Probability matching and reinforcement learning

Probability matching occurs when an action is chosen with a frequency equivalent to the probability of that action being the best choice. This sub-optimal behavior has been reported repeatedly by psychologists and experimental economists. We provide an evolutionary foundation for this phenomenon by showing that learning by reinforcement can lead to probability matching and, if the learning occurs sufficiently slowly, probability matching does not only occur in choice frequencies but also in choice probabilities. Our results are completed by proving that there exists no quasi-linear reinforcement learning specification such that the behavior is optimal for all environments where counterfactuals are observed.