Bargaining over Treatment Choice under Disagreement

A group of experts with different prior beliefs must make a collective decision over the choice of a treatment or policy. We propose a model where such disagreements are resolved through bargaining. We show that, when the outcome is determined according to the Nash bargaining solution, the collective decision is made as if a planner maximized expected utility with respect to a ``compromise belief'' that places greater weight on the more pessimistic experts. In interesting classes of environments, bargaining leads to an inefficient use of information in a strong sense: experts receive a lower payoff in every state, and thus for any prior belief. This inefficiency takes the form of under-reaction to information. We connect these findings to speculative betting and to the admissibility of statistical decision procedures.