Sorting in iterated incumbency contests

This paper analyzes incumbency contests in a large population setting. Incumbents repeatedly face different 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. Individuals are heterogeneous as regards their payoffs from being incumbent. We consider steady-state equilibria and study how and to which extent individuals sort into the incumbency positions depending on their type. In particular, we identify sufficient conditions for positive sorting, meaning that types with higher incumbency payoffs are overrepresented among the incumbents, and show that negative rather than positive sorting may also arise in equilibrium when these conditions are violated. Further results show how incumbency rents, surplus and sorting are affected by the frequency at which incumbency is contested.