Topics in medical economics: lessons of the prisoner's dilemma.

The jousting between surgeons and insurance companies over fees can be fierce, and to the outside observer it seems anything but playful. Nevertheless, the insights that surgeons need to prevail in this battle may lie in a branch of theoretical economics called game theory. The word game typically refers to a sport or contest, with the implicit connotation of recreation. The technical definition of a game, however, omits any notion of amusement. A game is defined as an encounter in which players execute plans of action under a set of rules to maximize their score—points, money, territory, whatever is at stake. Game theory, then, is the study of strategy and tactics. Game theory can be used to plan the moves of a chess game but can also be applied to any real-world situation in which the interaction between “players” satisfies the definition of a game. In fact, one of the first practical applications of game theory was far removed from the realm of fun and play: the Allied forces used game-theory methods to allocate resources and choose targets in World War II. The negotiations between buyers and sellers (such as insurance companies and doctors, food-makers and farmers, or automobile manufacturers and steel mills), the posturing of military opponents, or even the debate between a couple over the evening’s entertainment plan can take on the trappings of a game. Each side can make moves to maximize its “score.” Some scenarios in life and the strategies that they evoke can be reduced, in broad terms at least, to familiar gametheory concepts. When a situation under study resembles a particular game type or position, we say that the situation is isomorphic with the game. The usefulness of isomorphism is that, once a particular situation is recognized as a familiar game, many of the insights derived from careful study of the game can be applied to the situation at hand without repeated detailed analysis. From my perspective, the current imbroglio between managed-care companies and surgeons over payment for surgical work resembles a classic game-theory problem called the prisoner’s dilemma [3]. It should take no leap of the imagination to guess that it is the beleaguered doctor who plays the role of the prisoner here, yet I do not offer this comparison to make doctors feel even more besieged. Rather, I intend to share some of the analyses to resolve the prisoner’s dilemma offered over the years to help doctors cope with their obviously difficult situation. The prisoner’s dilemma is the prototype of a class of games in which use of a reasoned and logical strategy (the so-called dominant solution) leads to a suboptimal result. (In their book Decisions, Decisions: Game Theory and You, Bell and Coplans [2] entitled the chapter on the prisoner’s dilemma “Morons Do Better Than Logicians,” and they may be right.) I believe that the use of logical reasoning by doctors responding to the advent of managed care has made their position worse. I further believe that this logic was not faulty: rather, it was the use of logic itself that caused the problem. Let’s look at the prisoner’s dilemma to see why. The classic prisoner’s dilemma goes as follows: Smith and Jones are both accused of grand larceny and are taken to jail and placed in separate cells. The district attorney approaches them individually and offers a deal. “We don’t have enough evidence to convict you of grand larceny— only breaking and entering,” she says, “so I offer you the following deal: turn state’s evidence on your partner. If you confess, and he remains silent, I will let you go. But I warn you, if you remain silent, and he confesses, you will get the maximum ten-year sentence. Now, if you both confess, I can’t let both of you go, so you each will get a five-year term, and if you both remain silent, I am sure we can lock you up for a year on the breaking-and-entering charge. By the way, I have offered the same deal to your partner and told him that I was talking to you.” The various combinations of responses and the sentences that the prisoners could receive are described in the table below, a so-called payoff matrix. (By tradition, acting in the interest of the other player is termed “cooperation” and acting against that interest is “defection,” though one is not formally cooperating or defecting, since no communication is allowed (Table 1).) The dilemma for each is stark: if only the prisoners could communicate—or, more to the point, trust the good intentions of the other—they would guarantee themselves a oneyear sentence by remaining silent. But since they cannot communicate (and may not trust the other even if they could) they must employ logic, and logic gets them in trouble. *No benefits in any form have been received or will be received from a commercial party related directly or indirectly to the subject of this article. No funds were received in support of this article. †Reprinted with permission from Journal of Bone and Joint Surgery 2000; 82A:595–598. From the Department of Orthopaedic Surgery, Leonard Davis Institute of Health Economics, 424 Stemmler Hall, University of Pennsylvania School of Medicine, Philadelphia, PA. The University of Pennsylvania Orthopaedic Journal 14: 75–77, 2001 © 2001 The University of Pennsylvania Orthopaedic Journal