N‐person Prisoner's Dilemma†

Part of this paper was written at the Mental Health Research Institute, University of Michigan, Ann Arbor, where the author was Visiting Scientist, June‐August 1972. This work was supported by United States Public Health Services Grant MH20291–01.

Multi‐person versions of Prisoner's Dilemma are widely applicable in the social sciences. Examination of two important classes of real‐world situations reveals that although both can appropriately be called Prisoner's Dilemma, they have incompatible payoff structures. Thus Prisoner's Dilemma games constitute an important but apparently ambiguous set of models.

We therefore undertake a taxonomy of multi‐person Prisoner's Dilemma. Some aspects of the well‐studied two‐person case provide a useful beginning for the task. In the general multi‐person form, however, some properties of the two‐person game are found incompatible with others and so are dropped. Additional properties are suggested by strategic considerations and the associated social phenomena. We demonstrate interdependencies among the various properties and relate some of them to a simple graphical representation.

Notes

Part of this paper was written at the Mental Health Research Institute, University of Michigan, Ann Arbor, where the author was Visiting Scientist, June‐August 1972. This work was supported by United States Public Health Services Grant MH20291–01.