Multiple equilibria in asymmetric first-price auctions

Springer Science and Business Media LLC - Tập 3 - Trang 65-77 - 2014
Todd R. Kaplan1,2, Shmuel Zamir1,3
1Department of Economics, University of Exeter Business School, Exeter, UK
2Deptartment of Economics, University of Haifa, Haifa , Israel
3The Center for the Study of Rationality, The Hebrew University, Jerusalem, Israel

Tóm tắt

Maskin and Riley (Games Econ Behav 45:395–409, 2003) and Lebrun (Games Econ Behav 55:131–151, 2006) prove that the Bayes–Nash equilibrium of first-price auctions is unique. This uniqueness requires the assumption that a buyer never bids above his value (which amounts to the elimination of weakly dominated strategies). We demonstrate that, in asymmetric first-price auctions (with or without a minimum bid), the relaxation of this assumption results in additional equilibria that are substantial. Although in each of these additional equilibria no buyer wins with a bids above his value, the allocation of the object and the selling price may vary among the equilibria. In particular, we show that these yield higher revenue. We show that such phenomena can only occur under certain types of asymmetry in the distributions of values.

Tài liệu tham khảo

Baye, M., Morgan, J.: A folk theorem for one-shot Bertrand games. Econ. Lett. 65(1), 59–65 (1999)

Binmore, K.: Why experiment in economics? Econ. J. 109(453), 16–24 (1999)

Blume, A., Heidhues, P.: All equilibria of the Vickrey auction. J. Econ. Theory 114(1), 170–177 (2004)

Blume, A., Heidhues, P., Lafky, J., Münster, J., Zhang, M.: All equilibria of the multi-unit Vickrey auction. Games Econ. Behav. 66(2), 729–741 (2009)

Erlei, M.: Some forgotten equilibria of the Bertrand duopoly!? TUC Working Paper (2002)

Garratt, R.J., Walker, M., Wooders, J.: Behavior in second-price auctions by highly experienced eBay buyers and sellers. Exp. Econ. 15(1), 44–57 (2012)

Kagel, J., Levin, D.: Independent private value auctions: bidder behaviour in first-, second-and third-price auctions with varying numbers of bidders. Econ. J. 103(419), 868–879 (1993)

Kaplan, T., Turocy, T.: Bidding behavior in asymmetric first-price auctions. Working paper (2014)

Kaplan, T., Wettstein, D.: The possibility of mixed-strategy equilibria with constant-returns-to-scale technology under Bertrand competition. Spanish Econ. Rev. 2(1), 65–71 (2000)

Kaplan, T., Zamir, S.: Asymmetric first-price auctions with uniform distributions: analytic solutions to the general case. Econ. Theory 50(2), 269–302 (2012)

Lebrun, B.: Uniqueness of the equilibrium in first-price auctions. Working Paper (2004)

Lebrun, B.: Uniqueness of the equilibrium in first-price auctions. Games Econ. Behav. 55(1), 131–151 (2006)

Maschler, M., Solan, E., Zamir, S.: Game Theory. Cambridge University Press, Cambridge, UK (2013)

Maskin, E., Riley, J.: Uniqueness of equilibrium in sealed high-bid auctions. Games Econ. Behav. 45(2), 395–409 (2003)

McAdams, D.: Uniqueness in symmetric first-price auctions with affiliation. J. Econ. Theory 136(1), 144–166 (2007)

Myerson, R.B.: Optimal Auction Design. Math. Oper. Res. 6(1), 58–73 (1981)

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

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Springer Science and Business Media LLC

Tập 3

65-77

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