The Alternating Prisonerʹs Dilemma

Reciprocal altruism can often be modelled by a variant of the iterated Prisonerʹs Dilemma where players alternate in the roles of donor and recipient, rather than acting simultaneously. We consider strategies realised by simple transition rules based on the previous encounter, and show that the evolutionary outcome for the alternating Prisonerʹs Dilemma can be quite different from the simultaneous case. In particular, the winner of a simultaneous Prisonerʹs Dilemma is frequently a "win-stay, lose-shift" strategy based on the payoff experienced in the last round, whereas in the alternating Prisonerʹs Dilemma, the trend leads towards a "Generous Tit For Tat" strategy. If one allows only for reactive strategies based on the other playerʹs last move, the overall payoff is the same for the alternating or the simultaneous version, although the sequence of moves can be different. In the alternating game "win-stay, lose-shift" strategies can only be successful if there is a longer memory of past encounters. The alternating and simultaneous Prisonerʹs Dilemma are two very different situations, and the whole existing literature is based on the simultaneous game.