Mean and variance responsive learning

Decision makers are often described as seeking higher expected payo¤s and avoiding higher variance in payo¤s. We provide some necessary and some su¢ cient conditions for learning rules, that assume the agent has little prior and feedback information about the environment, to re‡ect such preferences. We adopt the framework of Börgers, Morales and Sarin (2004, Econometrica) who provide similar results for learning rules that seek higher expected payo¤s. Our analysis reveals that a concern for variance leads to quadratic transformations of payo¤s to appear in the learning rule.