IDEAS home Printed from https://ideas.repec.org/a/eee/indorg/v31y2013i3p211-222.html
   My bibliography  Save this article

Contest functions: Theoretical foundations and issues in estimation

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167718712000811
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ijindorg.2012.06.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Menezes, Flavio M. & Quiggin, John, 2010. "Markets for influence," International Journal of Industrial Organization, Elsevier, vol. 28(3), pages 307-310, May.
    2. 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.
    3. 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.
    4. Jörg Franke & Christian Kanzow & Wolfgang Leininger & Alexandra Väth, 2009. "Effort Maximization in Asymmetric N-Person Contest Games," CESifo Working Paper Series 2744, CESifo.
    5. Sunde, Uwe, 2003. "Potential, Prizes and Performance: Testing Tournament Theory with Professional Tennis Data," IZA Discussion Papers 947, Institute of Labor Economics (IZA).
    6. 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.
    7. J. Amegashie, 2006. "A contest success function with a tractable noise parameter," Public Choice, Springer, vol. 126(1), pages 135-144, January.
    8. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    9. 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.
    10. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    11. Yeon-Koo Che & Ian L. Gale, 2008. "Caps on Political Lobbying," Springer Books, in: Roger D. Congleton & Kai A. Konrad & Arye L. Hillman (ed.), 40 Years of Research on Rent Seeking 2, pages 337-345, Springer.
    12. 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.
    13. 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.
    14. Hirshleifer, Jack & Osborne, Evan, 2001. "Truth, Effort, and the Legal Battle," Public Choice, Springer, vol. 108(1-2), pages 169-195, July.
    15. Michael R. Baye & Dan Kovenock & Casper G. Vries, 2008. "Rigging the lobbying process: An application of the all-pay auction," Springer Books, in: Roger D. Congleton & Kai A. Konrad & Arye L. Hillman (ed.), 40 Years of Research on Rent Seeking 2, pages 331-336, Springer.
    16. 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.
    17. Birendra K. Rai & Rajiv Sarin, 2007. "Generalized Contest Success Functions," Jena Economics Research Papers 2007-082, Friedrich-Schiller-University Jena.
    18. Avinash Dixit, 2008. "Strategic Behavior in Contests," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 431-438, Springer.
    19. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555.
    20. 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.
    21. 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.
    22. Fang, Hanming, 2002. "Lottery versus All-Pay Auction Models of Lobbying," Public Choice, Springer, vol. 112(3-4), pages 351-371, September.
    23. Michael R. Baye & Dan Kovenock & Casper G. Vries, 1996. "The all-pay auction with complete information," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 209-223, Springer.
    24. 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.
    25. 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.
    26. James J. Heckman, 2008. "Econometric Causality," International Statistical Review, International Statistical Institute, vol. 76(1), pages 1-27, April.
    27. Hao Jia & Stergios Skaperdas, 2011. "Technologies of Conflict," Working Papers 101111, University of California-Irvine, Department of Economics.
    28. 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.
    29. Hausman, Jerry & McFadden, Daniel, 1984. "Specification Tests for the Multinomial Logit Model," Econometrica, Econometric Society, vol. 52(5), pages 1219-1240, September.
    30. Skaperdas, Stergios & Grofman, Bernard, 1995. "Modeling Negative Campaigning," American Political Science Review, Cambridge University Press, vol. 89(1), pages 49-61, March.
    31. 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.
    32. Konrad, Kai A., 2006. "Silent interests and all-pay auctions," International Journal of Industrial Organization, Elsevier, vol. 24(4), pages 701-713, July.
    33. repec:zbw:rwirep:0130 is not listed on IDEAS
    34. Fonseca, Miguel A., 2009. "An experimental investigation of asymmetric contests," International Journal of Industrial Organization, Elsevier, vol. 27(5), pages 582-591, September.
    35. Daughety, Andrew F & Reinganum, Jennifer F, 2000. "On the Economics of Trials: Adversarial Process, Evidence, and Equilibrium Bias," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 16(2), pages 365-394, October.
