A dynamic game under ambiguity: contracting for delegated experimentation

Conventional (single-prior) Bayesian games of incomplete information are limited in their ability to capture the extent of informational asymmetry. In particular, they are not capable of representing complete ignorance of an uninformed player about an unknown parameter of the environment. Using a framework of contracting for delegated experimentation, we formulate and analyze a dynamic game of incomplete information that incorporates a multiple-prior belief system. Specifically, we consider a game with a principal contracting with an expert agent for his (observable) effort on a novel experiment --- a Poisson process with unknown hazard rate. Although the expert agent has sufficient knowledge to form a single prior over the hazard rate, the principal initially has complete ignorance and her ambiguous beliefs are represented by the set of all plausible prior distributions over the hazard rate. We propose a new equilibrium concept --- Perfect Objectivist Equilibrium --- in which the principal, who has ambiguity aversion, draws inference about the agent's prior from the observed history of the game via likelihood ratio tests. The new equilibrium concept thus also embodies a novel model of learning under ambiguity in the context of a dynamic game. Although the game is rich in its contractual space and strategic interactions, the unique (Markov) equilibrium outcome is a remarkably simple pooling contract with appealing economic properties.