Sorting in Iterated Incumbency Contests

This paper analyzes iterated incumbency contests with heterogeneous valuations in a large population setting. Incumbents repeatedly face dierent challengers, holding on to their positions until defeated in a contest. Defeated incumbents turn into challengers until they win a contest against an incumbent, thereby regaining an incumbency position. We consider steady-state equilibria of this process and study how and to which extend individuals sort into the incumbency positions depending on their valuations. In particular, we identify sucient conditions for positive sorting, meaning that the share of individuals with a given valuation holding an incumbency position is increasing in the valuation, and provide an example to show that negative rather than positive sorting may arise in equilibrium. Further results show how incumbency rents and sorting are aected by the frequency at which incumbency is contested and the scarcity of the incumbency positions.