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Rationalizable Bidding in General First-Price Auctions

  • Pierpaolo Battigalli
  • Marciano Siniscalchi

We wish to analyze the consequences of strategically sophisticated bidding without assuming equilibrium behavior. As a first step, we characterize interim rationalizable bids in first-price auctions with interdependent values and affiliated signals. We show that (1) every non-zero bid below the equilibrium is rationalizable, (2) some bids above the equilibrium are rationalizable, (3) the upper bound on rationalizable bids of a given player is a continuous, non-decreasing function of her signal/valuation. In the special case of symmetric bidders with independent signals and quasi-linear valuation functions, (i) the least upper bound on rationalizable bids is increasing and concave; hence (ii) rationalizability is consistent with substantial shading for high valuations, but only little shading for low valuations. Our main technical contribution is to show that the set of rationalizable bids is essentially determined by iteratively solving a simple one-dimensional optimization problem. We argue that our theoretical analysis may shed some light on experimental findings about deviations from the risk-neutral Nash equilibrium.

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Paper provided by IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University in its series Working Papers with number 190.

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Handle: RePEc:igi:igierp:190
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  1. Morris, Stephen & Skiadas, Costis, 2000. "Rationalizable Trade," Games and Economic Behavior, Elsevier, vol. 31(2), pages 311-323, May.
  2. Goeree, Jacob K. & Holt, Charles A. & Palfrey, Thomas R., 2002. "Quantal Response Equilibrium and Overbidding in Private-Value Auctions," Journal of Economic Theory, Elsevier, vol. 104(1), pages 247-272, May.
  3. Eddie Dekel & Asher Wolinsky, 2001. "Rationalizable outcomes of large independent private-value first-price discrete auctions," Discussion Papers 1321, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Paul Klemperer, 1997. "Auctions with Almost Common Values: The Wallet Game and its Applications," Economics Series Working Papers 1998-W03, University of Oxford, Department of Economics.
  5. Friedman, Daniel, 1992. "Theory and Misbehavior of First-Price Auctions: Comment," American Economic Review, American Economic Association, vol. 82(5), pages 1374-78, December.
  6. Drew Fudenberg & Eddie Dekel, 1987. "Rational Behavior with Payoff Uncertainty," Working papers 471, Massachusetts Institute of Technology (MIT), Department of Economics.
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  8. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
  9. Roger B. Myerson, 1978. "Optimal Auction Design," Discussion Papers 362, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. Cox, James C & Smith, Vernon L & Walker, James M, 1988. " Theory and Individual Behavior of First-Price Auctions," Journal of Risk and Uncertainty, Springer, vol. 1(1), pages 61-99, March.
  11. Kagel, John H & Roth, Alvin E, 1992. "Theory and Misbehavior in First-Price Auctions: Comment," American Economic Review, American Economic Association, vol. 82(5), pages 1379-91, December.
  12. Cox, James C & Smith, Vernon L & Walker, James M, 1992. "Theory and Misbehavior of First-Price Auctions: Comment," American Economic Review, American Economic Association, vol. 82(5), pages 1392-412, December.
  13. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
  14. Harrison, Glenn W, 1989. "Theory and Misbehavior of First-Price Auctions," American Economic Review, American Economic Association, vol. 79(4), pages 749-62, September.
  15. Battigalli, P., 1999. "Rationalizability in Incomplete Information Games," Economics Working Papers eco99/17, European University Institute.
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