Transitional Dynamics in a Tullock Contest with a General Cost Function

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.