Only Valuable Experts Can Be Valued

Suppose a principal Alice wishes to reduce her uncertainty regarding some future payoff. Consider a self-proclaimed expert Bob that may either be an informed expert knowing an exact (or approximate) distribution of a future random outcome that may affect Alice’s utility, or an uninformed expert who knows nothing more than Alice does. Alice would like to hire Bob and solicit his signal. Her goal is to incentivize an informed expert to accept the contract and reveal his knowledge while deterring an uninformed expert from accepting the contract altogether. The starting point of this work is a powerful negative result (Olszewski and Sandroni, 2007), which tells us that in the general case for any contract which guarantees an informed expert some positive payoff an uninformed expert (with no extra knowledge) has a strategy which guarantees him a positive payoff as well.

At the face of this negative result, we reexamine the notion of an expert and conclude that knowing some hidden variable (i.e., the description of the aforementioned distribution), does not make Bob an expert, or at least not a “valuable expert”. The premise of our paper is that if Alice only tries to incentivize experts which are valuable to her decision making then she can indeed screen them from uninformed experts.

On a more technical level, we consider the case where Bob’s signal about the distribution of a future event cannot be an arbitrary distribution but rather comes from some subset P of all possible distributions. We give rather tight conditions on P (which relate to its convexity), under which screening is possible. We formalize our intuition that if these conditions are not met then an expert is not guaranteed to be valuable. We give natural and arguably useful scenarios where indeed such a restriction on the distribution arise.