Stochastic strategies in the prisoner's dilemma
In the repeated prisoner's dilemma, the (deterministic) Tit-for-Tat strategy has been known to be highly successful. Motivated by the observation that in biological applications there is always some uncertainty or noise, the author argues that it is more appropriate to consider stochastic (mixed) strategies. He gives a complete analysis of all strategies where the probability to cooperate depends only on the opponent's previous move for the infinitely repeated prisoner's dilemma. All Nash solutions are characterized. Specifically (ignoring the initial move which will not matter in the long run if the transition matrix generated by the strategies is mixing), a strategy is given by p and q, where p resp. q is the probability to cooperate given that the other player's previous choice was ``cooperate'' resp. ``defect''. It is shown that \(p=1\) (never defect after cooperation) is a necessary condition for stability against invasion by selection pressure. There exists a region of possible strategies where cooperation increases due to mutation-selection forces. There exists also a region where less cooperative strategies can invade.
scientific article; zbMATH DE number 4200032