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An axiomatization of difference-form contest success functions

Author

Listed:
  • María Cubel

    (Universitat de Barcelona & IEB)

  • Santiago Sanchez-Pages

    (Edinburgh School of Economics & University of Barcelona)

Abstract
This paper presents an axiomatic characterization of difference-form group contests, that is, contests fought among groups and where their probability of victory depends on the difference of their effective efforts. This axiomatization rests on the property of Absolute Consistency, stating that the difference in winning probabilities between two contenders in the grand contest must be the same as when they engage in smaller contests. This property overcomes some of the drawbacks of the widely-used ratio-form contest success functions. Our characterization shows that the criticisms commonly-held against difference-form contests success functions, such as lack of scale invariance, are unfounded. Finally, we extend our axiomatization to relative-difference contests where winning probabilities depend on the difference of contenders effective efforts relative to total aggregate effort.

Suggested Citation

  • María Cubel & Santiago Sanchez-Pages, 2015. "An axiomatization of difference-form contest success functions," Working Papers 2015/5, Institut d'Economia de Barcelona (IEB).
    • Handle: RePEc:ieb:wpaper:2013/6/doc2015-5
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    References listed on IDEAS

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    1. Jack Hirshleifer, 2000. "The Macrotechnology of Conflict," Journal of Conflict Resolution, Peace Science Society (International), vol. 44(6), pages 773-792, December.
    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. Qiang Fu & Jingfeng Lu, 2012. "Micro foundations of multi-prize lottery contests: a perspective of noisy performance ranking," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 497-517, March.
    5. 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.
    6. Rohner, Dominic, 2006. "Beach holiday in Bali or East Timor? Why conflict can lead to under- and overexploitation of natural resources," Economics Letters, Elsevier, vol. 92(1), pages 113-117, July.
    7. Timothy J. Besley & Torsten Persson, 2008. "The Incidence of Civil War: Theory and Evidence," NBER Working Papers 14585, National Bureau of Economic Research, Inc.
    8. Timothy Besley & Torsten Persson, 2009. "Repression or Civil War?," American Economic Review, American Economic Association, vol. 99(2), pages 292-297, May.
    9. Maria Arbatskaya & Hugo Mialon, 2010. "Multi-activity contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(1), pages 23-43, April.
    10. José Alcalde & Matthias Dahm, 2007. "Tullock and Hirshleifer: a meeting of the minds," Review of Economic Design, Springer;Society for Economic Design, vol. 11(2), pages 101-124, September.
    11. 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.
    12. María Cubel & Santiago Sanchez-Pages, 2014. "Difference-form group contests," Working Papers 2014/6, Institut d'Economia de Barcelona (IEB).
    13. 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.
    14. Hirshleifer, Jack, 1991. "The Technology of Conflict as an Economic Activity," American Economic Review, American Economic Association, vol. 81(2), pages 130-134, May.
    15. 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.
    16. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    17. Hao Jia & Stergios Skaperdas, 2011. "Technologies of Conflict," Working Papers 101111, University of California-Irvine, Department of Economics.
    18. Satya R. Chakravarty & Bhargav Maharaj, 2014. "New contest success functions," Working Papers 340, ECINEQ, Society for the Study of Economic Inequality.
    19. 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.
    20. Franke, Jörg, 2012. "Affirmative action in contest games," European Journal of Political Economy, Elsevier, vol. 28(1), pages 105-118.
    21. repec:shn:wpaper:2014-02 is not listed on IDEAS
    22. Blackorby, Charles & Donaldson, David, 1980. "A Theoretical Treatment of Indices of Absolute Inequality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 107-136, February.
    23. Gartzke, Erik & Rohner, Dominic, 2011. "The Political Economy of Imperialism, Decolonization and Development," British Journal of Political Science, Cambridge University Press, vol. 41(3), pages 525-556, July.
    24. María Cubel & Santiago Sanchez-Pages, 2014. "Difference-form group contests," Working Papers 2014/6, Institut d'Economia de Barcelona (IEB).
    25. Leonid Polishchuk & Alexander Tonis, 2013. "Endogenous contest success functions: a mechanism design approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 271-297, January.
    26. 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.
    27. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    28. Bozbay, Irem & Vesperoni, Alberto, 2018. "A contest success function for networks," Journal of Economic Behavior & Organization, Elsevier, vol. 150(C), pages 404-422.
    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. Levine, Paul & Smith, Ron, 1995. "The Arms Trade and Arms Control," Economic Journal, Royal Economic Society, vol. 105(429), pages 471-484, March.
    31. Hwang, Sung-Ha, 2012. "Technology of military conflict, military spending, and war," Journal of Public Economics, Elsevier, vol. 96(1), pages 226-236.
    32. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    33. 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.
    34. 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.
    35. 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.
    36. Jack Hirshleifer, 1983. "From weakest-link to best-shot: The voluntary provision of public goods," Public Choice, Springer, vol. 41(3), pages 371-386, January.
    37. 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.
    38. Hans Gersbach & Hans Haller, 2009. "The affectionate society: does competition for partners promote friendliness?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(3), pages 389-403, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Osório, António (António Miguel), 2018. "Group contest success function: The heterogeneous individuals case," Working Papers 2072/332583, Universitat Rovira i Virgili, Department of Economics.
    2. 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.
    3. Engelbert J. Dockner & Steffen Jørgensen, 2018. "Strategic Rivalry for Market Share: A Contest Theory Approach to Dynamic Advertising Competition," Dynamic Games and Applications, Springer, vol. 8(3), pages 468-489, September.
    4. Lu, Jingfeng & Wang, Zhewei, 2015. "Axiomatizing multi-prize nested lottery contests: A complete and strict ranking perspective," Journal of Economic Behavior & Organization, Elsevier, vol. 116(C), pages 127-141.
    5. Jingfeng Lu & Zhewei Wang, 2016. "Axiomatization of reverse nested lottery contests," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(4), pages 939-957, December.
    6. Bozbay, Irem & Vesperoni, Alberto, 2018. "A contest success function for networks," Journal of Economic Behavior & Organization, Elsevier, vol. 150(C), pages 404-422.
    7. Carmen Beviá & Luis Corchón, 2022. "Contests with dominant strategies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(4), pages 1-19, November.
    8. Christian Ewerhart, 2015. "Contest success functions: the common-pool perspective," ECON - Working Papers 195, Department of Economics - University of Zurich.
    9. Antoine Pietri, 2017. "Les modèles de « rivalité coercitive » dans l’analyse économique des conflits," Revue d'économie politique, Dalloz, vol. 127(3), pages 307-352.
    10. Kjell Hausken, 2020. "Additive multi-effort contests," Theory and Decision, Springer, vol. 89(2), pages 203-248, September.
    11. Kjell Hausken, 2021. "Axiomatizing additive multi-effort contests," SN Business & Economics, Springer, vol. 1(11), pages 1-12, November.
    12. Ewerhart, Christian & Sun, Guang-Zhen, 2024. "The n-player Hirshleifer contest," Games and Economic Behavior, Elsevier, vol. 143(C), pages 300-320.
    13. Mildenberger, Carl David & Pietri, Antoine, 2018. "How does size matter for military success? Evidence from virtual worlds," Journal of Economic Behavior & Organization, Elsevier, vol. 154(C), pages 137-155.
    14. repec:wsi:jeapmx:v:20:y:2018:i:04:n:s0219198918500093 is not listed on IDEAS

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    More about this item

    Keywords

    Contests; groups; contest success function; axioms;
    All these keywords.

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • 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

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