This paper analyzes the three-party contracting problem among the payer, the patient and the physician when the patient and the physician may collude to exploit mutually beneficial opportunities. Under the hypothesis that side transfer is ruled out, we analyze the mechanism design problem when the physician and the patient submit the claim to the payer through a reporting game. To induce truth telling by the two agents, the weak collusion-proof insurance payment mechanism is such that it is sufficient that one of them tells the truth. Moreover, we identify trade-offs of a different nature faced by the payer according to whether incentives are placed on the patient or the physician. We also derive the optimal insurance scheme for the patient and the optimal payment for the physician. Moreover, we show that if the payer is able to ask the two parties to report the diagnosis sequentially, the advantage of the veto power of the second agent allows the payer to achieve the first-best outcome.
