Cooperation and Group Size in the N-Person Prisoners' Dilemma

This study explores the relationship between group size and member cooperation when individual and group interests conflict. Existing theories incorrectly imply that larger groups should experience more difficulty in providing “public goods” (goods whose benefits are not confined to the purchaser). A theoretically based typology that identifies nine systematic patterns associated with changes in group size and parameters of individual and group payoff structure is presented. The typology describes nine different ways in which group size can affect cooperation in the provision of public goods. In a computer-administered experiment using three of these nine types and group sizes of three, six, and nine, 90 college students were given sequences of opportunities to choose between “cooperation” (which benefited everyone) and “noncooperation” (which benefited the chooser but harmed everyone else). For one of these types, a counter-intuitive but theoretically predicted positive relationship between group size and cooperation was found. Two explanations for a theoretically unexpected negative relation between group size and cooperation in the other conditions are developed, one based on Steiner's concept of a conjunctive task, the other based on the decreasing information value of responses in larger groups.

[1]  J. Kahan,et al.  The Uniform N-Person Prisoner's Dilemma Game , 1976 .

[2]  Henry Hamburger,et al.  Group Size and Cooperation , 1975 .

[3]  J. Kahan.  Rationality, the Prisoner's Dilemma, and Population1 , 1974 .

[4]  Rationality the prisoners dilemma and population. , 1974 .

[5]  H. Hamburger.  TAKE SOME-A FORMAT AND FAMILY OF GAMES , 1974 .

[6]  T. Schelling.  Hockey Helmets, Concealed Weapons, and Daylight Saving , 1973 .

[7]  David M. Messick,et al.  To join or not to join: An approach to the unionization decision. , 1973 .

[8]  Henry Hamburger,et al.  N‐person Prisoner's Dilemma† , 1973 .

[9]  J. Kahan.  Noninteraction in an anonymous three‐person prisoner's dilemma game , 1973 .

[10]  P. Bonacich.  Norms and cohesion as adaptive responses to potential conflict: an experimental study. , 1972, Sociometry.

[11]  G. Marwell,et al.  Cooperation in a Three-Person Prisoner's Dilemma. , 1972 .

[12]  R. Hardin,et al.  Collective action as an agreeable N-prisoners''dilemma , 1971 .

[13]  A. Rapoport.  From N=2 to N≥3. , 1971 .

[14]  H. Kelley,et al.  Social interaction basis of cooperators' and competitors' beliefs about others. , 1970 .

[15]  Anatol Rapoport,et al.  N-person game theory;: Concepts and applications , 1970 .

[16]  G. Hardin,et al.  The Tragedy of the Commons , 1968, Green Planet Blues.

[17]  D. G. Pruitt,et al.  Reward structure and cooperation: the decomposed Prisoner's Dilemma game. , 1967, Journal of personality and social psychology.

[18]  J. Tedeschi,et al.  Matrix indices and strategy choices in mixed-motive games , 1967 .

[19]  Robert Axelrod,et al.  Conflict of interest: an axiomatic approach , 1967 .

[20]  A. Rapoport.  Optimal policies for the Prisoner's Dilemma. , 1967, Psychological review.

[21]  Anatol Rapoport,et al.  A note on the "index of cooperation" for Prisoner's Dilemma , 1967 .

[22]  G. Shure,et al.  BARGAINING AND NEGOTIATION BEHAVIOR. , 1967 .

[23]  V. Edwin Bixenstine,et al.  Collaboration among six persons in a Prisoner's Dilemma game , 1966 .

[24]  R. L. Weil.  The N-person prisoner's dilemma: some theory and a computer-oriented approach. , 1966, Behavioral science.

[25]  M. Olson,et al.  The Logic of Collective Action , 1965 .

[26]  A RAPOPORT,et al.  Three-person non-zero-sum nonnegotiable games. , 2007, Behavioral science.