Profiling problems with partially identified structure

This article studies two classes of profiling problems where the relevant structural inputs to the problems may be only partially identified: that where profilees are not 'strategic' in altering their characteristics and that where profilees strategically alter their characteristics at a cost. The analysis is unified by assuming there is a utilitarian planner that attempts to optimise the sum of welfare. We compare maximin solutions and minimax-regret solutions in two contexts. An unexpected feature of the minimax-regret solution is that a minimax-regret planner may end up learning unknown features of the population it faces rather quickly relative to a maximin planner.