Skip to main content

A Rationalization of Cooperation in the Iterated Prisoner’s Dilemma

  • Chapter
Rationality, Rules, and Structure

Part of the book series: Theory and Decision Library ((TDLA,volume 28))

  • 201 Accesses

Abstract

According to the standard account, strategies respond to various possible circumstances. I conceive them rather as responding to various possible future decision situations (including all internal factors). This is far more general since changing decision situations may arise in a foreseeable way not only due to information, as in the standard account, but also due to forgetfulness, endogeneous changes of preferences etc.

The main problem, then, is to state an optimality criterion for such strategies. This is a problem since maximization of expected utility then becomes either unreasonable or even meaningless (maximization of which utility?). The problem is serious, as the widely disagreeing literature on the issue displays. I propose a general solution by essentially referring, in a specific way, to a relation of superiority/ inferiority between possible decision situations (which is part of the agent’s view). This is the first part of the paper.

The second part suggests how this framework provides new theoretical means for dealing with the iterated prisoner’s dilemma thus allowing for a full rationalization of cooperation. The ideas extend to Newcomb’s problem and related cases and are hence relevant to the debate between causal and evidential decision theory.

I am indebted to Arthur Merin for improving my English.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Aumann, R.: 1974, ‘Subjectivity and Correlation in Randomized Strategies’, Journal of Mathematical Economics, 1, 67–96.

    Article  Google Scholar 

  • Aumann, R.: 1995, ‘Backward Induction and Common Knowledge of Rationality’, Games and Economic Behavior, 8, 6–19.

    Article  Google Scholar 

  • Axelrod, R.: 1984, The Evolution of Cooperation. New York, Basic Books.

    Google Scholar 

  • Axelrod, R. and D. Dion: 1988, ‘The Further Evolution of Cooperation’, Science, 242, 1385–90.

    Article  Google Scholar 

  • Becker, G.S. and K.M. Murphy: 1988, ‘A Theory of Rational Addiction’, Journal of Political Economics, 96, 675–700.

    Article  Google Scholar 

  • Bicchieri, C.: 1989, ‘Self-Refuting Theories of Strategic Interaction: A Paradox of Common Knowledge’, Erkenntnis, 30, 69–85.

    Article  Google Scholar 

  • Binmore, K.: 1987, ‘Modeling Rational Players: Part I’, Economics and Philosophy, 3, 179–214.

    Article  Google Scholar 

  • Campbell, R. and L. Sowden, eds.: 1985, Paradoxes of Rationality and Cooperation. Vancouver, The University of British Columbia Press.

    Google Scholar 

  • Damme, E. van: 1991, Stability and Perfection of Nash Equilibria. Berlin, Springer, 2nd ed.

    Google Scholar 

  • Davis, L.: 1977, ‘Prisoners, Paradox, and Rationality’, American Philosophical Quarterly, 114, 31927.

    Google Scholar 

  • Eells, E.: 1982, Rational Decision and Causality. Cambridge, Cambridge University Press.

    Google Scholar 

  • Elster, J.: 1979, Ulysses and the Sirens. Cambridge, Cambridge University Press.

    Google Scholar 

  • Feldman, M.W. and E.A.C. Thomas: 1987, ‘Behavior-Dependent Contexts for Repeated Plays of the Prisoner’s Dilemma II: Dynamical Aspects of the Evolution of Cooperation’, Journal of Theoretical Biology, 128, 297–315.

    Article  Google Scholar 

  • Fishburn, P.C.: 1964, Decision and Value Theory. New York, Wiley.

    Google Scholar 

  • Fraassen, B.C.: 1984, ‘Belief and the Will’, Journal of Philosophy, 81, 235–56.

    Article  Google Scholar 

  • Gibbard, A. and W.L. Harper: 1978, ‘Counterfactuals and Two Kinds of Expected Utility’, in C.A. Hooker, J.J. Leach and E.F. McClennen, eds., Foundations and Applications of Decision Theory, Vol. 1. Dordrecht, Reidel, pp. 125–62.

    Chapter  Google Scholar 

  • Hammond, P.: 1976, ‘Changing Tastes and Coherent Dynamic Choice’, Review of Economic Studies, 43, 159–73.

    Article  Google Scholar 

  • Jeffrey, R.C.: 1965, The Logic of Decision. Chicago, Chicago University Press, 2nd. ed. 1983.

    Google Scholar 

  • Kavka, G.: 1983, ‘The Toxin Puzzle’, Analysis, 43, 33–6.

    Google Scholar 

  • Kreps, D.M., P. Milgrom, P.J. Roberts and R. Wilson: 1982, ‘Rational Cooperation in the Finitely Repeated Prisoners’ Dilemma’, Journal of Economic Theory, 27, 245–72.

