange, Gabrielle; Gale, David; Sotomayor, Marilda

doi:10.1086/261411

Cited by 491 publications

(409 citation statements)

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“…5 As such, our work echoes Demange, Gale and Sotomayor (1986) and Fox and Bajari's (2013) study of the FCC spectrum auctions, both of which apply an assignment game approach to multi-unit auctions.…”

Section: Introductionmentioning

confidence: 75%

To Score or Not to Score? Estimates of a Sponsored Search Auction Model

2015

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We estimate a structural model of a sponsored search auction model. To accommodate the "position paradox", we relax the assumption of decreasing click volumes with position ranks, which is often assumed in the literature. Using data from "Website X", one of the largest online marketplaces in China, we find that merchants of different qualities adopt different bidding strategies: high quality merchants bid more aggressively for informative keywords, while low quality merchants are more likely to be sorted to the top positions for vague keywords. Counterfactual evaluations show that the price trend becomes steeper after moving to a score-weighted generalized second price auction, with much higher prices obtained for the top position but lower prices for the other positions. Overall there is only a very modest change in total revenue from introducing popularity scoring, despite the intent in bid scoring to reward popular merchants with price discounts. JEL classification numbers: D44; D47; C11; C15

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Section: Introductionmentioning

confidence: 75%

To Score or Not to Score? Estimates of a Sponsored Search Auction Model

2015

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“…The optimal primal satisfies the conditions (4) and (5) which are same as (1) and (2). Complementary slackness conditions (7) and the fact βj = 0 and the dual feasibility conditions (6) give:…”

Section: A Parametrized Linear Programming Formulationmentioning

confidence: 99%

“…This algorithm has an auction interpretation, where traders outbid each other to acquire goods of their choice by submitting a bid that is a factor (1 + ǫ) of the current winning bid. Prior to this, auction algorithms have been proposed for maximum weight matching in bipartite graphs and network flow problems [6,3,2].…”

Section: An Auction Algorithm For Market Clearing Pricesmentioning

confidence: 99%

Auction Algorithms for Market Equilibrium

Garg

Kapoor

2006

Mathematics of OR

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In this paper we study algorithms for computing market equilibrium in markets with linear utility functions. The buyers in the market have an initial endowment given by a portfolio of items. The market equilibrium problem is to compute a price vector which ensures market clearing, i.e. the demand of a good equals its supply, and given the prices, each buyer maximizes its utility. The problem is of considerable interest in Economics. This paper presents a formulation of the market equilibrium problem as a parameterized linear program. We construct the dual of these parametrized linear programs. We show that finding the market equilibrium is the same as finding a linear-program from the family of programs where the optimal dual solution satisfies certain properties. The market clearing conditions arise naturally from complementary slackness conditions.We then define an auction mechanism which computes prices such that approximate market clearing is achieved. The algorithm we obtain outperforms previously known methods.

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“…Demange et al (1986) propose an ascending bid auction mechanism a version of the Hungarian algorithm for the assignment problem (Dantzig, 1963) and generalizes the Vickerey second-price auction. This auction, as well as Vickrey's, produces the minimum equilibrium price.…”

Section: Introductionmentioning

confidence: 99%

“…There is also a simple proof of Sotomayor (1999) using combinatorial arguments. Demange et al (1986) present two dynamic mechanisms that lead to the minimum competitive equilibria. Crawford and Knoer (1981) introduced one of these mechanisms, which is a generalization of the deferred acceptance algorithm of Gale and Shapley (1962).…”

Section: Introductionmentioning

confidence: 99%

A simultaneous descending bid auction for multiple items and unitary demand

Sotomayor¹

2002

Rev. Bras. Econ.

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Summary: 1. Introduction; 2. The competitive market and the auction mechanism; 3. The main results; 4. Concluding remarks.Keywords: auction mechanism; competitive equilibrium; demand set.JEL codes: C78 and D78. This paper proposes a new descending bid method for auctioning multiple objects. The auctioneer announces a current price, bidders indicate their demands at that price, and the auctioneer lowers the prices until every object can be allocated to a buyer who demands it and no buyer receives more than one item. The features of this mechanism lie on the facts that: the objects are sold simultaneously at prices that clear the market; every two similar objects are sold at the same price; the mechanism always produces the same final price, namely, the maximum competitive equilibrium price. In addition, the auctioneer can choose an efficient allocation.Este artigo propõe um novo método de lances descendentes para leiloar múltiplos objetos com demanda unitária. O leiloeiro anuncia um preço, os compradores indicam suas demandas ao preço anunciado, e o leiloeiro desce os preços até que todo objeto esteja alocado para algum comprador que o tenha demandado e ninguém esteja comprando mais do que um item. Os aspectos importantes deste mecanismo são que os objetos são vendidos simultaneamente a preços competitivos, quaisquer dois objetos similares são vendidos ao mesmo preço e independentemente das escolhas do leiloeiro o mecanismo sempre produz o mesmo preço final, o preço máximo de equilíbrio competitivo. Além disso,é sempre possível para o leiloeiro escolher uma alocação eficiente.

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Multi-Item Auctions

Cited by 491 publications

References 4 publications

To Score or Not to Score? Estimates of a Sponsored Search Auction Model

To Score or Not to Score? Estimates of a Sponsored Search Auction Model

Auction Algorithms for Market Equilibrium

A simultaneous descending bid auction for multiple items and unitary demand

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