Optimal Properties of Stimulus-Response Learning Models

We consider stimulus-response models of learning: an agent chooses an action with a probability, which is increasing in the payo® that has been associated to that action in past periods. A procedure is a speci ̄c way of making this association. We say that a procedure is optimal if the sequence of choices it generates converges to the action that maximizes the expected payo®. Which procedures are optimal depends in a substantial way on the information available to the agent. We say that an individual learning in isolation has partial information, because he can only observe the payo® to the action he has chosen; in social learning, he has full information, because he can learn from the action of the others the payo® associated to each action. The main conclusion of the paper is that linear procedures always converge to optimal action in the case of partial information, and do not in the case of full information. Exactly the opposite is true in the case of exponential procedures: in particular they fail to converge to the optimal action when only partial information is available. This result points to a substantial di®erence between the procedures that are likely to be adopted in social and isolated learning.