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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. Drew Fudenberg & David K. Levine, 1998. "Learning in Games," Levine's Working Paper Archive 2222, David K. Levine.
  2. Roger B. Myerson, 1978. "Optimal Auction Design," Discussion Papers 362, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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  4. Klemperer, Paul, 1998. "Auctions with almost common values: The 'Wallet Game' and its applications," European Economic Review, Elsevier, vol. 42(3-5), pages 757-769, May.
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  8. Battigalli, P., 1999. "Rationalizability in Incomplete Information Games," Economics Working Papers eco99/17, European University Institute.
  9. 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.
  10. E. Dekel & D. Fudenberg, 2010. "Rational Behavior with Payoff Uncertainty," Levine's Working Paper Archive 379, David K. Levine.
  11. 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.
  12. Stephen Morris & Skiadas Costis, 1999. "Rationalizable Trade," Cowles Foundation Discussion Papers 1211, Cowles Foundation for Research in Economics, Yale University.
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  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. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
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