Abstract
An intuitive expectation is that in a finitely repeated prisoner's dilemma, the players will achieve mutual cooperation in at least some periods. Existing explanations for equilibrium cooperation (with agents perfectly informed of one another's characteristics) require that the number of repetitions be unknown, which is in many cases an uncomfortably strong uncertainty assertion. This paper demonstrates that if agents have private information concerning the number of repetitions (as opposed to being completely uninformed), equilibrium mutual cooperation can occur in a finitely repeated game. This appears to be a weaker and more palatable assumption then that of complete uncertainty, and hence provides a natural and useful alternative foundation for mutual cooperation.
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I am indebted to an anonymous referee for helpful comments, which led (among other improvements) to the clarification of Proposition 1 and the proof of Proposition 2. Errors remain my responsibility. Financial support from the National Science Foundation is gratefully acknowledged.
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Samuelson, L. A note on uncertainty and cooperation in a finitely repeated prisoner's dilemma. Int J Game Theory 16, 187–195 (1987). https://doi.org/10.1007/BF01756290
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DOI: https://doi.org/10.1007/BF01756290