Two competing models of how people learn in games (first version)

Reinforcement learning and stochastic fictitious play are apparent rivals as models of human learning. They embody quite different assumptions about the processing of information and optimisation. This paper compares their properties and finds that they are far more similar than was thought. In particular, exponential fictitious play and a suitably perturbed reinforcement model have the same expected motion and therefore will have the same asymptotic behaviour. It is also shown that more general models of stochastic fictitious play and perturbed reinforcement learning have identical local stability properties. The main identifiable difference between the two models is speed: stochastic fictitious play gives rise to faster learning.