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Contest functions: Theoretical foundations and issues in estimation

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  • Jia, Hao
  • Skaperdas, Stergios
  • Vaidya, Samarth

Abstract

Contest functions (alternatively, contest success functions) determine probabilities of winning and losing as a function of contestants' effort. They are used widely in many areas of economics that employ contest games, from tournaments and rent-seeking to conflict and sports. We first examine the theoretical foundations of contest functions and classify them into four types of derivation: stochastic, axiomatic, optimally-derived, and microfounded. The additive form (which includes the ratio or “Tullock” functional form) can be derived in all four different ways. We also explore issues in the econometric estimation of contest functions, including concerns with data, endogeneity, and model comparison.

Suggested Citation

  • Jia, Hao & Skaperdas, Stergios & Vaidya, Samarth, 2013. "Contest functions: Theoretical foundations and issues in estimation," International Journal of Industrial Organization, Elsevier, vol. 31(3), pages 211-222.
  • Handle: RePEc:eee:indorg:v:31:y:2013:i:3:p:211-222
    DOI: 10.1016/j.ijindorg.2012.06.007
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    1. Schmalensee, Richard, 1978. "A Model of Advertising and Product Quality," Journal of Political Economy, University of Chicago Press, vol. 86(3), pages 485-503, June.
    2. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    3. Birendra Rai & Rajiv Sarin, 2009. "Generalized contest success functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(1), pages 139-149, July.
    4. Christian Riis & Derek J. Clark, 1997. "Contest success functions: an extension," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 201-204.
    5. Hirshleifer, Jack & Osborne, Evan, 2001. "Truth, Effort, and the Legal Battle," Public Choice, Springer, vol. 108(1-2), pages 169-195, July.
    6. Che, Yeon-Koo & Gale, Ian, 2000. "Difference-Form Contests and the Robustness of All-Pay Auctions," Games and Economic Behavior, Elsevier, vol. 30(1), pages 22-43, January.
    7. Birendra K. Rai & Rajiv Sarin, 2007. "Generalized Contest Success Functions," Jena Economic Research Papers 2007-082, Friedrich-Schiller-University Jena.
    8. Franke, Jörg & Kanzow, Christian & Leininger, Wolfgang & Väth, Alexandra, 2009. "Effort Maximization in Asymmetric N-person Contest Games," Ruhr Economic Papers 130, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    9. Ralph Rotte & Christoph Schmidt, 2003. "On the production of victory: Empirical determinants of battlefield success in modern war," Defence and Peace Economics, Taylor & Francis Journals, vol. 14(3), pages 175-192.
    10. Stergios Skaperdas & Samarth Vaidya, 2012. "Persuasion as a contest," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(2), pages 465-486, October.
    11. Fang, Hanming, 2002. "Lottery versus All-Pay Auction Models of Lobbying," Public Choice, Springer, vol. 112(3-4), pages 351-371, September.
    12. Hirshleifer, Jack, 1995. "Theorizing about conflict," Handbook of Defense Economics, in: Keith Hartley & Todd Sandler (ed.), Handbook of Defense Economics, edition 1, volume 1, chapter 7, pages 165-189, Elsevier.
    13. Dan Kovenock & Michael R. Baye & Casper G. de Vries, 1996. "The all-pay auction with complete information (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 291-305.
    14. Hao Jia & Stergios Skaperdas, 2011. "Technologies of Conflict," Working Papers 101111, University of California-Irvine, Department of Economics.
    15. James J. Heckman, 2008. "Econometric Causality," International Statistical Review, International Statistical Institute, vol. 76(1), pages 1-27, April.
    16. Hausman, Jerry & McFadden, Daniel, 1984. "Specification Tests for the Multinomial Logit Model," Econometrica, Econometric Society, vol. 52(5), pages 1219-1240, September.
    17. Ahn, T.K. & Isaac, R. Mark & Salmon, Timothy C., 2011. "Rent seeking in groups," International Journal of Industrial Organization, Elsevier, vol. 29(1), pages 116-125, January.
    18. J. Amegashie, 2006. "A contest success function with a tractable noise parameter," Public Choice, Springer, vol. 126(1), pages 135-144, January.
    19. Dasgupta, Ani & Nti, Kofi O., 1998. "Designing an optimal contest," European Journal of Political Economy, Elsevier, vol. 14(4), pages 587-603, November.
    20. Konrad, Kai A., 2000. "Spatial contests," International Journal of Industrial Organization, Elsevier, vol. 18(6), pages 965-974, August.
