Level-k Auctions: Can a Nonequilibrium Model of Strategic Thinking Explain the Winner's Curse and Overbidding in Private-Value Auctions?


  • Vincent P. Crawford,

    1. Dept. of Economics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0508, U.S.A.; vcrawfor@dss.ucsd.edu
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  • Nagore Iriberri

    1. Dept. of Economics and Business, Universitat Pompeu Fabra, Ramon Trias Fargas 25-27, 08005 Barcelona, Spain; nagore.iriberri@upf.edu
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    • Iriberri's work on this project began when she was affiliated with the University of California, San Diego. We are grateful to the National Science Foundation (Crawford), the Centro de Formación del Banco de España (Iriberri), and the Barcelona Economics Program of CREA (Iriberri) for research support; to Pierpaolo Battigalli, Yong Chao, Gary Charness, Olivier Compte, Ignacio Esponda, Erik Eyster, Drew Fudenberg, Charles Holt, Mark Isaac, Philippe Jehiel, John Kagel, Navin Kartik, Muriel Niederle, David Miller, Thomas Palfrey, Charles Plott, Matthew Rabin, Jose Gonzalo Rangel, Ricardo Serrano-Padial, Joel Sobel, Yixiao Sun, and, especially, Dan Levin for helpful discussions; and to Kagel for locating and providing the data from the experiments of Kagel and Levin (1986, 2002), Garvin and Kagel (1994), Kagel, Levin, and Harstad (1995), and Avery and Kagel (1997). A web appendix provides further analysis and detailed calculations.


This paper proposes a structural nonequilibrium model of initial responses to incomplete-information games based on “level-k” thinking, which describes behavior in many experiments with complete-information games. We derive the model's implications in first- and second-price auctions with general information structures, compare them to equilibrium and Eyster and Rabin's (2005) “cursed equilibrium,” and evaluate the model's potential to explain nonequilibrium bidding in auction experiments. The level-k model generalizes many insights from equilibrium auction theory. It allows a unified explanation of the winner's curse in common-value auctions and overbidding in those independent-private-value auctions without the uniform value distributions used in most experiments.