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Game Theory and Doctor-Patient Cooperation

Game theory is used to describe situations where the outcome depends on one’s decision and the decision of those they are interacting with. The relationship between doctors and patients can be modeled in this fashion. A doctor can cooperate by spending more time with a patient and correctly identifying and treating their illness. A doctor could not cooperate by quickly writing a prescription or by not putting effort into the case, either due to time constraints or frustration. The patient can cooperate by following the doctor’s orders or not cooperate by ignoring them. The Assurance game described by Tarrant et al. (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1743922/pdf/v013p00461.pdf) shows the use of game theory in medical interactions.

Doctor Cooperates

Doctor Does Not Cooperate

Patient Cooperates

4, 4,

1, 2,

Patient Does Not Cooperate

2, 1

3, 3

The Nash equilibria are for the patient and doctor to both cooperate or for the doctor and patient to not cooperate. In addition, there are no dominant strategies for either the patient or the doctor but the pareto optimal strategy is for both the patient and the doctor to cooperate, improving the patient’s condition and the doctor’s payoff. The mixed strategy probability for the doctor to cooperate is ¼ and for the patient to cooperate is ¼. These probabilities reflect that with the above payoffs, it is better for both the doctor and the patient not to cooperate and therefore not run the risk of ending up with the lowest payoff. However, the decisions made by the doctors or patients are not random and will always be influenced by situational factors.

I believe this model accurately describes doctor-patient interactions and payoffs. Ideally, doctors and patients should cooperate to benefit from the highest payoffs but it can be difficult in reality for both the doctor and patient to cooperate. In many cases, patients do not cooperate while the doctor cooperates. One example would be patients reluctant to visit doctors due to having strong beliefs in a specific religion or another healing system. These patients will often have different reasoning behind what is causing their illness and therefore will have a difficult time following the treatment. The doctor who is cooperating has a low payoff because he or she is trying to treat a patient that does not follow their advice. The patient’s payoff is higher than the doctors because the patient may be treating their illness in the way that they see fit, such as using certain herbs. Another example, given by the paper, is a doctor trying to help a patient quit smoking. The doctor often goes through a lot of trouble creating a cessation program that the patient ignores, therefore ending up with the lowest payoff.

These examples show that doctors and patients, unless they have the assurance of cooperation, should defect. However, defecting is not a practical strategy for the doctor or medical professional in the long run. A doctor cannot always choose to defect without further serious consequences and a dramatic change in the payoff structure. The authors of this study who are further researching the applications of game theory to medical practice should look into long-term payoffs.

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