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Transitional Dynamics in a Tullock Contest with a General Cost Function

Listed author(s):
  • Martin Grossmann

    ()

    (Institute for Strategy and Business Economics, University of Zurich)

  • Markus Lang

    ()

    (Institute for Strategy and Business Economics, University of Zurich)

  • Helmut Dietl

    ()

    (Institute for Strategy and Business Economics, University of Zurich)

This paper models an infinitely repeated Tullock contest in which two contestants contribute efforts to accumulate individual asset stocks over time. To investigate the transitional dynamics of the contest in the case of a general cost function, we linearize the model around the steady state. Our analysis shows that optimal asset stocks and their speed of convergence to the steady state crucially depend on the elasticity of marginal effort costs, the discount factor and the depreciation rate. We further analyze the effects of second prizes in the transition to the steady state as well as in the steady state itself. For a cost function with a constant elasticity of marginal costs, a lower discount factor, a higher depreciation rate and a lower elasticity imply a higher speed of convergence to the steady state. Moreover, a higher prize spread increases individual and aggregate asset stocks, but does not alter the balance of the contest in the long run. During the transition, a higher prize spread increases asset stocks and produces a more balanced contest in each period. Finally, a higher prize spread increases the speed of convergence to the steady state.

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File URL: http://repec.business.uzh.ch/RePEc/rsd/CRSA_WPS/32_CRSA_full.pdf
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Paper provided by University of Zurich, Center for Research in Sports Administration (CRSA) in its series Working Papers with number 0032.

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Length: 25 pages
Date of creation: Nov 2009
Date of revision: Dec 2010
Handle: RePEc:rsd:wpaper:0032
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  1. Helmut M. Dietl & Markus Lang & Stephan Werner, 2009. "Social Welfare in Sports Leagues with Profit-Maximizing and/or Win-Maximizing Clubs," Southern Economic Journal, Southern Economic Association, vol. 76(2), pages 375-396, October.
  2. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
  3. Michael R. Baye & Dan Kovenock & Casper G. Vries, 2005. "Comparative Analysis of Litigation Systems: An Auction-Theoretic Approach," Economic Journal, Royal Economic Society, vol. 115(505), pages 583-601, 07.
  4. Martin Grossmann & Helmut Dietl & Markus Lang, 2010. "Revenue Sharing and Competitive Balance in a Dynamic Contest Model," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 36(1), pages 17-36, February.
  5. Dana Sisak, 2009. "Multiple-Prize Contests - The Optimal Allocation Of Prizes," Journal of Economic Surveys, Wiley Blackwell, vol. 23(1), pages 82-114, 02.
  6. Helmut M. Dietl & Markus Lang & Alexander Rathke, 2011. "The Combined Effect Of Salary Restrictions And Revenue Sharing In Sports Leagues," Economic Inquiry, Western Economic Association International, vol. 49(2), pages 447-463, 04.
  7. Richard Schmalensee, 1976. "A Model of Promotional Competition in Oligopoly," Review of Economic Studies, Oxford University Press, vol. 43(3), pages 493-507.
  8. Claudio A. Piga, 1998. "A Dynamic Model of Advertising and Product Differentiation," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 13(5), pages 509-522, October.
  9. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, July.
  10. Martin Grossmann & Helmut M. Dietl, 2009. "Investment Behaviour in a Two-Period Contest Model," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 165(3), pages 401-417, September.
  11. Martin Grossmann & Helmut Dietl, 2012. "Asymmetric contests with liquidity constraints," Public Choice, Springer, vol. 150(3), pages 691-713, March.
  12. Chamley, Christophe, 1986. "Optimal Taxation of Capital Income in General Equilibrium with Infinite Lives," Econometrica, Econometric Society, vol. 54(3), pages 607-622, May.
  13. Garfinkel, Michelle R. & Skaperdas, Stergios, 2007. "Economics of Conflict: An Overview," Handbook of Defense Economics, Elsevier.
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