This seems like a mutual information problem. (https://en.wikipedia.org/wiki/Mutual_information https://en.wikipedia.org/wiki/Mutual_information) The price lev

This seems like a mutual information problem. (https://en.wikipedia.org/wiki/Mutual_information https://en.wikipedia.org/wiki/Mutual_information) The price leverage of the doctor is proportional to how much information the doctor has about how much money you have. If you can't keep it secret, you can add noise proportional to how much information the doctor likely has to cancel it out. The resulting "fair" price will be a function of the net shared information each side if the noise were removed. Negotiations theory was a pet interest of mine, and I came to believe that in zero sum adversarial bargaining situations like that, the domainant position was the side with the most information, so the best strategy was to use noise to diminish their information, and then use whatever information you retained as arbitrage. If you think of noise in terms of signal entropy, and low entropy as signal, you can figure out whether their gambit is signal or noise by repsonding with noise and gauging the entropy of their response. This is crazy armchair stuff that nobody articultes, but variations of it gets used in bureaucracy and politics all the time, it's basically the game theory of gaslighting.