The prisoner's dilemma game is used to describe situations, in which cooperation by everyone is profitable, but where free-riders can get a higher payoff than cooperators. Therefore, non-cooperative behaviour is tempting and cooperative behaviour is risky, which tends to destabilise cooperation. Our computer simulations are based on a circular network with 100 nodes, each of which is connected to the two nearest neighbours on the left and on the right. In addition, n links are added randomly. n is varied between zero and 900 in steps of 25. 50 agents are distributed over the resulting network and playing 2-person prisoner's dilemma games with all adjacent agents in the network. The payoffs of the prisoner's dilemma are assumed to be T=7, R=6, P=2, and S=1 (using the conventional parameters). Initially, all agents are non-cooperative, but their network locations and behaviours (cooperation or defection) are updated in a random sequential way as follows:
1. After the interaction with their neighbours, agents move with probability 0.5 up to 4 steps along existing links to an empty node that gives the highest payoff in a fictitious play step, assuming that the agents do not change their behaviours.
2. The agents imitate the behaviour of the respective direct neighbour with the highest payoff.
3. The agents spontaneously change their behaviour with probability 0.05. Simulations are stopped after 50,000 time steps.
Color Description: Blue circles represent cooperative behaviour, red circles non-cooperative behaviour, and black dots represent empty sites that agents may enter by success-driven migration.
Initially, the cooperation is enhanced by increasing the link density. However, as the connectivity passes a certain threshold, the level of cooperation goes down and erodes completely as the system becomes very densely connected.