Introduction:
Game theory is a branch of applied mathematics that provides tools for analyzing situations in which parties make decisions that are interdependent. This interdependence causes each player to consider the other player’s possible decisions, in formulating his own. A game describes the optimal decisions of the players, who may have similar, opposed, or mixed interests, and the outcomes that may result from these decisions.(1) Game theory has also been defined as a study of mathematical models of conflict and cooperation between intelligent and rational decision makers.(2) Although practical use of Game theory can be found throughout history, the credit of its invention goes to John von Neumann and Oskar Morgenstern(1944). Eight game-theorists have won the Nobel Prize in Economics, and John Maynard Smith was awarded the Crafoord Prize for his application of game theory to biology.(3)
Essential ingredients of a game
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Players are the decision makers in the game; a player can be an individual, group, institution or population.
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Strategies are the courses of action open to the players in a game.
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Payoffs are the final returns to players, which are usually stated in terms that are objectively understood by each player of the game.
Prisoner’s dilemma: An Illustrative Game
One of the most popular games is prisoner's dilemma. The police have arrested two robbers (players) whom they know have committed an armed robbery together. Unfortunately, the police lack enough admissible evidence to get a conviction. They however do have evidence to send each prisoner away for two years for theft of the getaway vehicle. The inspector locks the prisoners in separate cells and makes the following offer to each prisoner: if you will confess (strategy) to the robbery, implicating your partner, and he does not, then you will go free (pay-off) and he will get ten years. If you both confess, you will each get 5 years. If neither of you confess, then you will each get two years for the auto theft. Here, punishments can be converted into payoffs for each prisoner as 3 (free), 2 (2 years imprisonment), 1 (5 years imprisonment), and 0(10 years imprisonment). The game can be represented as follows, where numerals written first in each cell reflects the payoffs to prisoner A, while payoffs to prisoner B are mentioned subsequently.
| Table 1: Prisoner’s Dilemma |
|
Prisoner B |
|
Confess |
Refuses to confess |
| Prisoner A |
Confess |
1,1 |
3,0 |
|
| Refuses to confess |
0,3 |
2,2 |
|
Assuming that both prisoners are rational, each player will evaluate strategies available to him by comparing his payoffs, for each possible action by his partner (now opponent). It is obvious that for player A the pay-offs are better if he confesses, irrespective of whatsoever strategy his opponent chooses. Obviously, he would confess. Prisoner B, meanwhile, evaluates his actions by comparing his payoffs and comes to exactly the same conclusion. In the PD, therefore, confessing dominates (called dominant strategy) the refusing for both players. Thus, both players will confess, and go to prison for 5 years, neither the best nor the second best payoff for either of them.(4)
Game theory has been extensively used in economics, business and management. Political scientists, psychologists, biologists, sport coaches, military strategists and software programmers have made use of the theory to come to conclusions that are more beneficial in the real world. In medical sciences, the theory has been applied in almost all specialties including pharmacology (5), physiology (6) pathology (7), sports medicine (8), psychiatry (9), medical logistics (10), clinical medicine (11) and clinical decision-making.(12,13)
Game theory and Public Health
The application of game theory in public health is most relevant when the actions of individuals or groups affect the health of others. On some occasions, individual or group strategies for betterment lead to inferior outcomes for the greater population. Using game theory to model public health problems is not different from using it to model any other type of problem or decision-making scenario.
The Swamp: Extension of Prisoner’s dilemma
Consider a situation in which a swamp is located between two villages, Rampur and Sitapur. The mosquito breeding in the swamp is responsible for considerable morbidity due to malaria and other mosquito borne diseases. The problem can be remedied permanently by environmental measures ie filling the swamp. However, people of neither village are willing to act first because no incentives exist to take on the hard labour of leveling the swamp.
| Table 2: The Swamp - Extension of Prisoner’s dilemma |
|
Village Sitapur |
|
Contribute |
Not contribute |
| Village Rampur |
Contribute |
1,1 |
0,2 |
| Not contribute |
2,0 |
0,0 |
Similar to the game of Prisoner’s dilemma, the dominant strategy in this situation for villagers of both Sitapur and Rampur is ‘not to act’. The swamp survives; the worst outcome from public health point of view. Environmentalists can relate this game to innumerable real life situations. For example, is the attitudes of individuals, societies and even Nations towards the problem of global warming not akin to behaviour of Sita and Rampurians?
