Induced preferences and decision-making under risk and uncertainty

In this paper we suggest a new interpretation of non-additive probabilities. We study a decision-maker who follows the Savage axioms. We show the if (s)he is able to take unobservable actions which influence the probabilities of outcomes then it can appear to an outsider as if his/her subjective probabilities are non-additive. We make a related analysis of models with objective probabilities and show that the induced preferences can have the rank dependent expected utility form. Implications for multi-period decisions are explored.