Theory and Decision

, Volume 9, Issue 2, pp 127–159 | Cite as

The chain store paradox

  • Reinhard Selten

Abstract

The chain store game is a simple game in extensive form which produces an inconsistency between game theoretical reasoning and plausible human behavior. Well-informed players must be expected to disobey game theoretical recommendations.

The chain store paradox throws new light on the well-known difficulties arising in connection with finite repetitions of the prisoners’ dilemma game. Whereas these difficulties can be resolved by the assumption of secondary utilities arising in the course of playing the game, a similar approach to the chain store paradox is less satisfactory.

It is argued that the explanation of the paradox requires a limited rationality view of human decision behavior. For this purpose a three-level theory of decision making is developed, where decisions can be made on different levels of rationality. This theory explains why insight into the rational solution of a decision problem does not necessarily mean that the corresponding course of action will be taken.

References

  1. Aumann, R. J., ‘Mixed and Behavior Strategies in Infinite Extensive Games’, in: M. Dresher, L. S. Shapley and A. W. Tucker (eds.), Advances in Game Theory, Annals of Mathematics Studies 52 (Princeton, 1964), pp. 627–650.Google Scholar
  2. Bush, R. R. and F. Mosteller, Stochastic Models for Learning (New York, 1955).Google Scholar
  3. Dollard, J. L. Doob, N. Miller, O. Mowres and R. Sears, Frustration and Agression (New Haven, 1939).Google Scholar
  4. Evans, Gary W. and Charles M. Crumbaugh, ‘Effects of Prisoner's Dilemma Format on Cooperative Behavior’, Journal of Personality and Social Psychology 6 (1966), pp. 486–488.Google Scholar
  5. Festinger, L., A Theory of Cognitive Dissonance (Evanston Ill., 1957).Google Scholar
  6. Guyer, Melvin, John Fox and Henry Hamburger, ‘Format Effects in the Prisoner's Dilemma Game’, Journal of Conflict Resolution 17 (1973), pp. 719–743.Google Scholar
  7. Kuhn, H. W., ‘Extensive Games and the Problem of Information’, in: H. W. Kuhn and A. W. Tucker (eds.), Contributions to the Theory of Games, Vol. II, Annals of Mathematics Studies 28 (Princeton, 1953), pp. 193–216.Google Scholar
  8. Lave, Lester B., ‘An Empirical Approach to the Prisoner's Dilemma’, Quarterly Journal of Economics 76 (1962), pp. 424–436.Google Scholar
  9. Lave, Lester B., ‘Factors Affecting Cooperation in the Prisoner's Dilemma’, Behavioral Science 10 (1965), pp. 26–38.Google Scholar
  10. Luce, Duncan R. and Howard Raiffa, Games and Decisions (New York-London-Sidney, 1957).Google Scholar
  11. Morehous, L. G., ‘One-play, Two-play, Five-play and Ten-play Runs of Prisoner's Dilemma’, Journal of Conflict Resolution 11 (1967), pp. 354–362.Google Scholar
  12. Neumann, J.v. and O. Morgenstern, Theory of Games and Economic Behavior, Princeton, 1944.Google Scholar
  13. Pruitt, D. G., ‘Reward Structure and Cooperation: the Decomposed Prisoner's Dilemma Game’, Journal of Personality and Social Psychology 7 (1967), pp. 21–27.Google Scholar
  14. Pruitt, D. G., ‘Motivational Processes in the Decomposed Prisoner's Dilemma Game’, Journal of Personality and Social Psychology 14 (1970), pp. 227–238.Google Scholar
  15. Rapoport, Anatol and Philip S. Dale, ‘The “End” and “Start” Effects in the Iterated Prisoner's Dilemma’, Journal of Conflict Resolution 11 (1967), pp. 354–462.Google Scholar
  16. Restle, Frank and James G. Greeno, Introduction to Mathematical Psychology (Addison Wesley Publishing Company, 1970).Google Scholar
  17. Selten, R., ‘Bewertung strategischer Spiele’, Zeitschrift für die gesamte Staatwissenschaft (1960), pp. 221–282.Google Scholar
  18. Selten, R., ‘Valuation of n-Person Games’, in: Advances in Game Theory, Annals of Mathematics Studies 52 (Princeton N.J., 1964), pp. 565–578.Google Scholar
  19. Selten, R., ‘Spieltheoretische Behandlung eines Oligopolmodells mit Nachfrageträgheit’, Zeitschrift für die gesamte Staatswissenschaft 121 (1965), Teil I, pp. 301–324, Teil II, pp. 667–689.Google Scholar
  20. Selten, R., ‘An Oligopoly Model with Demand Inertia’, Working Paper No. 250 (Center for Research in Management Science, University of California, Berkeley, 1968).Google Scholar
  21. Selten, R., ‘A Simple Model of Imperfect Competition, Where 4 are Few and 6 are Many’, International Journal of Game Theory 2 (1973), pp. 141–201.Google Scholar
  22. Selten, R., ‘Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games’, International Journal of Game Theory 4 (1975), pp. 25–55.Google Scholar

Copyright information

© D. Reidel Publishing Company 1978

Authors and Affiliations

  • Reinhard Selten
    • 1
  1. 1.Institut für Mathematische Wirtschaftsforschung Universität BielefeldBielefeldGermany

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