For specifically the doctor version of the principle-agent problem, Robin Hanson published an incentive-compatible solution over 25 years ago: http://mason.gmu.edu/~rhanson/buyhealth.html
> There are, however, two big problems with this approach. The first is that even though my life may be worth $10 million to me, most of the (huge) insurance premium to pay for this insurance would be wasted from my point of view -- there probably is not one person to whom I would want to give this much money when I die. The other problem is moral hazard -- heavy insurance may reduce my incentive to keep myself healthy, and may even create incentives for my relatives to try and hurt me. It might be a problem if I could only give my doctor a 50 percent interest in my life by taking away 50 percent of my own interest, or by giving a minus 50 percent interest to my relatives.