Induced preferences, nonadditive beliefs, and multiple priors

We study a decision maker who follows the Savage axioms, We show that if he or she is able to take unobservable actions that influence the probabiliti es of outcomes, then it can appear to an outsider as if his or her subjecti ve probabilities are nonadditive. Implications for multiperiod decision are explored. We extend the model to include a second individual who is also a ble to take a hidden action. We show that this may induce uncertainty-avers e preferences over some class of acts, even if the second individual acts t o help the decision maker with high probability.