Evolution of Learning among Pavlov Strategies in a Competitive Environment with Noise

Pavlov denotes a family of stochastic learning strategies that achieves the mutually cooperative outcome in the iterated prisoner's dilemma against a wide variety of strategies, although it can be exploited to some extent by some. When restricted to an environment of only Pavlov-type strategies, slower learning mutants cannot invade an initial dominant population. More surprising, mutants who learn much faster than the current population tend to overreact and also cannot invade. In particular, the “immediate learning” version of Pavlov, sometimes called win-stay-lose-switch, often fares poorly in this environment. Only those strategies that learn marginally faster than the dominant variety will have greater fitness. Although faster learners will eventually dominate a given homogeneous Pavlov population, the process must proceed through a gradual increase in the rate of learning.