Evolutionary strategies of stochastic learning automata in the prisoner's dilemma

Stochastic learning automata (SLA) model stimulus-response species which receive feedback from the environment and adjust their mixed strategies in a Prisoner's Dilemma. A large heterogeneous population consists of SLA applying different strategies (i.e. different learning parameters) and other players applying deterministic strategies, Tit-For-Tat (TFT) or Always-Defect (ALLD). The predicted equilibria determine the payoffs within a generation for applying particular strategies and these equilibria are confirmed by simulation. The resultant population dynamics over many generations show that SLA with insensitive penalty responses strongly favor defection and dominate in subsequent generations over SLA with sensitive penalty responses. The SLA strategies are not evolutionarily stable as they can be invaded by TFT or ALLD. With the introduction of memory in the stimulus-response model, SLA learn to cooperate with TFT players.