Abstract

This work provides a game theoretical analysis of the classical idea of a social contract. According to what we might call the Hobbesian justification of the state, coercion is necessary in order to provide people with basic security and to enable them to successfully engage in mutually beneficial cooperation. The establishment and maintenance of a central coercive power, i.e. a state, can therefore be said to be in everyone's interest. The aim of this essay is to examine and evaluate these claims. It is common to interpret the problem of cooperation in a Hobbesian state of nature as a Prisoner's Dilemma game. In this kind of game, each agent prefers that cooperation is brought about, but each also prefers not to cooperate herself, regardless of what others do. Most studies, however, have focused on the prospects for spontaneous cooperation in the 2-player PD. This work focuses instead on the generalized, n-player version of the same game. Invoking an evolutionary game theoretical model, it is argued that the prospects for spontaneous cooperation to emerge in an n-player PD are much worse than in the 2-player case. In order to analyze how the existence of sanctions might affect the prospects for cooperation, a model of a limited sanction system is developed. It is demonstrated that the game that emerges when an n-player PD is modified by a suitable system of sanctions is an n-player version of what Sen has called an Assurance game. It is also demonstrated that in this game, unlike the n-player PD, general cooperation is evolutionarily stable. It is also discussed whether the establishment and maintenance of such a sanction system does itself constitute an n-player PD. It is argued that it does not