Abstract
This paper presents a unified framework for characterizing symmetric equilibrium in simultaneous move, two-player, rank-order contests with complete information, in which each player’s strategy generates direct or indirect affine “spillover” effects that depend on the rank-order of her decision variable. These effects arise in natural interpretations of a number of important economic environments, as well as in classic contests adapted to recent experimental and behavioral models where individuals exhibit inequality aversion or regret. We provide the closed-form solution for the symmetric Nash equilibria of this class of games, and show how it can be used to directly solve for equilibrium behavior in auctions, pricing games, tournaments, R&D races, models of litigation, and a host of other contests.
Article PDF
Similar content being viewed by others
References
Basu K.: The traveler’s dilemma: paradoxes of rationality in game theory. Am Econ Rev 84(2), 391–395 (1994)
Baye M.R., Kovenock D.: How to sell a pickup truck—beat-or-pay advertisements as facilitating devices. Int J Ind Organ 12(1), 21–33 (1994)
Baye M.R., Morgan J.: The folk theorem for one-shot Bertrand games. Econ Lett 65(1), 59–65 (1999)
Baye M.R., Kovenock D., de Vries C.G.: It takes 2 to Tango—equilibria in a model of sales. Games Econ Behav 4(4), 493–510 (1992)
Baye M.R., Kovenock D., de Vries C.G.: Rigging the lobbying process: an application of the all-pay auction. Am Econ Rev 83(1), 289–294 (1993)
Baye M.R., Kovenock D., de Vries C.G.: The all-pay auction with complete information. Econ Theory 8(2), 291–305 (1996)
Baye M.R., Kovenock D., de Vries C.G.: Comparative analysis of litigation systems: an auction-theoretic approach. Econ J 115(505), 583–601 (2005)
Bertrand J.: (Review of) Theorie Mathematique de la Richesse Sociale par Leon Walras: Recherches sur les Principes Mathematiques de la Theorie des Richesses par Augustin Cournot. Journal Des Savants 67, 499–508 (1883)
Che Y.K., Gale I.L.: Caps on political lobbying. Am Econ Rev 88(3), 643–651 (1998)
Che Y.K., Gale I.: Optimal design of research contests. Am Econ Rev 93(3), 646–671 (2003)
Chung K.L.: A Course in Probability Theory, 2nd edn. Academic Press, Orlando (1974)
Dasgupta P.: The theory of technological competition. In: Stiglitz, J.E., Mathewson, G.F. (eds) New Developments in the Analysis of Market Structure, pp. 519–547. MIT Press, Cambridge (1986)
Dasgupta P., Maskin E.: The existence of equilibrium in discontinuous economic games. I. Theory. Rev Econ Stud 53, 1–26 (1986)
Dasgupta S., Tsui K.: Auctions with cross-shareholdings. Econ Theory 24, 163–194 (2004)
D’Aspremont C., Jacquemin A.: Cooperative and noncooperative R- and-D in Duopoly with spillovers. Am Econ Rev 78(5), 1133–1137 (1988)
Engelbrecht-Wiggans R.: The effect of regret on optimal bidding in auctions. Manag Sci 35(6), 685–692 (1989)
Engelbrecht-Wiggans R., Katok E.: Regret in auctions: theory and evidence. Econ Theory 33, 81–101 (2007)
Engers, M., McManus, B.: Chairity Auctions. University of Virginia Working Paper (2004)
Ettinger D.: Efficiency in auctions with crossholdings. Econ Lett 80, 1–7 (2003)
Fehr E., Schmidt K.M.: A theory of fairness, competition, and cooperation. Quart J Econ 114(3), 817–868 (1999)
Filiz-Ozbay E., Ozbay E.Y.: Auctions with anticipated regret: theory and experiment. Am Econ Rev 97(4), 1407–1418 (2007)
Fu Q.: A theory of affirmative action in college admissions. Econ Inq 44(3), 420–428 (2006)
Goeree J.K., Maasland E., Onderstal S., Turner J.L.: How (Not) to raise money. J Political Econ 113, 897–918 (2005)
Groh, C., Moldovanu, B., Sela, A., Sunde, E.: Optimal seedings in elimination tournaments. Econ Theory (2009) (forthcoming)
Hehenkamp B., Leininger W., Possajennikov A.: Evolutionary equilibrium in Tullock contests: spite and overdissipation. Eur J Political Econ 20, 1045–1057 (2004)
Helsey R.W., Strange W.C.: A game-theoretic analysis of skyscrapers. J Urban Econ 64, 49–64 (2008)
Hillman A., Riley J.: Politically contestable rents and transfers. Econ Politics 1, 17–40 (1989)
Jehiel P., Moldovanu B., Stacchetti E.: How (Not) to sell nuclear weapons. Am Econ Rev 86, 814–829 (1996)
Kaplan T.R., Luski I., Wettstein D.: Innovative activity and sunk cost. Int J Ind Org 21(8), 1111–1133 (2003)
Kittsteiner T.: Partnerships and double auctions with interdependent valuations. Games Econ Behav 44, 54–76 (2003)
Konrad K.A.: Inverse campaigning. Econ J 114(492), 69–82 (2004)
Kura T.: Dilemma of the equality: an all-pay contest with individual differences in resource holding potential. J Theor Biol 198(3), 395–404 (1999)
Lin J.: Price matching in a model of equilibrium price dispersion. South Econ J 55, 57–65 (1988)
Lizzeri A., Persico N.: Uniqueness and existence of equilibrium in auctions with a reserve price. Games Econ Behav 30(1), 83–114 (2000)
Maasland E., Onderstal S.: Auctions with financial externalities. Econ Theory 32, 551–574 (2007)
Maynard Smith J.: The theory of games and the evolution of animal conflicts. J Theor Biol 47, 209–221 (1974)
Png I.P.L., Hirshleifer D.: Price-discrimination through offers to match price. J Business 60(3), 365–383 (1987)
Riley J.G., Samuelson W.S.: Optimal auctions. Am Econ Rev 71, 381–392 (1981)
Rosenthal R.: A model in which an increase in the number of sellers leads to a higher price. Econometrica 48(6), 1575–1580 (1980)
Sahuguet N., Persico N.: Campaign spending regulation in a model of redistributive politics. Econ Theory 28(1), 95–124 (2006)
Schaffer M.: Evolutionary stable strategies for a finite population and a variable contest size. J Theor Biol 132, 469–478 (1988)
Varian H.: A model of sales. Am Econ Rev 70, 651–659 (1980)
Vickrey W.: Counterspeculation, auctions and sealed tenders. J Finance 16, 8–37 (1961)
Zhou H.: R&D tournaments with spillovers. Atl Econ J 34, 327–339 (2006)
Open Access
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
We are grateful to two referees for exceptionally lucid and helpful reports. We have also benefited from conversations with Murali Agastya, Chaim Fershtman, Srihari Govindan, Rick Harbaugh, Wolfgang Leininger, Benny Moldovanu, and Michael Rauh. Finally, we thank Nels Leader, participants in the conference on “Contests: Theory and Applications” at the Stockholm School of Economics, and participants at the 2008 CESifo Workshop on “Advances in the Theory of Contests and its Applications” in Venice. Kovenock has benefited from the financial support of the Wissenschaftszentrum Berlin für Sozialforschung.
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Baye, M.R., Kovenock, D. & de Vries, C.G. Contests with rank-order spillovers. Econ Theory 51, 315–350 (2012). https://doi.org/10.1007/s00199-009-0489-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00199-009-0489-2