Transitional Dynamics in a Tullock Contest with a General Cost Function
AbstractThis 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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Bibliographic InfoPaper provided by University of Zurich, Institute for Strategy and Business Economics (ISU) in its series Working Papers with number 0117.
Length: 25 pages
Date of creation: Nov 2009
Date of revision: Dec 2010
Dynamic contest; transitional dynamics; logit contest; multiple prizes; rent-seeking;
Other versions of this item:
- Martin Grossmann & Markus Lang & Helmut Dietl, 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 17.
- Martin Grossmann & Markus Lang & Helmut Dietl, 2009. "Transitional Dynamics in a Tullock Contest with a General Cost Function," Working Papers 0032, University of Zurich, Center for Research in Sports Administration (CRSA), revised Dec 2010.
- 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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- Martin Grossmann, 2011. "Endogenous Liquidity Constraints in a Dynamic Contest," Working Papers 0148, University of Zurich, Institute for Strategy and Business Economics (ISU).
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