Coasian Dynamics under Informational Robustness

This paper studies durable goods monopoly without commitment under an informationally robust objective. A seller cannot commit to future prices and does not know the information arrival process according to which a representative buyer learns about her valuation. To avoid known conceptual difficulties associated with formulating a dynamically-consistent maxmin objective, we posit the seller's uncertainty is resolved by an explicit player (nature) who chooses the information arrival process adversarially and sequentially. Under a simple transformation of the buyer's value distribution, the solution (in the gap case) is payoff-equivalent to a classic environment where the buyer knows her valuation at the beginning. This result immediately delivers a sharp characterization of the equilibrium price path. Furthermore, we provide a (simple to check and frequently satisfied) sufficient condition which guarantees that no arbitrary (even dynamically-inconsistent) information arrival process can lower the seller's profit against this equilibrium price path. We call a price path with this property a reinforcing solution, and suggest this concept may be of independent interest as a way of tractably analyzing limited commitment robust objectives. We consider alternative ways of specifying the robust objective, and also show that the analogy to known-values in the no-gap case need not hold in general.