Investment on human capital in a dynamic contest model

Abstract

Although most contest games are modeled in such a way that the outcome depends only on the efforts exerted by the contestants, what is arguably more important is the contestants’ effective efforts which may be influenced also by their ability, human capital, strength, etc. In this paper, we investigate an extensive model including such an effectiveness parameter and analyze the optimal investment behavior in a dynamic conflict framework. At each period, two contestants compete for a common prize by choosing contest efforts and investment levels. Each contestant’s investment accumulates as his/her human capital which depreciates through time. Who wins the component contest at a particular period is determined by the contestants’ effective efforts, defined as increasing functions of their efforts and human capitals. Following the analysis of subgame perfect Nash equilibrium in a two-period model and of open-loop equilibrium in an infinite-horizon model, we provide intuitive comparative static results.