Behaviorally consistent optimal stopping rules

This paper characterizes optimal stopping rules in a bounded sequential search model without recall for searchers whose preferences are nonlinear in the probabilities. The optimal search strategy may be dynamically inconsistent. However, if the searcher is behaviorally consistent, i.e., if he restricts his choice to strategies that consist of an optimal move at every stage provided that the same rule is followed in every subsequent stage then (a) if the preferences are quasiconvex then the optimal stopping rule has the familiar reservation level property, (b) if the preferences are quasiconcave then the optimal procedure may be a mixed strategy.