    21. Konrad, Kai A., 2006. "Silent interests and all-pay auctions," International Journal of Industrial Organization, Elsevier, vol. 24(4), pages 701-713, July.
    22. Baye, Michael R & Kovenock, Dan & de Vries, Casper G, 1993. "Rigging the Lobbying Process: An Application of the All-Pay Auction," American Economic Review, American Economic Association, vol. 83(1), pages 289-294, March.
    23. Rosen, Sherwin, 1986. "Prizes and Incentives in Elimination Tournaments," American Economic Review, American Economic Association, vol. 76(4), pages 701-715, September.
    24. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring.
    25. Luis Corchón & Matthias Dahm, 2010. "Foundations for contest success functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(1), pages 81-98, April.
    26. Alex Robson & Stergios Skaperdas, 2008. "Costly enforcement of property rights and the Coase theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(1), pages 109-128, July.
    27. Luis Corchón, 2007. "The theory of contests: a survey," Review of Economic Design, Springer;Society for Economic Design, vol. 11(2), pages 69-100, September.
    28. Che, Yeon-Koo & Gale, Ian L, 1998. "Caps on Political Lobbying," American Economic Review, American Economic Association, vol. 88(3), pages 643-651, June.
    29. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
    30. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    31. Gil Epstein & Shmuel Nitzan, 2006. "The Politics of Randomness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(2), pages 423-433, October.
    32. Richard L. Fullerton & R. Preston McAfee, 1999. "Auctioning Entry into Tournaments," Journal of Political Economy, University of Chicago Press, vol. 107(3), pages 573-605, June.
    33. Johannes Münster, 2009. "Group contest success functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 41(2), pages 345-357, November.
    34. Menezes, Flavio M. & Quiggin, John, 2010. "Markets for influence," International Journal of Industrial Organization, Elsevier, vol. 28(3), pages 307-310, May.
    35. Blavatskyy, Pavlo R., 2010. "Contest success function with the possibility of a draw: Axiomatization," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 267-276, March.
    36. Glenn C. Loury, 1979. "Market Structure and Innovation," The Quarterly Journal of Economics, Oxford University Press, vol. 93(3), pages 395-410.
    37. Knoeber, Charles R & Thurman, Walter N, 1994. "Testing the Theory of Tournaments: An Empirical Analysis of Broiler Production," Journal of Labor Economics, University of Chicago Press, vol. 12(2), pages 155-179, April.
    38. Muller, Holger M & Warneryd, Karl, 2001. "Inside versus Outside Ownership: A Political Theory of the Firm," RAND Journal of Economics, The RAND Corporation, vol. 32(3), pages 527-541, Autumn.
    39. Johannes Münster, 2006. "Lobbying Contests With Endogenous Policy Proposals," Economics and Politics, Wiley Blackwell, vol. 18(3), pages 389-397, November.
    40. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387, February.
    41. Sung Ha Hwang, 2009. "Contest Success Functions: Theory and Evidence," UMASS Amherst Economics Working Papers 2009-04, University of Massachusetts Amherst, Department of Economics.
    42. Froeb, Luke M & Kobayashi, Bruce H, 1996. "Naive, Biased, Yet Bayesian: Can Juries Interpret Selectively Produced Evidence?," Journal of Law, Economics, and Organization, Oxford University Press, vol. 12(1), pages 257-276, April.
    43. Ehrenberg, Ronald G & Bognanno, Michael L, 1990. "Do Tournaments Have Incentive Effects?," Journal of Political Economy, University of Chicago Press, vol. 98(6), pages 1307-1324, December.
    44. Hao Jia, 2008. "A stochastic derivation of the ratio form of contest success functions," Public Choice, Springer, vol. 135(3), pages 125-130, June.
    45. Jack Hirshleifer, 1989. "Conflict and rent-seeking success functions: Ratio vs. difference models of relative success," Public Choice, Springer, vol. 63(2), pages 101-112, November.
    46. Che, Yeon-Koo & Gale, Ian, 1997. "Rent Dissipation When Rent Seekers Are Budget Constrained," Public Choice, Springer, vol. 92(1-2), pages 109-126, July.
    47. Small, Kenneth A & Hsiao, Cheng, 1985. "Multinomial Logit Specification Tests," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 619-627, October.
    48. Sunde, Uwe, 2003. "Potential, Prizes and Performance: Testing Tournament Theory with Professional Tennis Data," IZA Discussion Papers 947, Institute of Labor Economics (IZA).
