The Uniform N-Person Prisoner's Dilemma Game: Construction and Test of an Index of Cooperation

The familiar two-person prisoner's dilemma (PD) game can be considered a special case of a general family of games with more than two players. This family of games is of particular interest, having been suggested as a model for a variety of social conflict situations. A subset of this family of games, called the uniform PD, is defined, for which the members of the subset may be scaled along a dimension of competitiveness for any given number of players. An index of competitiveness was derived and tested for the three-person case. Sixty volunteer subjects played one of five three-person uniform PD games, chosen to vary across the range of values of the index. Each triad played 150 trials of the same game for points which were converted to cash at the end of the experiment. Subjects were run in triads homogeneous with respect to sex; effects due to that variable were absent. The obtained proportions of cooperative response were found to be strongly related to the value of the index. The approach offers a theoretical basis for assessment of behavior in multiperson conflict situations of the PD variety.