Error and Discounting in the Iterated Prisoner's Dilemma

Since 1981 a large body of research has focused on the Iterated Prisoner's Dilemma as a "basic paradigm" for the study of non-kin cooperation. Current evidence, however, shows that animals consistently defect in controlled Prisoner's Dilemmas. In this paper, an attempt is made to understand this by studying the effects of error and discounting (the tendency to devalue future rewards) on the stability of two strategies, tit-for-tat and Pavlov, against the clear experimental winner, all-defection. When considering strategic error, it is found that there are some payoff combinations in which the "cooperative strategy (tit-for-tat or Pavlov) can never be stable against all defection, and others where low levels of temporal discounting and/or large levels of game repetition can stabilize the cooperative strategy, as the conventional view suggests. These no-cooperation regions are characterized and compared for tit-for-tat and Pavlov. When tit-for-tat is pitted against all defection, however, there is also a third set of payoff combinations in which tit-for-tat is stable against all defection at intermediate levels, but unstable at both very low and very high levels of temporal discounting. For both strategies, increasing error rates increase this no-cooperation region. Similarly, as error increases weaker temporal discounting is required to stabilize a cooperative strategy against all defection. The most modest requirements for stability occur when the "temptation to defect" is negligible and the benefits of mutual cooperation greatly exceed the benefits of mutual defection. Estimates of the relevant discounting parameters are presented and discounting rates that are at least an order of magnitude smaller than values that seem plausible under the conventional "game repetition" view of the Iterated Prisoner's Dilemma are estimated. The prediction is that animal cooperation in Prisoner's Dilemmas will be restricted to a very small set of payoff combinations.