Transitional Dynamics in a Tullock Contest with a General Cost Function

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.

Investment on human capital in a dynamic contest model

“…This is an important difference, since "accumulation" implies that the investment in period t also indirectly affects the outcomes of all the contests throughout. In that regard, our model is much closer to the models studied by Grossmann and Dietl (2009) and Grossmann et al (2011). However, we also differ from their models in the following sense.…”

“…Grossmann et al (2010) show that linear costs imply immediate convergence of the asset stocks to the steady state. Later,Grossmann et al (2011) show that if the cost function is convex, then the speed of convergence significantly depends on the elasticity of the cost function. In contrast to these results, we find that even with linear cost functions, non-immediate convergence is possible such that the speed of convergence depends on multiple model parameters.…”

A Dynamic Contest Model of Platform Competition in Two-Sided Markets

“…Refs. [30][31][32] provide dynamic models with heterogeneous contestants. However, their models are limited to only two contestants.…”

Endogenous Liquidity Constraints in a Dynamic Contest

“…Other multistage contests are analyzed byHarris and Vickers (1985),Rosen (1986),Klumpp and Polborn (2006),Konrad and Kovenock (2009) andKonrad and Kovenock (2010). Some economists discuss the optimal investment behavior of contestant with an infinite time horizon(Leininger and Yang (1994);Shaffer and Shogren (2008);Grossmann et al (2010);Grossmann et al (2011)). …”

“…Note that there is no time preference for the first-period profit in order to simplify matters. SeeGrossmann and Dietl (2009) andGrossmann et al (2011) for an analysis of a time discount factor in a dynamic Tullock contest without liquidity constraints.…”