Is it Accidental or Intentional? A Symbolic Approach to the Noisy Iterated Prisoner’s Dilemma

The Iterated Prisoner’s Dilemma (IPD) has become well known as an abstract model of a class of multi-agent environments in which agents accumulate payoffs that depend on how successful they are in their repeated interactions with other agents. An important variant of the IPD is the Noisy IPD, in which there is a small probability, called the noise level, that accidents will occur. In other words, the noise level is the probability of executing “cooperate” when “defect” was the intended move, or vice versa. Accidents can cause difficulty in cooperations with others in real-life situations, and the same is true in the Noisy IPD. Strategies that do quite well in the ordinary (non-noisy) IPD may do quite badly in the Noisy IPD [Axelrod and Dion, 1988; Bendor, 1987; Bendor et al., 1991; Molander, 1985; Mueller, 1987; Nowak and Sigmund, 1990]. For example, if two players both use the well-known Tit-For-Tat (TFT) strategy, then an accidental defection may cause a long series of defections by both players as each of them punishes the other for defecting. This chapter reports on a strategy called the Derived Belief Strategy (DBS), which was the best-performing non-master-slave strategy in Category 2 (noisy environments) of the 2005 Iterated Prisoner’s Dilemma competition (see Table 10.1).