The Role and Evolution of Central Authorities

In this paper we consider the way in which authorities arise in response to the need for coordination. In a model of local interaction, an authority is understood as a self-enforcing coordination selection structure, where the threat of violence ensures compliance. Such authorities form if mutually connected individuals with sufficient combined punishment potential have signalled their willingness to form such an authority, conditional upon the willigness of others to do so. Given a specific timing of decisions, we analyse the conditions under which authorities arise and under which they evolve into a steady situation with only one or several remaining authorities.