Skip to main content

A choice of auction format in seller cheating: a signaling game analysis

Abstract

In this paper, we examine which auction format, first-price or second-price, a seller will choose when he can profitably cheat in a second price auction by observing all bids by possible buyers and submitting a shill bid as pretending to be a buyer. We model this choice of auction format in seller cheating as a signaling game in which the buyers may regard the selection of a second price auction by the seller as a signal that he is a shill bidder. By introducing trembling-hand perfectness as a refinement of signaling equilibrium, we find two possible strictly perfect signaling equilibria. One is a separating equilibrium in which a noncheating honest seller selects a first price auction and a cheating seller does a second price auction. In another pooling equilibrium, however, both cheating and non-cheating sellers select a second price auction. The conclusion that a seller chooses a second price auction even if he cannot cheat is in contrast to the previous literature, which focused on the case of independent values.

This is a preview of subscription content, access via your institution.

References

  1. Bag P.K., Dinlersoz E.M., Wang R. (2000) More on phantom bidding. Econ Theory 15: 701–707

    Article  Google Scholar 

  2. Banks J.S., Sobel J. (1987). Equilibrium selection in signaling games. Econometrica 55: 647–663

    Article  Google Scholar 

  3. Chakraborty I., Kosmopoulou G. (2004). Auctions with shill bidding. Econ Theory 24: 271–287

    Article  Google Scholar 

  4. Cho I.K., Kreps D. (1987). Signaling games and stable equilibria. Q J Econ 102: 179–221

    Article  Google Scholar 

  5. Graham D.A., Marshall R.C., Richard J.-F. (1990). Phantom bidding against heterogeneous bidders. Econ Lett 32: 13–17

    Article  Google Scholar 

  6. Grossman S.J., Perry M. (1986). Sequential bargaining under asymmetric information. J Econ Theory 39: 97–119

    Article  Google Scholar 

  7. Iwasaki A., Yokoo M., Terada K. (2005). A robust open ascending-price multi-unit auction protocol against false-name bids. Decis Support Syst 39(1): 23–39

    Article  Google Scholar 

  8. Krishna V. (2002). Auction Theory. New York, Academic

    Google Scholar 

  9. McAfee R.P., McMillan J. (1987). Auctions and bidding. J Econ Lit 25: 699–738

    Google Scholar 

  10. Menezes F.M., Monteiro P.K. (2005). An Introduction to Auction Theory. Oxford, Oxford University Press

    Google Scholar 

  11. Milgrom P., Weber R. (1982). A theory of auctions and competitive bidding. Econometrica 50: 1089–1122

    Article  Google Scholar 

  12. Myerson R. (1981). Optimal auction design. Math Oper Res 6: 58–73

    Article  Google Scholar 

  13. Okada A. (1981). On stability of perfect equilibrium points. Int J Game Theory 10: 67–73

    Article  Google Scholar 

  14. Porter R., Shoham Y. (2005). On cheating in sealed-bid auctions. Decis Support Syst 39: 41–54

    Article  Google Scholar 

  15. Rothkopf M.H., Harstad R.M. (1995). Two models of bid-taker cheating in Vickrey auctions. J Bus 68: 257–267

    Article  Google Scholar 

  16. Rothkopf M.H., Teisberg T.J., Kahn E.P. (1990). Why are Vickrey auctions rare?. J Polit Econ 98: 94–109

    Article  Google Scholar 

  17. Selten R. (1975). Reexamination of the perfectness concept for equilibrium points in extensive games. Int J Game Theory 4: 25–55

    Article  Google Scholar 

  18. Vickrey W. (1961). Counterspeculation, auctions, and competitive sealed tenders. J Finance 16(1): 8–37

    Article  Google Scholar 

  19. Watanabe, T., Yamato, T.: Cheating in second price auctions with affiliated values. In: Proceedings of IEEE Pacific Rim International Workshop on Electronic Commerce 2006, (forthcoming) (2006)

  20. Yokoo M., Sakurai Y., Matsubara S. (2001). Robust combinatorial auction protocol against false-name bids. Artif Intell J 130(2): 167–181

    Article  Google Scholar 

  21. Yokoo M., Sakurai Y., Matsubara S. (2004). The effect of false-name bids in combinatorial auctions: new fraud in Internet auctions. Games Econ Behav 46(1): 174–188

    Article  Google Scholar 

  22. Yokoo M., Sakurai Y., Matsubara S. (2005). Robust double auction protocol against false-name bids. Decis Support Syst 39(2): 241–252

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Takahiro Watanabe.

Additional information

We thank an anonymous referee for useful comments that have improved the paper. This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (B) 15310023 and (C) 18530139.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Watanabe, T., Yamato, T. A choice of auction format in seller cheating: a signaling game analysis. Economic Theory 36, 57–80 (2008). https://doi.org/10.1007/s00199-007-0262-3

Download citation

Keywords

  • Auction
  • Cheating
  • Signaling game

JEL Classification Numbers

  • C72
  • D44
  • D82