    36. 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.
    37. 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.
    38. 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.
    39. Joseph E. Stiglitz & G. Frank Mathewson (ed.), 1986. "New Developments in the Analysis of Market Structure," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262690934, April.
    40. Dasgupta, Ani & Nti, Kofi O., 1998. "Designing an optimal contest," European Journal of Political Economy, Elsevier, vol. 14(4), pages 587-603, November.
    41. 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.
    42. 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.
    43. Sandler,Todd & Hartley,Keith, 1995. "The Economics of Defense," Cambridge Books, Cambridge University Press, number 9780521447287, September.
    44. Konrad, Kai A., 2000. "Spatial contests," International Journal of Industrial Organization, Elsevier, vol. 18(6), pages 965-974, August.
    45. Stefan Szymanski, 2010. "The Economic Design of Sporting Contests," Palgrave Macmillan Books, in: The Comparative Economics of Sport, chapter 1, pages 1-78, Palgrave Macmillan.
    46. Rosen, Sherwin, 1986. "Prizes and Incentives in Elimination Tournaments," American Economic Review, American Economic Association, vol. 76(4), pages 701-715, September.
    47. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring.
    48. 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.
    49. Ronald G. Ehrenberg & Michael L. Bognanno, 1990. "The Incentive Effects of Tournaments Revisited: Evidence from the European PGA Tour," ILR Review, Cornell University, ILR School, vol. 43(3), pages 74, April.
    50. repec:cte:werepe:we075126 is not listed on IDEAS
    51. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
    52. 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.
    53. Nti, Kofi O., 2004. "Maximum efforts in contests with asymmetric valuations," European Journal of Political Economy, Elsevier, vol. 20(4), pages 1059-1066, November.
    54. 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.
    55. Keith Hartley & Todd Sandler (ed.), 1995. "Handbook of Defense Economics," Handbook of Defense Economics, Elsevier, edition 1, volume 1, number 1.
    56. 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.
    57. 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.
    58. Harold Gulliksen & John Tukey, 1958. "Reliability for the law of comparative judgment," Psychometrika, Springer;The Psychometric Society, vol. 23(2), pages 95-110, June.
    59. 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.
    60. 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.
    61. Pavlo Blavatskyy, "undated". "Contest success function with the possibility of a draw: axiomatization," IEW - Working Papers 208, Institute for Empirical Research in Economics - University of Zurich.
    62. R. Schmalensee & R. Willig (ed.), 1989. "Handbook of Industrial Organization," Handbook of Industrial Organization, Elsevier, edition 1, volume 2, number 2.
    63. repec:cte:werepe:we070401 is not listed on IDEAS
    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. 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.
    66. 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.
    67. 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.
    68. Lawrence Friedman, 1958. "Game-Theory Models in the Allocation of Advertising Expenditures," Operations Research, INFORMS, vol. 6(5), pages 699-709, October.
    69. 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.
    70. Glenn C. Loury, 1979. "Market Structure and Innovation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 93(3), pages 395-410.
    71. 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.
    72. Nitzan, Shmuel, 1994. "Modelling rent-seeking contests," European Journal of Political Economy, Elsevier, vol. 10(1), pages 41-60, May.
    73. Johannes Münster, 2006. "Lobbying Contests With Endogenous Policy Proposals," Economics and Politics, Wiley Blackwell, vol. 18(3), pages 389-397, November.
    74. 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.
    75. Sung Ha Hwang, 2009. "Contest Success Functions: Theory and Evidence," UMASS Amherst Economics Working Papers 2009-04, University of Massachusetts Amherst, Department of Economics.
    76. R. Schmalensee & R. Willig (ed.), 1989. "Handbook of Industrial Organization," Handbook of Industrial Organization, Elsevier, edition 1, volume 1, number 1.
    77. Froeb, Luke M & Kobayashi, Bruce H, 1996. "Naive, Biased, Yet Bayesian: Can Juries Interpret Selectively Produced Evidence?," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 12(1), pages 257-276, April.
