Modeling the abusive of some doctors of patient trust using Markov chain and ZD strategy

Document Type : Research Paper


1 ریاضیات محض، دانشگاه سمنان، سمنان، ایران

2 گروه ریاضی آمار، دانشگاه سمنان، سمنان، ایران


In the present study, the abusive of some doctors from trusting a patient to earn the more financial benefits is investigated using the Markov chain and Zero-Determinant (ZD) strategy. When someone gets sick and visits a doctor, it is clear that the patient should trust the doctor and considers medical advices certainly. The doctors who abuse the trust of patients, they usually use tricks (including scare the patient from getting worse of disease, performing unnecessary tests and performing unnecessary surgery) to prolong the course of the patient's treatment especially for acute diseases. In order to model this problem, the ZD strategy is used for Repetitive games. This strategy helps the doctors to unilaterally consider the probable outcome of opponent (patient) with the desired amount, or to apply a linear relationship between doctor and opponent's consequences. According to the results of the game between the doctor and the patient, it can be concluded that when the doctor’s recommendations aren’t effective for the patient, the patient must go to another doctor to obtain the correct treatment


Main Subjects

  1. Bourne, P. A., Francis, C. G., and Kerr-Campbell, M. D., (2010). “Patient Care: Is Interpersonal Trust Missing?”, North American Journal of Medical Sciences, Vol. 2, No. 3, P. 126.
  2. Cunningham, P. J., (2009), “High Medical Cost Burdens, Patient Trust, and Perceived Quality of Care”, Journal of General Internal Medicine, Vol. 24, No. 3, Pp. 415–420.
  3. Mcavoy, A., and Hauert, C., “Autocratic Strategies for Alternating Games”, Theoretical Population Biology, Vol. 113, PP. 13–22.
  4. Conybeare, J., (1984). “Public Goods, Prisoners’ Dilemmas and the International Political Economy”, International Studies Quarterly,Vol. 28, No. 1, PP. 5–22.
  5. Gibbons, R., (1992). Game Theory for Applied Economists, Princeton University Press.
  6. Corfman, K., and Lehmann, D., “The Prisoner’s Dilemma and the Role of Information in Setting Advertising Budgets”, Journal of Advertising, Vol .23, No. 2, PP. 35–48.
  7. Press, W. H., and Dyson, F. J., (2012). “Iterated Prisoner’s Dilemma Contains Strategies That Dominate Any Evolutionary Opponent”, Proceedings of the National Academy of Sciences, Vol. 109, No. 26, PP. 10409–10413.
  8. Adami, C., and Hintze, A., (2013). “Evolutionary Instability of Zero-Determinant Strategies Demonstrates That Winning Is Not Everything”, Nature Communications, Vol. 4, P. 2193.
  9. Pan, L., Hao, D., Rong, Z., and Zhou, T., (2015). “Zero-Determinant Strategies in Iterated Public Goods Game”, Scientific Reports, Vol. 5, P. 13096.

10. Benoit, J. P., and Krishna, V., (1985) ,“Finitely Repeated Games,”,Econometrica, vol. 53, issue 4, 905-22. 

11. Bernheim, B. D., “Rationalizable Strategic Behavior”, Econometrica: Journal of the Econometric Society, PP. 1007–1028, 1984.

12. Nash, J., (1951). “Non-Cooperative Games”. Annals of Mathematics, PP. 286–295.

13. Osborne, M. J., and Rubinstein, A., (1994). A Course in Game Theory. MIT Press.