Consumers can choose whether to be served by a safe provider or by a risky one. The risky service is less likely to succeed but it costs less.
Consumers differ in their probability of being successfully served by a risky provider.
The risky providers announce a contract consisting of a pair of prices, one that they will be paid if the service succeeds and the other that they will be paid if it fails. After announcing his contract and after diagnosing a consumer, the risky provider decides whether he himself should serve this consumer or whether he should refer him to a safe provider. We first characterize the socially efficient referrals rule. According to this rule there is a certain probability of successful service by a risky provider, above which the provider should accept the consumer and below which he should refer him to a safe provider. We show that competition among the risky providers leads to an equilibrium referral rule that is socially efficient.