Abstract

We depart from the classic setting of bandit problems by endowing the agent with a disappointment-elation utility function. The disutility of a loss is assumed to be greater than the elation associated with same-size gain, according to Kahneman-Tversky findings on the attitude of agents towards a change in wealth. We characterise the optimal experimentation strategy of an agent in a two-armed bandit problem setting with infinite horizon and we derive an existence theorem, specifying a condition on the disappointment aversion parameter. The model, solved in closed form in a one-armed bandit setting, shows that an agent who feels disappointment experiments more intensively than the agent characterised by the standard expected utility model, despite disappointment, but only if the degree of disappointment is under a certain threshold level. The threshold level depends both on the probability of rewards along the unknown projects relative to the expected number of trials and on the expected reward of the unknown project.