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

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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.

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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)

  • 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 

  • 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 

  • 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 

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Correspondence to Takahiro Watanabe.

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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.

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Watanabe, T., Yamato, T. A choice of auction format in seller cheating: a signaling game analysis. Economic Theory 36, 57–80 (2008).

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