    Article  Google Scholar 

  • Kreps, D.M. and R. Wilson: 1982, ‘Sequential Equilibria’, Econometrica, 50, 863–94.

    Article  Google Scholar 

  • Kusser, A.: 1989, Dimensionen der Kritik von Wünschen. Frankfurt a.M., Athenäum.

    Google Scholar 

  • Kusser, A. and W. Spohn: 1992, ‘The Utility of Pleasure is a Pain for Decision Theory’, Journal of Philosophy, 89, 10–29.

    Article  Google Scholar 

  • Lewis, D.: 1981, Why Ain’cha Rich?, Noüs, 15, 377–80

    Google Scholar 

  • McCain, R.A.: 1979, ‘Reflections on the Cultivation of Taste’, Journal of Cultural Economics, 3, 3052

    Article  Google Scholar 

  • McClennen, E.F.: 1990, Rationality and Dynamic Choice. Cambridge, Cambridge University Press.

    Book  Google Scholar 

  • Meek, C. and C. Glymour: 1994, ‘Conditioning and Intervening’, British Journal for the Philosophy of Science, 45, 1001–21.

    Article  Google Scholar 

  • Nozick, R.: 1969, ‘Newcomb’s Problem and Two Principles of Choice’, in N. Rescher et al.,eds., Essays in Honor of Carl G. Hempel. Dordrecht, Reidel, pp. 114–46.

    Google Scholar 

  • Osborne, M.J. and A. Rubinstein: 1994, A Course in Game Theory. Cambridge, Mass., MIT Press

    Google Scholar 

  • Peleg, B. and M.E. Yaari: 1973, ‘On the Existence of a Consistent Course of Action When Tastes are Changing’, Review of Economic Studies, 40, 391–401.

    Article  Google Scholar 

  • Pettit, P. and R. Sugden: 1989, ‘The Backward Induction Paradox’, Journal of Philosophy, 86, 16–982.

    Article  Google Scholar 

  • Pollak, R.A.: 1968, ‘Consistent Planning’, Review of Economic Studies, 35, 201–8.

    Article  Google Scholar 

  • Pratt, J.W., H. Raiffa and R. Schlaifer: 1995, Introduction to Statistical Decision Theory. Cambridge, Mass., MIT Press.

    Google Scholar 

  • Raiffa, H.: 1968, Decision Analysis. Reading, Mass., Addison-Wesley.

    Google Scholar 

  • Savage, L.J.: 1954, The Foundations of Statistics. New York, Dover, 2nd. ed. 1972.

    Google Scholar 

  • Selten, R.: 1975, ‘Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Gases’, International Journal of Game Theory, 4, 25–55.

    Article  Google Scholar 

  • Sobel, J.H.: 1993, ‘Backward-Induction Arguments: A Paradox Regained’, Philosophy of Science, 60, 114–33.

    Article  Google Scholar 

  • Sorensen, R.A.: 1985, ‘The Iterated Versions of Newcomb’s Problem and the Prisoner’s Dilemma’, Synthese, 63, 157–66.

    Article  Google Scholar 

  • Spohn, W.: 1977, ‘Where Luce and Krantz Do Really Generalize Savage’s Decision Model’, Erkenntnis, 11, 113–34.

    Article  Google Scholar 

  • Spohn, W.: 1978, Grundlagen der Entscheidungstheorie. Kronberg/Ts., Scriptor.

    Google Scholar 

  • Spohn, W.: 1982, ‘How to Make Sense of Game Theory’, in W. Stegmüller, W. Balzer and W. Spohn, eds., Philosophy of Economics. Berlin, Springer, pp. 239–70.

    Chapter  Google Scholar 

  • Spohn, W.: 1999, ‘Strategic Rationality’, Forschungsberichte der DFG-Forschergruppe ‘Logik in der Philosophie’, Nr. 24, Konstanz.

    Google Scholar 

  • Strotz, R.H.: 1955/56, ‘Myopia and Inconsistency in Dynamic Utility Maximization’, Review of Economic Studies,23, 165–80.

    Google Scholar 

  • Yaari, M.E. van: 1977, ‘Endogeneous Changes in Tastes: A Philosophical Discussion’, Erkenntnis, 11, 157–96.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Spohn, W. (2000). A Rationalization of Cooperation in the Iterated Prisoner’s Dilemma. In: Nida-Rümelin, J., Spohn, W. (eds) Rationality, Rules, and Structure. Theory and Decision Library, vol 28. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9616-9_5

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-9616-9_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5463-0

  • Online ISBN: 978-94-015-9616-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics