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Game theory is a way of reasoning through problems. Although its use can be found throughout history, it was only formally stylized by the economists John von Neumann and Oskar Morganstern in the 1940s. Game theory takes the logic behind complex strategic situations and simplifies them into models that can be used to explain how individuals reach decisions to act in the real world. Game theory models attempt to abstract from personal, interpersonal, and institutional details of problems how individuals or groups may behave given a set of given conditions. This modeling allows a researcher or planner to get at the root of complex human interactions. The major assumption underlying most game theory is that people and groups tend to work toward goals that benefit them. That is, they have ends in mind when they take actions.

The most important application of game theory to public health occurs 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. One particularly illustrative game is called the Prisoners' Dilemma, illustrated below. This game is often used to show the need for public resources and services. That is, sometimes individuals who choose certain strategies end up with an inferior outcome because of the incentives they were presented with. In public health, the problem becomes apparent quickly.

In order to place these events into a context in which game theory can be employed, four commonly defined criteria are used:

• Players are the decision makers in the game; a player can be an individual, group, or population that must decide how to use the resources available within given constraints.
• Rules are the constraints; all activity is defined by rules and gives the model an analytical credence to be tested for validity in the real world.
• Strategies are the courses of action open to the players in a game; players may choose their action dependent upon different situations they are presented with.
• Payoffs are the final returns to players, which are usually stated in terms that are objectively understood by each player of the game.

Consider a situation in which two groups of people border a malarial swamp. One group is named Alpha and the other is Beta. The swamp causes both groups to be plagued by malaria and other diseases. The problem could easily be remedied by draining the swampland. However, neither group is willing to act first because no incentives exist to take on the hard labor of draining the swamp alone. The greater utility that would be conveyed to both groups is lost because there is no incentive for either individual group to act.

THE SWAMP: A PRISONERS' DILEMMA

The game called Prisoners' Dilemma can be modeled using game theory. The game matrix shown in Table 1 is an example of a common tool in game theory modeling. The players are named in the

Table 1

outer boxes, the rule is that the players may not communicate before simultaneously acting, the strategies are to contribute or not contribute, and the payoffs are in the innermost boxes.

Look at the situation as it is presented to the Alpha group. They realize that the outcome depends on the action the Beta group takes. If Beta contributes, it pays Alpha to avoid contributing, for in that instance, Alpha will benefit twice as much as if they worked with Beta to drain the swamp (2 points rather than 1). The reason the payoff for not contributing is greater is that Alpha will receive the benefit of draining the swamp without doing any of the work. However, if Beta does not contribute, Alpha still benefits by not contributing rather than contributing alone (the payoff is 0 instead of −1). That is, Alpha will choose not to bear the costs of draining the swamp alone.

The Alpha group reasons that regardless of Beta's action, their own best action is to not help drain the swamp. Because Beta's options are symmetric to Alpha's, they also reason that they benefit most through inaction. As a result, the swamp does not get drained, and both groups end up with an inferior outcome. This game leads to a special equilibrium called a Nash equilibrium, which means both players' strategies will lead them to the same payoff regardless of the strategy chosen by the opposing player.

PUBLIC HEALTH IMPLICATIONS

The implication for public health is that the best strategies for individuals or groups are sometimes not the best strategies for everyone taken as a whole. Public health professionals need to be vigilant to these special circumstances and use interventions to create better incentive systems. For example, Alpha and Beta could each be levied a tax, by some authority over both, to pay for the draining of the swamp. The disincentives for progress would then be circumvented and both groups would benefit.

Game theory has been used to model a number of subjects important to public health, including organ donation, ethics, and the patient-provider relationship. 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.

PETER S. MEYER

NANCY L. ATKINSON

ROBERT S. GOLD

(SEE ALSO: Community Health; Community Organization; Ethics of Public Health)