Game Theory and the Medical Arms Race (MAR)

Describes how game theory helps explain the "medical arms race" among hospitals up to about 20 years ago.

The 2002 Academy Award-winning movie A Beautiful Mind brought considerable public attention to John Nash and his contributions to game theory. Game theory is a powerful analytical tool used increasingly in economics and many other disciplines. It can be used, for example, to show why it may be in the best interests for each hospital to engage in a MAR even when hospitals as a whole are negatively affected. Game theory begins with a payoff matrix of the type shown in Figure 14-1. Suppose there are two large hospitals, A and B, in a market, each facing the decision of whether to add an expensive heart transplant unit without knowing what its rival will do. The payoff matrix shows the total profit for each hospital (with values for A's profit shown first) resulting from the four combinations of strategies. For example, if both adopt (the "northwest" cell), each hospital will have a total annual profit of $100 (million). If A alone adopts (the "northeast" cell), assume that it will have a significant advantage resulting in a profit of $200 (million), while B loses $50 (million).

Game theory tries to predict a solution, that is, the strategy chosen by each participant. It is clear that both hospitals with a combined profit of $300 (million) will be better off if neither introduces the unit. However, if the hospitals cannot agree (e.g.,, they may not trust each other or they may believe that antitrust laws preclude cooperation), game theory predicts a solution in which each hospital will adopt the unit and combined profits will be $200 (million). Why? Given the payoff matrix, each hospital has a dominant strategy. That is, regardless of what Hospital B does, A will always have a higher profit by adopting rather than not adopting, that is, $100 (million) versus -$50 (million) if B adopts and $200 (million) versus $150 (million) if B does not adopt. Similarly B's dominant strategy is to adopt and, hence, a scenario results consistent with the MAR hypothesis.

Students of game theory will recognize this as an example of the prisoner's dilemma and the solution as a Nash equilibrium. McKay (1994) and Calem and Rizzo (1995) provide other applications of game theory to other decisions including hospital quality and specialty mix. In addition to decisions involving the acquisition of technology and introduction of new services, game theory can provide insight into hospital advertising and other forms of non-price competition.

(1) Explain what a "dominant strategy" is in game theory.

(2) Using Box 14-1, replace the "Adopt, Adopt" entry (first row, first column) with 300, 300.  Replace the "Do Not Adopt, Do Not Adopt" entry (second row, second column) with 50, 50.  Does A have a dominant strategy?  Does B?   What is the solution to this game?

Text Book - The Economics of Health and Health Care, Seventh Edition, Authors - Sherman Folland, Allen C. Goodman and Miron Stano.