A Model of Anticipated Regret and Endogenous Beliefs

This paper clarifies and extends the model of anticipated regret and endogenous beliefs based on the Savage (1951) Minmax Regret Criterion developped in Suryanarayanan (2006a). A decision maker chooses an action with state contingent consequences but cannot precisely assess the true probability distribution of the state. She distrusts her prior about the true distribution and surrounds it with a set of alternative but plausible probability distributions. The decision maker minimizes the worst expected regret over all plausible probability distributions and alternative actions, where regret is the loss experienced when the decision maker compares an action to a counterfactual feasible alternative for a given realization of the state. Preliminary theoretical results provide a systematic algorithm to find the solution to the decision problem and show how models of Minmax Regret differs from models of ambiguity aversion and expected utility. In particular, the solution to the decision problem can always be represented as a saddle point solution to an equivalent zerosum game problem. This new problem jointly produces the solution to the Anticipated Regret problem and the endogenous belief. We then use the endogenous belief to define the implicit certainty equivalent and to build an infinite horizon and time consistent problem for a decision maker minimizing her lifetime worst expected regrets.