Bertrand-Edgeworth competition under non-exclusivity

The work introduces a simple framework to study the relationship between competition and incentives under non-exclusivity. We characterize the equilibria of an insurance market where intermediaries compete over the contracts they offer to a single consumer in the presence of moral hazard. Non-exclusivity is responsible for under-insurance and positive profits in an otherwise competitive set-up. A relevant notion of optimality is also introduced and it is argued that market equilibria fail to be constrained-efficient.