Game+theory

Primary author: Kaitlyn Shaw

Game Theory is a mathematical theory developed by John von Newmann and Oskar Morgenstern in the 1940’s (Ross, 2010). It is used to model how individuals and groups interact in the world and to explain why certain outcomes (sometimes adverse) result from these interactions. The model or game can be used for “any situation in which players (participants) make strategic decisions that take into account each other’s actions and responses.” (Pindyck & Rubinfeld, 2001, p. 462). The crucial point of game theory is the idea that every action or interaction we take has associated costs and benefits or opportunity costs. When interacting in an environment where other individuals and groups are also making similar decisions self-interested entities may come to final actions which do not maximize the utility of the whole population. This concept is critical in public health, as what is a health maximizing behavior for one group or individual may not be health maximizing for the population.
 * Game Theory**

Game theory is usually modeled with a matrix showing costs and benefits of decisions. A classic example is the prisoner’s dilemma which models the outcomes of getting a confession out of two criminals. For this example imagine that two criminals are caught performing a crime of some sort together, however, the police do not have enough evidence to convict both of them on all charges without a confession from at least one individual. Each prisoner is given the following choices. If they confess and the other prisoner does not they get no time, if both of them confess they each get five years, if neither one confesses they get 2 years, and if they do not confess but the other prisoner does they get ten years. These decisions are modeled in a matrix as seen below (Ross, 2010).
 * |||||| ** Prisoner 1 ** ||
 * ** Prisoner 2 ** ||  || **Confess** || **Refuse** ||
 * ^  || **Confess** || 5 years, 5 years || 0 years, 10 years ||
 * ^  || **Refuse** || 10 years, 0 years || 2 years, 2 years ||

Now, as can be seen the total minimum time spent in prison is 4 years, which would be the minimal cost for both prisoners. However, Game Theory predicts that if faced with these options, and being unaware of the actions of the other that both will confess. If they confess and the other does not they get no time, if they do not confess and the other does they get 10 years, and if both confess they get five years. The optimal solution of only four total years being spent in jail, will not occur.

How does this apply to public health? Let’s take an example of a group of people living next to a malarial swamp. Now, draining the swamp is a solution to help prevent the incidence of malaria. If there was one cohesive group living around this swamp the assumption is that they would undertake the project to improve their health. However, if there were two separate groups living around the same swamp who did not communicate with each other, the outcome could be different. Draining the swamp would benefit the entire population around the swamp, however, it also requires resources to be expended to complete this project. The below table outlines the outcomes: [1
 * |||||| == **Group 1** == ||
 * == **Group 2** == ||  || ** Drain the Swamp ** || ** Don’t Drain the Swamp ** ||
 * ^  || ** Drain the Swamp ** || If both groups drain the swamp together resources are split equally and they both benefit || If one group drains the swamp and the other does not they both benefit, however only one expends resources ||
 * ^  || ** Don’t Drain the Swamp ** || If one group drains the swamp and the other does not they both benefit, however only one expends resources || If neither group drains the swamp neither group benefits and neither expends resources. ||

In this situation Game Theory predicts that neither group will elect to spend the resources to drain the swamp. Both groups will save their resources and hope that the other group takes action to make the swamp less of a health hazard. This situation could be seen with similar infrastructure improvements such as sidewalks or paths between neighborhoods or towns that may never be constructed because the differing groups cannot decide on an equitable division of resources (Ross, 2010). This provides a foundation for public health professionals to identify and work to form coalitions to improve the health of the entire population.

Game Theory assumes that entities making these strategic decisions are self-interested and testing of these games in experimental settings seems to support these theories. However, results have been shown to vary along certain population subgroups. Results from experiments with these games differ depending on the population who is playing them. Woman have been shown to be more collaborative and selfless than men (Eckel & Grossman, 1998), and far flung cultures such as the Amazon Tsimane (Heinrich, 2000) and the Machiguenga (Gruven, 2004) have consistently different outcomes than the predicted outcomes discussed above. This indicates that basic behavioral structures differ among populations.

These differences provide the backing for different social and behavioral approaches in dealing with the health of populations. If dealing with a population that is self-interested and behaves as the above game theory would predict, then it is critical to realize that a health intervention that does not take this into account may not have positive outcomes, and that the design of the program needs to reflect the self-interest of the population. However, not all populations display the same behaviors when posed with strategic choices. One example that stands out is how the education of woman in developing countries has been shown to result in benefits associated with more than just economic growth associated with increased productivity and wage earning potential. For example, educating women has been show to reduce infant mortality, reduce fetal mortality, reduce maternal mortality, prevent the spread of AIDS and yield important environmental benefits (Summers, 1992). These benefits associated with the education of woman which are not see in strong association when men are educated can be tied back to how women resolve problems differently when presented with strategic decisions in a game theory model.

Game Theory helps the public health professional understand that many groups will act in their own self interest, possible to the detriment of the whole population. However, it also helps to identify subgroups where interventions may have greater affect due to differing perspectives on collaboration, self-interest, and altruism in different cultural or gender defined populations. Game theory has been used to model decision making affecting public health such as organ donation, ethics, and the patient-provider relationship (Meyer et al., 2002).

Eckel, C.C., Grossman, P.J. (1998). Are women less selfish than men? Evidence from dictator experiments. //The Economic Journal, Vol. 108 (no. 448), 726-735.// Gruven, M. (2004). Economic games among the amazonian Tsimane: Exploring the roles of market access, costs of giving, and cooperation on pro-social game behavior. //Experimental economics: a journal of the Economic Science Association, Vol. 7 (no. 1), 5-24.// Henrich, J. (2000). Does culture matter in economic behavior? Ultimatum game bargaining among the Machinguenga of the Peruvian Amazon. //The American Economic Review, Vol. 90 (no. 4), 973-979.// Meyer, P.S., Atkinson, N.L., Gold, R.S. (2002). Game Theory. Encyclopedia of Public Health. Ed. Lester Breslow. Gale Cengage. Retrieved online: http://www.enotes.com/public-health-encyclopedia/ game-theory Pindyck, R.S., Rubinfeld, D.L. (2001). //Microeconomics (5th Edition).// Upper Saddle River, New Jeresy: Prentice Hall. Ross, D. (2010). Game theory. Stanford Encyclopedia of Philosophy. Retrieved online: [] Summers, L. H. (1992). //Investing in all the people: Educating women in developing countries.// Economic Development Institute of The World Bank. Retrieved online: []
 * References:**

[1 Table adapted from (Meyer et al, 2002)