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