Numerical Analysis of Asymmetric First Price Auctions

Marshall, Robert C.; Meurer, Michael; Richard, Jacques; Stromquist, Walter

doi:10.1006/game.1994.1045

Cited by 161 publications

(114 citation statements)

References 10 publications

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“…The dominant strategy in second-price, private-values auctions does not depend on symmetry. Marshall et al (1994) calculate numerically the independent private-values first-price equilibrium for the example of uniformly distributed types, either two bidders or one bidder facing a cartel. Waehrer (1994), Maskin and Riley (2000a), and Lebrun (1999) have some qualitative characterizations of independent private-values first-price equilibria.…”

Section: Introductionmentioning

confidence: 99%

Is Subsidizing Inefficient Bidders Actually Costly?

Rothkopf

Harstad

2003

Management Science

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A widespread practice, particularly in public-sector procurement and dispersal, is to subsidize a class of competitors believed to be at an economic disadvantage. Arguments for such policies vary, but they typically assume that benefits of subsidization must be large enough to outweigh a presumed economic cost of the subsidy. When disadvantaged competitors compete in auctions, the subsidy serves to make them more competitive rivals. Other bidders rationally respond by bidding more aggressively. We consider a model of procurement auctions and show that a policy of subsidizing inefficient competitors can lower expected project cost and also enhance economic efficiency. Some subsidy is generally better than no subsidy for a wide range of parameters.

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Section: Introductionmentioning

confidence: 99%

Is Subsidizing Inefficient Bidders Actually Costly?

Rothkopf

Harstad

2003

Management Science

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“…The previous reasoning can be applied to establish the stability of a bidding ring R N if v is superadditive on R. Such a property indeed holds in examples proposed by McAfee and McMillan (1992) and Marshall et al (1994).…”

Section: Standard …Rst Price Auctionsmentioning

confidence: 60%

“…The ex ante formation of rings is assumed explicitly in Bajari (2001), Marshall et al (1994) and Waehrer (1999). In these papers, ring mechanisms are investigated within an a priori given partition of the bidders.…”

Section: Introductionmentioning

confidence: 99%

“…Krishna (2002)). Lebrun (1991Lebrun ( , 1999, Marshall et al (1994), Waehrer (1999) and Bajari (2001) introduce bidding rings in …rst price auctions as prototypes of asymmetric bidders. However, in these papers, rings operate as single entities, which automatically share their information, without relying on any (incentive compatible) mechanism.…”

Section: Introductionmentioning

confidence: 99%

“…Thanks to results of Lebrun (1999) and Waehrer (1999), we establish that the grand coalition is always core-stable in a …rst price auction (proposition 3). In the absence of general, analytical solutions for …rst price auctions with asymmetric bidders, we only check that all coalitions are corestable in two speci…c examples, borrowed from McAfee and McMillan (1992) and Marshall et al (1994).…”

Section: Introductionmentioning

confidence: 99%

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Core-stable rings in auctions with independent private values

Biran¹,

Forges²

2011

Games and Economic Behavior

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. We propose a semi-cooperative game theoretic approach to check whether a given coalition is stable in a Bayesian game with independent private values. The ex ante expected utilities of coalitions, at an incentive compatible (noncooperative) coalitional equilibrium, describe a (cooperative) partition form game. A coalition is core-stable if the core of a suitable characteristic function, derived from the partition form game, is not empty. As an application, we study collusion in auctions in which the bidders' final utility possibly depends on the winner's identity. We show that such direct externalities offer a possible explanation for cartels' structures (not) observed in practice. Terms of use: Documents in EconStor mayJEL-Code: C71, C72, D44.

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Approximation of Nash equilibria in Bayesian games

Armantier

Florens

Richard

2008

J of Applied Econometrics

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We de…ne a new concept of Constrained Strategic Equilibrium (CSE) for Bayesian games. We show that a sequence of CSEs approximates an equilibrium under standard conditions. We also provide an algorithm to implement the CSE approximation method numerically in a broad class of Bayesian games, including games without analytically tractable solutions. Finally, we illustrate the ‡exibility of the CSE approximation with a series of auction examples, including a complex multi-unit auction. Olivier Armantier and Jean-Francois Richard acknowledge …nancial support from the National Science Foundation grant SBR-9601220. We would like to thank Marie-Anne Hugo, John Kagel, Philip Reny, Alvin Roth, and Yves Sprumont for helpful discussions. We are especially grateful to Soiliou Daw Namoro for his help with one of the proofs. Finally, we would like to thank the three referees and the editors for their comments. All remaining errors are ours.

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Numerical Analysis of Asymmetric First Price Auctions

Cited by 161 publications

References 10 publications

Is Subsidizing Inefficient Bidders Actually Costly?

Is Subsidizing Inefficient Bidders Actually Costly?

Core-stable rings in auctions with independent private values

Approximation of Nash equilibria in Bayesian games

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