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Asymmetric budget constraints in a first-price auction. (English) Zbl 1432.91063
Summary: I solve a first-price auction for two bidders with asymmetric budget distributions and known valuations for one object. I show that in any equilibrium, the expected utilities and bid distributions of both bidders are unique. If budgets are sufficiently low, the bidders will bid their entire budget in any equilibrium. For sufficiently high budgets, mass points in the equilibrium strategies arise. A less restrictive budget distribution could make both bidders strictly worse off. If the budget distribution of one bidder is dominated by the budget distribution of the other bidder in the reverse-hazard-rate order, the weaker bidder will bid more aggressively than the stronger bidder. In contrast to existing results for symmetric budget distributions, with asymmetric budget distributions, a second-price auction can yield a strictly higher revenue than a first-price auction. Under an additional assumption, I derive the unique equilibrium utilities and bid distributions of both bidders in an all-pay auction.

91B26 Auctions, bargaining, bidding and selling, and other market models
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[1] Bagnoli, M.; Bergstrom, T., Log-concave probability and its applications, Econ. Theory, 26, 445-469 (2005) · Zbl 1077.60012
[2] Benoît, J.-P.; Krishna, V., Multiple-object auctions with budget constrained bidders, Rev. Econ. Stud., 68, 155-179 (2001) · Zbl 1114.91314
[3] Blume, A., Bertrand without fudge, Econ. Lett., 78, 167-168 (2003) · Zbl 1032.91009
[4] Boulatov, A.; Severinov, S., Optimal and efficient mechanisms with asymmetrically budget constrained buyers (2018), Working Paper
[5] Cantillon, E., The effect of bidders’ asymmetries on expected revenue in auctions, Games Econ. Behav., 62, 1-25 (2008) · Zbl 1135.91353
[6] Che, Y.-K.; Gale, I., Expected revenue of all-pay auctions and first-price sealed-bid auctions with budget constraints, Econ. Lett., 50, 373-379 (1996) · Zbl 0875.90273
[7] Che, Y.-K.; Gale, I., Standard auctions with financially constrained bidders, Rev. Econ. Stud., 65, 1-21 (1998) · Zbl 0909.90121
[8] Che, Y.-K.; Gale, I., Optimal mechanism for selling to a budget constrained buyer, J. Econ. Theory, 92, 198-233 (2000) · Zbl 0998.91017
[9] Che, Y.-K.; Gale, I., Revenue comparisons for auctions when bidders have arbitrary types, Theor. Econ., 1, 95-118 (2006)
[10] Cheng, H., Ranking sealed high-bid and open asymmetric auctions, J. Math. Econ., 42, 471-498 (2006) · Zbl 1141.91394
[11] Dobzinski, S.; Lavi, R.; Nisan, N., Multi-unit auctions with budget limits, Games Econ. Behav., 74, 486-503 (2012) · Zbl 1279.91080
[12] Fibich, G.; Gavious, A., Asymmetric first price auctions - a perturbation approach, Math. Oper. Res., 28, 836-852 (2003) · Zbl 1082.91043
[13] Fibich, G.; Gavious, A.; Sela, A., Revenue equivalence in asymmetric auctions, J. Econ. Theory, 115, 309-321 (2004) · Zbl 1073.91022
[14] Gavious, A.; Minchuk, Y., Ranking asymmetric auctions, Int. J. Game Theory, 43, 369-393 (2014) · Zbl 1296.91125
[15] Kaplan, T. R.; Zamir, S., Asymmetric first-price auctions with uniform distributions: analytic solutions to the general case, Econ. Theory, 50, 269-302 (2012) · Zbl 1245.91039
[16] Kotowski M., forthcoming. First-price auctions with budget constraints. Theor. Econ.
[17] Kotowski, M.; Li, F., On the continuous equilibria of affiliated-value, all-pay auctions with private budget constraints, Games Econ. Behav., 85, 84-108 (2014) · Zbl 1290.91067
[18] Lebrun, B., Auctions with almost homogenous bidders, J. Econ. Theory, 144, 1341-1351 (2009) · Zbl 1159.91379
[19] Malakhov, A.; Vohra, R., Optimal auctions for asymmetrically budget constrained bidders, Rev. Econ. Des., 12, 245-257 (2008) · Zbl 1165.91385
[20] Maskin, E.; Riley, J., Asymmetric auctions, Rev. Econ. Stud., 67, 413-438 (2000) · Zbl 0981.91029
[21] Plum, M., Characterization and computation of Nash-equilibria for auctions with incomplete information, Int. J. Game Theory, 20, 393-418 (1992) · Zbl 0763.90037
[22] Salant, D., Up in the air: GTE’s experience in the MTA auction for personal communications services licenses, J. Econ. Manag. Strategy, 6, 549-572 (1997)
[23] Zheng, C. Z., High bids and broke winners, J. Econ. Theory, 100, 129-171 (2001) · Zbl 0998.91018
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