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Part of the book series: Theory and Decision Library ((TDLC,volume 5))

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Abstract

An optimal model for the Prisoner’s Dilemma game is suggested. The model is normative in the sense that given few assumptions about the way the game is perceived by the players, an optimal policy is prescribed to each player maximizing his long-run expected gain. The dilemma is “resolved” by restructuring the game as a supergame composed of several component games such that transitions among them are possible. Dynamic programming is used to derive the optimal policy.

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References

  • Bellman, R. Dynamic programming. Princeton: Princeton University Press, 1957. (a)

    Google Scholar 

  • Bellman, R. A Markovian decision process. Journal of Mathematics and Mechanics, 1957, 6, 679–684. (b)

    Google Scholar 

  • Bellman, R. Adaptive control processes: A guided tour. Princeton: Princeton University Press, 1961.

    Google Scholar 

  • Bellman, R., & Dreyfus, S. E. Applied dynamic programming. Princeton: Princeton University Press, 1962.

    Google Scholar 

  • Gallo, P. S., & McClintock, C. G. Cooperative and competitive behavior in mixed-motive games. Journal of Conflict Resolution, 1965, 9, 68–78.

    Article  Google Scholar 

  • Howard, R. A. Dynamic programming and Markov processes. New York: M. I. T. and Wiley, 1960.

    Google Scholar 

  • Luce, R. D., & Raiffa, H. Games and decisions. New York: Wiley, 1957.

    Google Scholar 

  • Rapoport, Amnon. A study of human decisions in a stationary Markov process with rewards. Chapel Hill: Psychometric Laboratory Report No. 48, 1966.

    Google Scholar 

  • Rapoport, Amnon, & Mowshowitz, A. Experimental studies of stochiastic models for the Prisoner’s Dilemma. Behavioral Science, 1966, 11, 444 458.

    Google Scholar 

  • Rapoport, Anatol. A stochastic model for the Prisoner’s Dilemma. In J. Garland (Ed.), Stochastic models in medicine and biology. Madison: University of Wisconsin Press, 1964.

    Google Scholar 

  • Rapoport, Anatol, & Chammah, A. M. Prisoner’s Dilemma: A study in conflict and cooperation. Ann Arbor: University of Michigan Press, 1965.

    Google Scholar 

  • Rapoport, Anatol, & Orwant, C. Experimental games: A review. Behavioral Science, 1962, 7, 1–37.

    Google Scholar 

  • Riis, J. O. Discounted Markov programming in a periodic process. Operations Research, 1965, 13, 920–929.

    Article  Google Scholar 

  • Scodel, A., Minas, J. S., Ratoosh, P., & Lipetz, M. Some descriptive aspects of two-person non-zero-sum games. Journal of Conflict Resolution, 1959, 3, 114–119.

    Article  Google Scholar 

  • Shubik, M. Some reflections on the design of game theoretic models for the study of negotiation and threats. Journal of Conflict Resolution, 1963, 7, 1–12.

    Article  Google Scholar 

  • Suppes, P., & Atkinson, R. C. Markov learning models for multiperson interaction. Stanford: Stanford University Press, 1960.

    Google Scholar 

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© 1990 Kluwer Academic Publishers

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Rapoport, A. (1990). Optimal Policies for the Prisoner’s Dilemma. In: Experimental Studies of Interactive Decisions. Theory and Decision Library, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1992-1_1

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  • DOI: https://doi.org/10.1007/978-94-009-1992-1_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7391-2

  • Online ISBN: 978-94-009-1992-1

  • eBook Packages: Springer Book Archive

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