    49. Main, Brian G M & O'Reilly, Charles A, III & Wade, James, 1993. "Top Executive Pay: Tournament or Teamwork?," Journal of Labor Economics, University of Chicago Press, vol. 11(4), pages 606-628, October.
    50. Theofanis Tsoulouhas & Charles Knoeber & Anup Agrawal, 2007. "Contests to become CEO: incentives, selection and handicaps," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(2), pages 195-221, February.
    51. Skaperdas, Stergios & Grofman, Bernard, 1995. "Modeling Negative Campaigning," American Political Science Review, Cambridge University Press, vol. 89(1), pages 49-61, March.
    52. Szidarovszky, Ferenc & Okuguchi, Koji, 1997. "On the Existence and Uniqueness of Pure Nash Equilibrium in Rent-Seeking Games," Games and Economic Behavior, Elsevier, vol. 18(1), pages 135-140, January.
    53. Fonseca, Miguel A., 2009. "An experimental investigation of asymmetric contests," International Journal of Industrial Organization, Elsevier, vol. 27(5), pages 582-591, September.
    54. Daughety, Andrew F & Reinganum, Jennifer F, 2000. "On the Economics of Trials: Adversarial Process, Evidence, and Equilibrium Bias," Journal of Law, Economics, and Organization, Oxford University Press, vol. 16(2), pages 365-394, October.
    55. Gregory Levitin & Kjell Hausken, 2010. "Resource Distribution in Multiple Attacks Against a Single Target," Risk Analysis, John Wiley & Sons, vol. 30(8), pages 1231-1239, August.
    56. Bull, Clive & Schotter, Andrew & Weigelt, Keith, 1987. "Tournaments and Piece Rates: An Experimental Study," Journal of Political Economy, University of Chicago Press, vol. 95(1), pages 1-33, February.
    57. Stefan Szymanski, 2003. "The Economic Design of Sporting Contests," Journal of Economic Literature, American Economic Association, vol. 41(4), pages 1137-1187, December.
    58. Garfinkel, Michelle R. & Skaperdas, Stergios, 2007. "Economics of Conflict: An Overview," Handbook of Defense Economics, in: Keith Hartley & Todd Sandler (ed.), Handbook of Defense Economics, edition 1, volume 2, chapter 22, pages 649-709, Elsevier.
    59. Nti, Kofi O., 2004. "Maximum efforts in contests with asymmetric valuations," European Journal of Political Economy, Elsevier, vol. 20(4), pages 1059-1066, November.
    60. Reinganum, Jennifer F., 1989. "The timing of innovation: Research, development, and diffusion," Handbook of Industrial Organization, in: R. Schmalensee & R. Willig (ed.), Handbook of Industrial Organization, edition 1, volume 1, chapter 14, pages 849-908, Elsevier.
    61. Baik, Kyung Hwan, 1998. "Difference-form contest success functions and effort levels in contests," European Journal of Political Economy, Elsevier, vol. 14(4), pages 685-701, November.
    62. Harold Gulliksen & John Tukey, 1958. "Reliability for the law of comparative judgment," Psychometrika, Springer;The Psychometric Society, vol. 23(2), pages 95-110, June.
    63. Barry J. Nalebuff & Joseph E. Stiglitz, 1983. "Prices and Incentives: Towards a General Theory of Compensation and Competition," Bell Journal of Economics, The RAND Corporation, vol. 14(1), pages 21-43, Spring.
    64. Andrew F. Daughety & Jennifer F. Reinganum, 2000. "Appealing Judgments," RAND Journal of Economics, The RAND Corporation, vol. 31(3), pages 502-526, Autumn.
    65. Edward Miguel & Shanker Satyanath & Ernest Sergenti, 2004. "Economic Shocks and Civil Conflict: An Instrumental Variables Approach," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 725-753, August.
    66. Dixit, Avinash K, 1987. "Strategic Behavior in Contests," American Economic Review, American Economic Association, vol. 77(5), pages 891-898, December.
    67. Nitzan, Shmuel, 1994. "Modelling rent-seeking contests," European Journal of Political Economy, Elsevier, vol. 10(1), pages 41-60, May.
    68. Baye, Michael R. & Hoppe, Heidrun C., 2003. "The strategic equivalence of rent-seeking, innovation, and patent-race games," Games and Economic Behavior, Elsevier, vol. 44(2), pages 217-226, August.
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    More about this item

    Keywords

    Rent-seeking; Conflict; Tournaments; Litigation; Advertising;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions
    • L41 - Industrial Organization - - Antitrust Issues and Policies - - - Monopolization; Horizontal Anticompetitive Practices
    • L23 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Organization of Production
    • M37 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - Advertising

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