Diversified Treatment under Ambiguity

This paper develops a broad theme about treatment under ambiguity through study of a particular decision criterion. The broad theme is that a planner may often want to cope with ambiguity by diversification, assigning observationally identical persons to different treatments. Study of the minimax-regret (MR) criterion substantiates the theme. The paper significantly extends my earlier analysis of one-period planning with individualistic treatment and a linear welfare function. I show that MR treatment allocations are fractional in a large class of planning problems with nonlinear welfare functions, interacting treatments, learning, and non-cooperative aspects. I also call attention to some problems of treatment under ambiguity in which the MR allocation is not fractional. This research was supported in part by National Science Foundation grant SES-0549544. This paper revises and supercedes an earlier working paper “Fractional Treatment Rules for Social Diversification of Indivisible Private Risks,” NBER Working Paper W11675, September 2005. I have benefitted from the opportunity to present this work at an invited session of the 2009 North American Winter Meeting of the Econometric Society and in seminars at Collegio Carlo Alberto, The Hebrew University of Jerusalem, Northwestern University, Princeton University, Universitat Pompeu Fabra, Université Paris 1, UCLA, University College London, and the University of Washington.