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Medicine, Medical Consultations, and Game Theory

Medicine and Game Theory

 

We’ve discussed in class the past few weeks the importance of game theory and the number of applications that it has in the world. Primarily, game theory is used in biology, economics, political science, psychology, and computer science. However, I would like to delve into the uses of game theory in healthcare and treatment practices.

Let’s set up a simple model to understand the choices and strategies in healthcare implementation. The simplest model of game theory, rationalizes decision-making based on the strategies of two individuals. In medicine and healthcare, this model would include a doctor and the patient. For future reference, let’s call the doctor individual “D” and the patient individual “P”. The doctor has the choice to simply recommend a standard procedure, or do a full analysis to recommend another procedure (or the same procedure after the time put in for the analysis). However, as is the power of all patients, he or she has the ultimate decision to accept or reject the doctor’s advice. Let’s call these strategies “A” and “B”, for accept and do not accept, listed respectively. The combination of strategies would create a prescriptive decision-making that would be qualitatively and quantitatively different from standard decision analysis. Let’s input some payoffs for each strategy in a sample game theory model. For this model, let’s think about a patient that may have a broken bone. The doctor can do an x-ray and run a few tests to see if the bone is broken, or they can simply give the patient a cast to wear for a period of time.

 

  A: Accept doctor’s strategy B: Reject doctor’s strategy
R: X-Ray, Decision post analysis 2,7 1,4
S: Simply recommend cast 4,3 3,5

 

Without doing an analysis of the model, one would think that the best strategy would be for the doctor to do a complete analysis of the bone and for the patient to accept his recommendation – (R, A). However, this model in medical consultation shows that there would be a Nash equilibrium for (S, B), in which the doctor would simply recommend the use of a cast and the patient would reject the recommendation of the doctor. (S, B) is a nash equilibrium because no individual can gain from a change in their strategy. While (R, A) would result in the highest quality of care for the patient and the best overall result, it is a dominant strategy for the doctor to simply recommend a cast, without putting in all the time and work to get an analysis. The best response by the patient, would be to reject the doctor’s strategy. The Nash equilibrium could cause problems because the result is the lowest quality of healthcare that can be provided. The Washington Post article and the blog from Presh Talwalkar describe the downfalls of healthcare because of strategies that can be explained by game theory. The problem with healthcare (with respect to game theory) is that the best result may not be the best strategic outcome.

 

https://www.washingtonpost.com/news/wonk/wp/2015/09/16/how-the-doctor-patient-relationship-has-become-a-prisoners-dilemma/

http://mindyourdecisions.com/blog/2009/08/18/how-to-improve-health-care-using-game-theory-the-prisoners-dilemma/

https://www.ncbi.nlm.nih.gov/pubmed/3734022

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