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Asymmetry in first-price auctions with affiliated private values


  • Campo, S.
  • Perrigne, I.
  • Vuong, Q.H.


The existence of cartels, collusion and heterogeneity across firms is known to introduce some asymmetry in bidding games. A major difficulty when considering asymmetric auctions is that the equilibrium strategies are solutions of an intractable system of differential equations. This paper proposes a simple method for estimating asymmetric firs-price auctions within the affiliated private value (APV) paradigm. Specifically, we consider two types of bidders and derive the differential equations characterizing the Bayesian Nash equilibrium strategies. We show that these differential equations can be rewritten using the distribution of observed bids. We then establish the identification of the asymmetric APV model, characterize its theoretical restrictions, and propose an indirect two-step nonparametric estimation procedure for estimating the private value distribution of each type from observed bids. An attractive computational feature of our indirect procedure is that it does not require solving the differential equations for the equilibrium strategies. Moreover, the method can be easily generalized to many types of bidders. An empirical analysis of joint bidding is provided as an illustration. ...French Abstract : L'existence de cartels de firmes, de collusion entre firmes et de différences entre firmes fait naître de l'asymétrie dans les jeux d'enchères. Une difficulté majeure des enchères asymétriques est que les stratégies d'équilibre sont les solutions d'un système complexe d'équations différentielles. Cet article propose une méthode simple pour estimer des modèles d'enchères au premier prix asymétriques dans le paradigme des valeurs privées affiliées (VPA). On considère deux types d'enchereurs et on dérive le système d'équations différentielles caractérisant les stratégies d'équilibre bayesiennes de Nash. Ces équations différentielles peuvent être exprimées à partir des distributions des enchères observées. On montre alors que le modèle est identifié et que le modèle donne des restrictions sur les observables. Une méthode d'estimation nonparamétrique en deux étapes permet d'estimer la distribution des valeurs privées pour chaque type d'enchereurs. Cette méthode présente l'avantage de ne pas avoir à résoudre le système d'équations différentielles et peut être généralisée à plusieurs types d'enchéreurs. Une application à l'analyse d'encherissage par un cartel d'entreprises est proposée.

Suggested Citation

  • Campo, S. & Perrigne, I. & Vuong, Q.H., 2000. "Asymmetry in first-price auctions with affiliated private values," Economics Working Paper Archive (Toulouse) 13, French Institute for Agronomy Research (INRA), Economics Laboratory in Toulouse (ESR Toulouse).
  • Handle: RePEc:rea:inrawp:13

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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