Cooperation Model with Costly Punishment

In recent years the issue of costly punishment in systems where free-riding occurs has been a subject of extensive research in the field of game theory. This issue is present in many areas of human activities like paying taxes, using public transport, wireless Internet or P2P networks. It is one of the most common dilemmas in modern societies. In this work we present a simple model of cooperation with three possible strategies (cooperate, defect or punish). In the model players explore the available strategies according to their interactions with other players. We introduce two groups of parameters. The first group is sociological-like and it describes the social acceptance for the free riding behavior. The other group of parameters describes the economical aspects of the system - the cost and efficiency of punishers. Using differential equations approach, as well as an agent based model, we look for equilibrium properties of the system.