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October 26, 2005
2:00:00 PM - 3:30:00 PM
Room C303
Game Theory and the Operating Room Staff: Cooperation in a Prisoner's Dilemma Game
Alan P. Marco, M.D., M.M.M., M. Afzal Upal, Ph.D., Barbara K. Chesney, Ph.D.
Anesthesiology, Medical University of Ohio, Toledo, Ohio, United States
Introduction and Objectives

Game theory is a branch of mathematics that can be used to study human behavior, economics, and evolution. John von Neumann and Oskar Morgenstern pioneered this field and John Nash was awarded the Nobel Prize for his work in game theory. In modeling human behavior, games that have 2 or more players, some choice of action where strategy matters, one or more outcomes (e.g. someone wins, someone loses), and outcomes that depend on the strategies chosen by all players are the most interesting. A common model for such interactions is a game known as the Prisoner's Dilemma (PD). In this game, two prisoners are given the choice to confess (defect) or keep silent (cooperate). If both keep silent, they go free. If both confess, a small prison term results. However, if one confesses and the other doesn't, the confessor (defector) goes free! This game belongs to a class of games called non-zero-sum games, in which the total value of the game depends on the choices made by the players. Cooperation between players in the PD game leads to greater value in the game. This study was undertaken to measure physicians' and nurses' strategies of cooperation in PD games.


A novel web-based interactive program was developed to allow participants to play repeated iterations of a standard PD game. Participants were recruited by e-mail, posters, and flyers. Participants played a series of three games in random order against the computer: the computer played a pure cooperation strategy, a pure defect strategy, or a mixed strategy. The players could choose to cooperate or defect on each round. The total score (pay-off) of the game increased if both players cooperated, but the individual could improve his performance (or minimize harm) by defecting.[table1]Participants were instructed to attempt to maximize their own score. Participants were not told how many rounds would be played in each game. Participants were deemed to be “cooperators” if they played “Cooperate” at least 75% of the time when playing against the “Always Cooperate” strategy. Playing “Cooperate” more than 10% of the time against the “Always Defect” strategy also was deemed to demonstrate cooperative behavior.


39 participants (18 physicians and 21 nurses) completed the study. Participants were significantly more likely to cooperate in the “Always Cooperate” scenario (mean cooperation rate = 87%; 95% CI 79-95) than in the “Always Defect” (mean cooperation rate = 22%; 95% CI 15-29) or Mixed Scenarios (mean cooperation rate = 66%; 95% CI 53-79); (one-way ANOVA F = 41.7, p < 0.001). Examined individually, 32 participants (82.0%) were deemed cooperators in the Always Cooperate scenario and 25 (64.1%) were deemed to be cooperators in the Always Defect scenario. This compares favorably to a study of cooperative PD play in twins where the average cooperative play was 22.5% and another study where participants selected for cooperative play choose cooperation 67% of the time.


This novel web-based PD model shows that physicians and nurses preferentially choose cooperative behavior strategies. The high cooperation rate against Always Cooperate and the cooperation rate of 22% against the Always Defect strategy suggest an overall desire to cooperate.

Anesthesiology 2005; 103: A1177
Pay-Offs in the Prisoner's Dilemma Game
Computer DefectsComputer Cooperates
Player Defects1,16,0
Player Cooperates0,63,3