Contracting for innovation under knightian uncertainty
Series/Report no.Cahier de recherche #2012-15
At any given point in time, the collection of assets existing in the economy is observable. Each asset is a function of a set of contingencies. The union taken over all assets of these contingencies is what we call the set of publicly known states. An innovation is a set of states that are not publicly known along with an asset (in a broad sense) that pays contingent on those states. The creator of an innovation is an entrepreneur. He is represented by a probability measure on the set of new states. All other agents perceive the innovation as ambiguous: each of them is represented by a set of probabilities on the new states. The agents in the economy are classiﬁed with respect to their attitude towards this Ambiguity: the ﬁnanciers are (locally) Ambiguity-seeking while the consumers are Ambiguity-averse. An entrepreneur and a ﬁnancier come together when the former seeks funds to implement his project and the latter seeks new proﬁt opportunities. The resulting contracting problem does not fall within the standard theory due to the presence of Ambiguity (on the ﬁnancier’s side) and to the heterogeneity in the parties’ beliefs. We prove existence and monotonicity (i.e., truthful revelation) of an optimal contract. We characterize such a contract under the additional assumption that the ﬁnanciers are globally Ambiguity-seeking. Finally, we re-formulate our results in an insurance framework and extend the classical result of Arrow  and the more recent one of Ghossoub. In the case of an Ambiguity-averse insurer, we also show that an optimal contract has the form of a generalized deductible.