Mean and variance responsive learning

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