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Game Theory in the Medical Field

As we discussed in class, game theory has a wide range of applications. It is used when individuals make decisions based on one or more ways of acting. The individuals, typically called players, use strategies which ultimately determine their payoff. In a payoff matrix, there is a Nash equilibrium if the matrix includes a set of strategies that are best responses to each other. For instance if a pair of strategies (S, T) is a nash, then S has to be the best response to T and T has to be the best response to S.

The article applies different game theory models to the medical practice, and specifically the patient-doctor interaction. The first game theory model proposed is based on the prisoner’s dilemma, whereby there are 2 prisoners, and each must choose where or not to confess. By both confessing, they will both be both be convicted; by both not confessing, both will be acquitted. If one of the two confesses, the one who confessed will be acquitted (with the best possible payoff) and the other will receive a heavy sentence (the worst possible payoff).

This model was then applied to medical consultation in primary care. The hypothetical scenario involves a busy Friday afternoon surgery at a general practitioner’s office. A patient comes in with a sore throat. The practitioner has to choose between quickly diagnosing the patient by giving him/her a prescription for a generic antibiotic, or spending more time with the patient to assess other factors and to make a more comprehensive diagnosis. The two options for the doctor are to work in the patient’s best interests and give a comprehensive diagnosis (C) and to simply prescribe the antibiotic (D). The two options for the patient are to either cooperate, and follow the doctors orders (C) or to not go along with the doctor’s advice (D). The possible outcomes are represented in the payoff matrix below, where the doctor is represented by I and the patient by II:

Here, the best possible outcome is obviously at (C,C) where the doctor takes time to give the patient a comprehensive diagnosis, and the patient complies with the doctor’s orders. The nash equilibrium, however, is at (D,D), because (C,C) doesn’t give the best response to the other player’s strategy. For instance, if the doctor chooses to to spend more time giving advice to the patient (C), then it would be in the patient’s best interest to not follow advice (payoff of 8 is greater than 7). Additionally, if the patient chooses to take the advice (C), then it would be more favorable for the doctor to not give the extra advice and just give the prescription (D) as that would result in a higher payoff (4 is greater than 3). Therefore, only at (D,D) would there be a nash (when the patient doesn’t follow advice, the doctor shouldn’t invest time in giving a complete diagnosis and vice versa).  The problem with the prisoner’s dilemma in medical consultation is that it results in a very poor outcome, and low-quality care for the patient. Another factor that limits the effectivity of this model is that the players (doctor and patient) are seen as interchangeable, even though the stakes will probably be higher for the patient (the doctor’s decision about whether or not to give high quality care will impact the patient a lot more than the patient’s decision about whether or not to follow advice will impact the doctor).
Two other game models discussed in the article are the assurance game (similar to the cooperation game described in class) and the centipede game. The assurance model gives the best possible outcomes when cooperation between the patient and the practitioner occurs (if both choose C or both choose D). However, if one of two chooses to cooperate while the other doesn’t, then this will result in the worst possible outcome for the one that chose to cooperate. The centipede game involves the alternation of each player in deciding whether to defect (which is shown by moving down) or to cooperate (where the player moves across). When one player chooses to defect, the game terminates at that point. For instance if Player two defects during his first turn, player one will receive a payoff of -1, and player one will receive a payoff of 10.  While the best outcome for both players would be to cooperate the entire time and end up with (18,18) payoff, there is an incentive for each player to defect along the way. The nash equilibrium of this game is at (0,0), because if the player guesses the other player’s next move, then he will choose to defect. For example at the end of the centipede, player two would choose to defect because he/she would be able to earn a payoff of 19 instead of 18 by defecting instead of cooperating. However, in the previous turn, player one would foresee that player two would defect,  and would therefore defect during that turn for a payoff of 9 instead of 8. This pattern continues all the way to (0,0). This can be seen in patient/doctor interactions as a doctor could defect by referring the patient to another doctor. The patient could cooperate by taking the doctor’s advice but could also defect by not complying with the doctor’s advice, or by severing contact with the doctor to see someone else.
Assurance Game
Centipede Game
The article mentions that these could all be applied to medical consultation but with limitations. The most important predictor of cooperation is the patient/doctor’s repeated contacts or previous contacts. If the doctor knows that he/she will have more encounters with the patient in the future, or already has established a relationship with the patient, the doctor will be more likely to cooperate. The same goes for the patient. More research needs to be done in this domain: what types of relationships and to what degree do these relationships affect trust and cooperation?
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1743922/pdf/v013p00461.pdf
-Al

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