Optimality under noise: Higher memory strategies for the Alternating Prisoner's Dilemma

The Alternating Prisoner's Dilemma is a variant of the iterated Prisoner's Dilemma in which the players alternate in the roles of actor and recipient. We searched for strategies which are "optimal" in the Alternating Prisoner 's Dilemma with noise (a non-zero probability that a player's decision will be transmitted incorrectly). In order to achieve success against a variety of other strategies, a strategy must be "self-cooperating" (able to achiev e mutual cooperation with its clone), "C-exploiting" (able to exploit uncon ditional cooperators), and "D-unexploitable" (able to resist exploitation b y defectors). It must also have high evolutionary "dominance", a general me asure of evolutionary performance Which. considers both resistance to invas ion, and the ability to invade other strategies. A strategy which meets the se optimality criteria can evolve cooperation by invading a population of d efectors and establishing a stable cooperative society. Most of the strategies commonly discussed in the Alternating Prisoner's Dil emma literature are low-memory strategies such as Tit For Tat, Pavlov, and Firm But Fair, but none of these strategies can simultaneously meet all of the optimality criteria. However, we discovered a class of higher memory "F irm Pavlov" strategies, which not only meet our stringent optimality criter ia, but also achieve remarkable success in round-robin tournaments and evol utionary interactions. These higher memory strategies are friendly enough t o cooperate with their clone, pragmatic enough to exploit unconditional coo perators, and wary enough to resist exploitation by defectors: they are tru ly "optimal under noise" in the Alternating Prisoner's Dilemma. (C) 2001 Ac ademic Press.