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Economic Theory

, Volume 51, Issue 2, pp 315–350 | Cite as

Contests with rank-order spillovers

  • Michael R. Baye
  • Dan Kovenock
  • Casper G. de Vries
Open Access
Symposium

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.

Keywords

Contests Auctions Spillovers 

JEL Classification

C72 C73 D43 D44 D74 

Notes

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.

References

  1. Basu K.: The traveler’s dilemma: paradoxes of rationality in game theory. Am Econ Rev 84(2), 391–395 (1994)Google Scholar
  2. 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)CrossRefGoogle Scholar
  3. Baye M.R., Morgan J.: The folk theorem for one-shot Bertrand games. Econ Lett 65(1), 59–65 (1999)CrossRefGoogle Scholar
  4. 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)CrossRefGoogle Scholar
  5. 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)Google Scholar
  6. Baye M.R., Kovenock D., de Vries C.G.: The all-pay auction with complete information. Econ Theory 8(2), 291–305 (1996)Google Scholar
  7. 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)CrossRefGoogle Scholar
  8. 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)Google Scholar
  9. Che Y.K., Gale I.L.: Caps on political lobbying. Am Econ Rev 88(3), 643–651 (1998)Google Scholar
  10. Che Y.K., Gale I.: Optimal design of research contests. Am Econ Rev 93(3), 646–671 (2003)CrossRefGoogle Scholar
  11. Chung K.L.: A Course in Probability Theory, 2nd edn. Academic Press, Orlando (1974)Google Scholar
  12. 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)Google Scholar
  13. Dasgupta P., Maskin E.: The existence of equilibrium in discontinuous economic games. I. Theory. Rev Econ Stud 53, 1–26 (1986)CrossRefGoogle Scholar
  14. Dasgupta S., Tsui K.: Auctions with cross-shareholdings. Econ Theory 24, 163–194 (2004)CrossRefGoogle Scholar
  15. D’Aspremont C., Jacquemin A.: Cooperative and noncooperative R- and-D in Duopoly with spillovers. Am Econ Rev 78(5), 1133–1137 (1988)Google Scholar
  16. Engelbrecht-Wiggans R.: The effect of regret on optimal bidding in auctions. Manag Sci 35(6), 685–692 (1989)CrossRefGoogle Scholar
  17. Engelbrecht-Wiggans R., Katok E.: Regret in auctions: theory and evidence. Econ Theory 33, 81–101 (2007)CrossRefGoogle Scholar
  18. Engers, M., McManus, B.: Chairity Auctions. University of Virginia Working Paper (2004)Google Scholar
  19. Ettinger D.: Efficiency in auctions with crossholdings. Econ Lett 80, 1–7 (2003)CrossRefGoogle Scholar
  20. Fehr E., Schmidt K.M.: A theory of fairness, competition, and cooperation. Quart J Econ 114(3), 817–868 (1999)CrossRefGoogle Scholar
  21. Filiz-Ozbay E., Ozbay E.Y.: Auctions with anticipated regret: theory and experiment. Am Econ Rev 97(4), 1407–1418 (2007)CrossRefGoogle Scholar
  22. Fu Q.: A theory of affirmative action in college admissions. Econ Inq 44(3), 420–428 (2006)CrossRefGoogle Scholar
  23. Goeree J.K., Maasland E., Onderstal S., Turner J.L.: How (Not) to raise money. J Political Econ 113, 897–918 (2005)CrossRefGoogle Scholar
  24. Groh, C., Moldovanu, B., Sela, A., Sunde, E.: Optimal seedings in elimination tournaments. Econ Theory (2009) (forthcoming)Google Scholar
  25. Hehenkamp B., Leininger W., Possajennikov A.: Evolutionary equilibrium in Tullock contests: spite and overdissipation. Eur J Political Econ 20, 1045–1057 (2004)CrossRefGoogle Scholar
  26. Helsey R.W., Strange W.C.: A game-theoretic analysis of skyscrapers. J Urban Econ 64, 49–64 (2008)CrossRefGoogle Scholar
  27. Hillman A., Riley J.: Politically contestable rents and transfers. Econ Politics 1, 17–40 (1989)CrossRefGoogle Scholar
  28. Jehiel P., Moldovanu B., Stacchetti E.: How (Not) to sell nuclear weapons. Am Econ Rev 86, 814–829 (1996)Google Scholar
  29. Kaplan T.R., Luski I., Wettstein D.: Innovative activity and sunk cost. Int J Ind Org 21(8), 1111–1133 (2003)CrossRefGoogle Scholar
  30. Kittsteiner T.: Partnerships and double auctions with interdependent valuations. Games Econ Behav 44, 54–76 (2003)CrossRefGoogle Scholar
  31. Konrad K.A.: Inverse campaigning. Econ J 114(492), 69–82 (2004)CrossRefGoogle Scholar
  32. 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)CrossRefGoogle Scholar
  33. Lin J.: Price matching in a model of equilibrium price dispersion. South Econ J 55, 57–65 (1988)CrossRefGoogle Scholar
  34. Lizzeri A., Persico N.: Uniqueness and existence of equilibrium in auctions with a reserve price. Games Econ Behav 30(1), 83–114 (2000)CrossRefGoogle Scholar
  35. Maasland E., Onderstal S.: Auctions with financial externalities. Econ Theory 32, 551–574 (2007)CrossRefGoogle Scholar
  36. Maynard Smith J.: The theory of games and the evolution of animal conflicts. J Theor Biol 47, 209–221 (1974)CrossRefGoogle Scholar
  37. Png I.P.L., Hirshleifer D.: Price-discrimination through offers to match price. J Business 60(3), 365–383 (1987)CrossRefGoogle Scholar
  38. Riley J.G., Samuelson W.S.: Optimal auctions. Am Econ Rev 71, 381–392 (1981)Google Scholar
  39. Rosenthal R.: A model in which an increase in the number of sellers leads to a higher price. Econometrica 48(6), 1575–1580 (1980)CrossRefGoogle Scholar
  40. Sahuguet N., Persico N.: Campaign spending regulation in a model of redistributive politics. Econ Theory 28(1), 95–124 (2006)CrossRefGoogle Scholar
  41. Schaffer M.: Evolutionary stable strategies for a finite population and a variable contest size. J Theor Biol 132, 469–478 (1988)CrossRefGoogle Scholar
  42. Varian H.: A model of sales. Am Econ Rev 70, 651–659 (1980)Google Scholar
  43. Vickrey W.: Counterspeculation, auctions and sealed tenders. J Finance 16, 8–37 (1961)CrossRefGoogle Scholar
  44. Zhou H.: R&D tournaments with spillovers. Atl Econ J 34, 327–339 (2006)CrossRefGoogle Scholar

Copyright information

© The Author(s) 2009

Authors and Affiliations

  • Michael R. Baye
    • 1
  • Dan Kovenock
    • 2
  • Casper G. de Vries
    • 3
  1. 1.Department of Business Economics and Public PolicyIndiana UniversityBloomingtonUSA
  2. 2.Department of EconomicsUniversity of IowaIowa CityUSA
  3. 3.Erasmus School of EconomicsErasmus University RotterdamRotterdamThe Netherlands

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