Abstract We investigate two-stage parallel contests with a finite number of heterogeneous agents with various skills (cost of efforts) and reputations, as well as a finite number of heterogeneous contests. Each agent’s value of winning is a combination of a nominal value and the reputation of the competing agents. We demonstrate that reputation in contests may lead to an unstable environment. We present a sufficient condition for resolving this instability, which results in the existence of a subgame perfect equilibrium with pure strategies which cannot be explicitly calculated. However, we arrive at this equilibrium by introducing algorithms that describe dynamic processes in which the agents’ strategies approach the equilibrium point. We demonstrate that our equilibrium is far more likely to hold in an environment where the agents’ skills and reputations are correlated.
Cohen et al. (Mon,) studied this question.