Abstract
Learning to take turns in repeated game situations is a robust phenomenon in both laboratory experiments and in everyday life. Nevertheless, it has received little attention in recent studies of learning dynamics in games. We investigate the simplest and most obvious extension of fictitious play to a learning rule that can recognize patterns, and show how players using this rule can spontaneously learn to take turns.
Similar content being viewed by others
REFERENCES
Aumann, R.: 1974, 'Subjectivity and Correlation in Randomized Strategies', Journal of Mathematical Economics 1, 67-96.
Aumann, R.: 1987, 'Correlated Equilibrium as an Expression of Bayesian Rationality', Econometrica 55, 1-18.
Brown, G. W.: 1951, 'Iterative Solutions of Games by Fictitious Play', in T.C. Koopmans (ed.), Activity Analysis of Production and Allocation, Wiley, New York, pp. 374-376.
Carnap, R.: 1971, 'A Basic System of Inductive Logic, Part 1', in R. Carnap and R. Jeffrey (eds.), Studies in Inductive Logic and Probability, vol. I, University of California Press, Berkeley.
Carnap, R.: 1980, 'A Basic System of Inductive Logic, Part 2', in R. Jeffrey (ed.), Studies in Inductive Logic and Probability, vol. II, University of California Press, Berkeley.
Cowan, S.: 1992, Dynamical Systems Arising From Game Theory, Doctoral Dissertation, Department of Mathematics, University of California, Berkeley.
Fudenberg, D. and D. Levine: 1998, The Theory of Learning in Games, MIT Press, Cambridge, MA.
Fudenberg, D. and D. Levine: 1999, 'Conditional Universal Consistency', Games and Economic Behavior 29, 104-130.
Hume, David: (1740, 1888) 1976, in L. A. Selby-Bigge (ed.), A Treatise of Human Nature, rev. 2nd. ed., P. H. Nidditch, Clarendon Press, Oxford.
Kuipers, T. A. F.: 1988, 'Inductive Logic by Similarity and Proximity', in D. A. Helman (ed.), Analogical Reasoning, Kluwer, Dordrecht.
Lewis, D.: 1969, Convention: A Philosophical Study, Harvard University Press, Cambridge, MA.
Martin, J. J.: 1967, Bayesian Decision Problems and Markov Chains, Wiley, New York.
Milgrom, P. and J. Roberts: 1991, 'Adaptive and Sophisticated Learning in Normal Form Games', Games and Economic Behavior 3, 82-100.
Miyasawa, K.: 1961, 'On the Convergence of the Learning Process in a 2 × 2 Non-Zero Sum Two Person Game', Economic Research Program, Princeton University, Research Memorandum No. 33.
Nash, J.: 1950, 'Equilibrium Points in n-person Games', Proceedings of the National Academy of Sciences of the United States 36, 48-49.
Nash, J.: 1951, 'Non-Cooperative Games', Annals of Mathematics 54, 286-295.
Prisbey, J.: 1992, 'An Experimental Analysis of Two-Person Reciprocity Games', California Institute of Technology, Social Science Working Paper 787.
Rapoport, A., M. Guyer, and D. Gordon: 1976, The 2 × 2 Game, The University of Michigan Press, Ann Arbor.
Richards, D.: 1997, 'The Geometry of Inductive Reasoning in Games', Economic Theory 10, 185-193.
Shapley, L. S.: 1964, 'Some Topics in Two-person Games', in M. Drescher, L. S. Shapley and A. W. Tucker (eds.), Advances in Game Theory, Princeton University Press, Princeton.
Skyrms, B.: 1990, The Dynamics of Rational Deliberation, Harvard University Press, Cambridge, MA.
Skyrms, B.: 1991a, 'Inductive Deliberation, Admissible Acts, and Perfect Equilibrium', in M. Bacharach and S. Hurley (ed.), Foundations of Decision Theory, Blackwell, Oxford and Cambridge, MA, pp. 220-241.
Skyrms, B.: 1991b, 'Carnapian Inductive Logic for Markov Chains', Erkenntnis 35, 439-460.
Sonsino, D.: 1997, 'Learning to Learn, Pattern Recognition, and Nash Equilibrium', Games and Economic Behavior 18, 286-331.
Sugden, R.: 1986, The Economics of Rights, Co-operation and Welfare, Basil Blackwell, Oxford.
Vanderschraaf, P.: 1998, 'The Informal Game Theory in Hume's Account of Convention', Economics and Philosophy 14, 215-247.
Vanderschraaf, P.: 2001, Learning and Coordination, Routledge, New York.
Vanderschraaf, P. and B. Skyrms: 1993, 'Deliberational Correlated Equilibria', Philosophical Topics 21, 191-227.
Von Neumann, J. and O. Morgenstern: 1944, Theory of Games and Economic Behavior, Princeton University Press, Princeton.
Zabell, S.: 1995, 'Characterizing Markov Exchangeable Sequences', Journal of Theoretical Probability 8, 175-178.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vanderschraaf, P., Skyrms, B. Learning to Take Turns. Erkenntnis 59, 311–347 (2003). https://doi.org/10.1023/A:1026046625024
Issue Date:
DOI: https://doi.org/10.1023/A:1026046625024