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Resolute Choice in Sequential Decision Problems with Multiple Priors

Helene Fargier, Gildas Jeantet and Olivier Spanjaard

This paper is devoted to sequential decision making under uncertainty, in the multi-prior framework of Gilboa and Schmeidler (1989). In this setting, a set of probability measures (priors) is defined instead of a single one, and the decision maker selects a strategy that maximizes the minimum possible value of expected utility over this set of priors. This decision criterion is often called maxmin expected utility (or Gamma-Maximin) in the literature. We are interested here in the resolute choice approach, where one initially commits to a complete strategy and never deviates from it later. Given a decision tree representation with multiple priors, we study the problem of determining an optimal strategy from the root according to Gamma-Maximin. We prove the intractability of evaluating a strategy in the general case. We then identify different properties of a decision tree that enables to design dedicated resolution procedures. Finally, experimental results are presented that evaluate the operationality of these procedures.