How to Buy Advice with Limited Instruments

Abstract

A decision maker, whose payoff is influenced by an unknown stochastic process, seeks the advice of an advisor, who may be informed about the process. We establish that there exists a strategy of the decision maker that will yield him an almost first-best payoff in every period when interacting with an informed advisor. An important feature of this strategy is that it only requires a fixed budget - regardless of the realizations of the stochastic process and whether or not the advisor is actually informed about it, the total payoff to the decision maker will never fall below a fixed threshold. The strategy also has the property that per-period compensation to the advisor is independent of the present realization of the process, and depends solely on the expected value of the advice as reported by the advisor.