Studies on Dynamics in the Classical Iterated Prisoner's Dilemma with Few Strategies

In this paper we study Classical Iterated Prisoner’s Dilemma (CIPD) dynamics of pure strategies in a discrete and determinist simulation context. We show that, in some very rare cases, they are not quiet and ordered. We propose a classification of ecological evolutions into categories which represent complex dynamics, such as oscillatory movements. We also show that those simulations are very sensitive to initial conditions. These experimentations could call into question classical conclusions about interest of cooperation between entities playing CIPD. They may be used to explain why it is not true that cooperation is always the convergent phenomenon observed in life. 1 The Classical Iterated Prisoner’s Dilemma When they were at the RAND Corp. Merill M. Flood and Melvin Dresher tried to introduce some kind of irrationality in Game Theory, [13, 11]. They introduced a simple two person, non zero-sum, non cooperative and simultaneous game, [6]. This game, very simple to describe, covers a large scale of real life situations and seems to catch the definition of conflicts of interests. Thus a lot of different kind of work has been done on it, involving not only mathematicians, but also social, zoological, biological as well as computer scientists. The game becomes the most used theoretical model for studying the cooperation and the evolution of cooperation in population of agents. The game, called the Prisoner’s Dilemma, could be described very simply in the following way: let us meet two artificial agents having two choices (two strategies): – COOPERATE, let us write C, and say to be nice – DEFECT, let us write D, and say to be naughty The payoff of each player depends on the moves played by the two agents. Tab. 1 names the score of each case. The dilemma comes when exploitation of one by the other (T ) is better payed than cooperation between the two (R), which itself pays more than a case where Table 1. CIPD payoff matrix. Row player score are given first.