The Virtues of Hesitation

Abstract. In many economic, political and social situations, circumstances change at random points in time, reacting is costly, and reactions appropri- ate to present circumstances may become inappropriate upon future changes, requiring further costly reaction. Waiting is informative if arrival of the next change has non-constant hazard rate. We identify two classes of situations: in the first, delayed reaction is optimal only when the hazard rate of further changes is decreasing; in the second, it is optimal only when the hazard rate of further changes is increasing. These results in semi-Markovian decision theory provide motivations for building delay into decision systems.