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Transitional Dynamics in a Tullock Contest with a General Cost Function

Author

Listed:
  • Grossmann Martin

    () (University of Zurich)

  • Lang Markus

    () (University of Zurich)

  • Dietl Helmut

    () (University of Zurich)

Abstract

This paper constructs and analyzes open-loop equilibria in 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. In the case of 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. We further analyze the effects of second prizes in the contest. 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, produces a more balanced contest in each period and increases the speed of convergence to the steady state.

Suggested Citation

  • Grossmann Martin & Lang Markus & Dietl Helmut, 2011. "Transitional Dynamics in a Tullock Contest with a General Cost Function," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-26, August.
  • Handle: RePEc:bpj:bejtec:v:11:y:2011:i:1:n:17
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    References listed on IDEAS

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    Cited by:

    1. Martin Grossmann, 2011. "Endogenous Liquidity Constraints in a Dynamic Contest," Working Papers 0148, University of Zurich, Institute for Strategy and Business Economics (ISU).
    2. Boudreau, James W. & Sanders, Shane & Shunda, Nicholas, 2017. "The Role of Noise in Alliance Formation and Collusion in Conflicts," MPRA Paper 81533, University Library of Munich, Germany.
    3. Boudreau, James W. & Shunda, Nicholas, 2015. "Tacit Collusion in Repeated Contests with Noise," MPRA Paper 65671, University Library of Munich, Germany.

    More about this item

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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