A simple dynamic contest with a parameterized strength of competition

Abstract

This paper analyzes the effect of competition in a dynamic contest in which agents of two types (A and B) differ in their expected performances; environments where type A outperforms type B are more frequent than those where B outperforms A. In each period, the population of agents is randomly matched in groups of n members (each group faces a particular environment), with the top k<n performing agents from each group being the winners of the prizes. Hence, the ratio frac{k}{n} determines the proportion of winning agents in each group. This ratio also describes the strength of competition in the group: the lower frac{k}{n} is, the higher the level of competition is. Our results show that type A eventually dominates the entire population with moderate competition, but type B survives in the long run for high levels of competition. Hence, we obtain that no matter how low the expected success rate of a type is, if the strength of competition is high enough those agents with the lowest expected success rate survive in the long run.