Rubella Vaccination: Anotherillustration of use of Game theory in Public Health is arriving at policy decision regarding Rubella vaccine. Rubella is a highly contagious childhood disease that causes relatively mild symptoms. However, the infection causes severe congenital defects, known as congenital rubella syndrome (CRS), if transmitted from a mother to fetus. Consequently, women have higher incentive to vaccinate against rubella than men do. While the vaccination protects the vaccinated, but also increases the average age of infection, which in case of rubella would increase the risk of CRS among unvaccinated females. To evaluate the interplay among these factors, the Game theorists developed an epidemiological model of rubella transmission and vaccination, and found that high levels of vaccination for both genders are most effective in maximizing average utility across the population by decreasing the risk of CRS. The results suggested that the rubella vaccination by males on voluntary basis would be far lower than the population optimum, if rubella vaccine were offered separately, instead of combined with measles and mumps vaccination as the MMR vaccine.(14)
Other areas of public health where game theory has been applied to obtain tangible solution to public health issues include role of social distancing in control of an epidemic (15), sustaining effective coalitions between public and private health care facilities (16), medical ethics (17), organ donation (18), bio-terrorism (19), medical-resource development (20), and improving acceptability of primary health care.(21) In general, Game theory provides a strong modeling device for public health professionals and illustrates the need of public intervention when the incentives of individuals impede progress for the group.
Conclusion
Community medicine specialists in India are generally unaware of Game theory and its potential use in public health and biomedical research. It is recommended that the subject of Game theory be introduced to post-graduate students of Community Medicine. It would empower the new generations of public health experts with this ‘tool’ that has the potentials to suggest logical solutions to public health issues. We, the community health educationists should realize that our pay-offs are better if the game is played early.
References
- Game theory. Encyclopædia Britannica available at http://www.britannica.com/EBchecked/topic/224893/game-theory.
- Myerson RB. Game Theory : Analysis of Conflict. Harvard University Press; 1991.
- Game Theory. Available athttp://en.wikipedia.org/wiki/Game_theory.
- Heylighen F. The Prisoners' Dilemma. Available at http://pespmc1.vub.ac.be/PRISDIL.html.
- Hughes D. Medicines concordance and game theory. Br J Clin Pharmacol. 2008;66(4):577.
- Lee D. Game theory and neural basis of social decision-making. Nat Neurosci 2008;11(4):404–409.
- Martin, M. Can game theory explain invasive tumor metabolism? Journal of the National Cancer Institute 2009;101(4):220-222
- Shermer M. The doping dilemma: Game theory helps to explain the pervasive abuse of drugs in cycling, baseball and other sports. Scientific American. April 2008;92-94.
- Van’t Wout M, Sanfey AG. Interactive decision making in people with schizotypal traits: a game theory approach. Psychiatry Research 2011;185(1):92-96.
- Shumei Y, Qiujun G, Weijie G. A signal game theory based reputation model of supply chain of medicine retail enterprises.5523349 Proceeding of International Conference on abstract. Intelligent Computation Technology and Automation 2010;1:343–346.
- Doosthosseini E, Navidi H, Hassanpour-ezatti M. Comparison of AHP and game theory methods to determine optimal dose of Atorvastatin in CHD patients. Advanced Studies in Biology 2011;3(1):25-33.
- Diamond GA, Rozanski A, Steuer M. Playing doctor: application of game theory to medical decision-making. J Chronic Dis. 1986;39(9):669-682.
- Tarrant C, Stokes T, Colman AM. Models of the medical consultation: opportunities and limitations of a game theory perspective. Qual Saf Health Care 2004;13:461-466.
- Shim E, Kochin B, Galvani A. Insights from epidemiological Game Theory into gender-specific vaccination against Rubella. Mathematical Biosciences and Engineering 2009;6(4):841–856
- Reluga TC. Game Theory of Social Distancing in Response to an Epidemic. PLoS Comput Biol 2010;26(5) Available at http://www.ploscompbiol.org/article/info%3Adoi%2F10.1371%2Fjournal.pcbi.1000793;jsessionid=CFDB528A1B992D6134F2128D525084E4
- Ford E, Wells R, Bailey B. Sustainable network advantages: A game theoretic approach to community-based health care coalitions. Health Care Management Review 2004;2:159-169.
- Riggs JE. Medical ethics, logic traps, and game theory: an illustrative tale of brain death. J Med Ethics 2004;30:359-361.
- O'Brien BJ. A Game-Theoretic Approach to Donor Kidney Sharing. Social Science and Medicine. 1988;26(11):1109–1116.
- Hamilton R, McCain R. Smallpox, risks of terrorist attacks, and the Nash equilibrium: An introduction to game theory and an examination of a smallpox vaccination program. Prehospital Disast Med. 2009;24(3):231–238.
- Roth AE. The evolution of the labor market for medical Interns and residents: A case study in game theory. Journal of Political Economy 1984;61:991-1016.
- Tarrant C, Dixon-Woods M, Colman AM, Stokes T. Continuity and trust in primary care: A qualitative study informed by game theory. Annals of Family Medicine 2010;8(5):440-446.
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