    78. Hao Jia, 2008. "A stochastic derivation of the ratio form of contest success functions," Public Choice, Springer, vol. 135(3), pages 125-130, June.
    79. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hao Jia & Stergios Skaperdas, 2011. "Technologies of Conflict," Working Papers 101111, University of California-Irvine, Department of Economics.
    2. Konrad, Kai A., 2007. "Strategy in contests: an introduction [Strategie in Turnieren – eine Einführung]," Discussion Papers, Research Unit: Market Processes and Governance SP II 2007-01, WZB Berlin Social Science Center.
    3. Sakshi Gupta & Ram Singh, 2018. "On Existence and Properties of Pure-strategy Equilibria under Contests," Working Papers id:12840, eSocialSciences.
    4. 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.
    5. Kimbrough, Erik O. & Laughren, Kevin & Sheremeta, Roman, 2020. "War and conflict in economics: Theories, applications, and recent trends," Journal of Economic Behavior & Organization, Elsevier, vol. 178(C), pages 998-1013.
    6. Ewerhart, Christian, 2017. "Contests with small noise and the robustness of the all-pay auction," Games and Economic Behavior, Elsevier, vol. 105(C), pages 195-211.
    7. Cedric Duvinage & Peter-J. Jost, 2019. "The Role of Referees in Professional Sports Contests," Journal of Sports Economics, , vol. 20(8), pages 1014-1050, December.
    8. Subhasish M. Chowdhury & Patricia Esteve‐González & Anwesha Mukherjee, 2023. "Heterogeneity, leveling the playing field, and affirmative action in contests," Southern Economic Journal, John Wiley & Sons, vol. 89(3), pages 924-974, January.
    9. Pelosse, Yohan, 2009. "Mediated Contests and Strategic Foundations for Contest Success Functions," MPRA Paper 18664, University Library of Munich, Germany.
    10. Corchón, Luis & Dahm, Matthias, 2011. "Welfare maximizing contest success functions when the planner cannot commit," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 309-317.
    11. Gil Epstein & Yosef Mealem, 2015. "Politicians, governed versus non-governed interest groups and rent dissipation," Theory and Decision, Springer, vol. 79(1), pages 133-149, July.
    12. Beviá, Carmen & Corchón, Luis C., 2013. "Endogenous strength in conflicts," International Journal of Industrial Organization, Elsevier, vol. 31(3), pages 297-306.
    13. 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.
    14. Cason, Timothy N. & Masters, William A. & Sheremeta, Roman M., 2020. "Winner-take-all and proportional-prize contests: Theory and experimental results," Journal of Economic Behavior & Organization, Elsevier, vol. 175(C), pages 314-327.
    15. Pelosse, Yohan, 2011. "Equivalence of optimal noisy-ranking contests and Tullock contests," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 740-748.
    16. Emmanuel Dechenaux & Dan Kovenock & Roman Sheremeta, 2015. "A survey of experimental research on contests, all-pay auctions and tournaments," Experimental Economics, Springer;Economic Science Association, vol. 18(4), pages 609-669, December.
    17. Kyung Hwan Baik & Jong Hwa Lee, 2013. "Endogenous Timing In Contests With Delegation," Economic Inquiry, Western Economic Association International, vol. 51(4), pages 2044-2055, October.
    18. Helmut Dietl & Egon Franck & Martin Grossmann & Markus Lang, 2009. "Contest Theory and its Applications in Sports," Working Papers 0029, University of Zurich, Center for Research in Sports Administration (CRSA).
    19. Boudreau, James W. & Shunda, Nicholas, 2012. "On the evolution of prize perceptions in contests," Economics Letters, Elsevier, vol. 116(3), pages 498-501.
    20. Alberto Vesperoni, 2016. "A contest success function for rankings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(4), pages 905-937, December.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:indorg:v:31:y:2013:i:3:p:211-222. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505551 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.