Summary
The perfect folk theorem (Fudenberg and Maskin [1986]) need not rely on excessively complex strategies. We recover the perfect folk theorem for two person repeated games with discounting through neural networks (Hopfield [1982]) that have finitely many associative units. For any individually rational payoff vector, we need neural networks with at most 7 associative units, each of which can handle only elementary calculations such as maximum, minimum or threshold operation. The uniform upper bound of the complexity of equilibrium strategies differentiates this paer from Ben-Porath and Peleg [1987] in which we need to admit ever more complex strategies in order to expand the set of equilibrium outcomes.
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References
Ben-Porath, E., Peleg, B.: On the folk theorem and finite automata, mimeo, Hebrew University of Jerusalem, 1987
Cho, I.-K.: Perceptrons play repeated prisoner's dilemma, mimeo, University of Chicago, 1992
Cho, I.-K.: Perceptrons play repeated games with imperfect monitoring, mimeo, University of Chicago, 1993
Fudenberg, D., Kreps, M., Maskin, E.: Repeated games with long run and short run players. Rev. Econ. Stud.57, 555–573 (1990)
Fudenberg, D., Maskin, E.: The folk theorem in repeated games with discounting or with incomplete information. Econometrica54, 522–554 (1986)
Hertz, J., Krogh, A., Palmer, R.G.: Introduction to the theory of neural computation. Lecture note vol. I, Santa Fe Institute, Addison-Wesley, 1991
Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilities. Proc. Nat. Acad. Sci.79, 2554–2558 (1982)
Kalai, E., Stanford, W.: Finite rationality and interpersonal complexity in repeated games. Econometrica56, 397–410 (1988)
Mount, K.R., Reiter, S.: A model of computing with human agents, mimeo, Northwestern University, 1990
Rissanen, J.: Stochastic complexity in statistical inquiry. World Scientific Publishing Company, 1989
Rubinstein, A.: Finite automata play the repeated prisoner's dilemma. J. Econ. Theory39, 83–96 (1986)
Selten, R.: Re-examination of the perfectness concept for equilibrium points in extensive games. Int. J. Games Theory,4, 25–55 (1975)
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I would like to thank Hao Li and John Curran for excellent research assistance. Financial support from National Science Foundation (SES-9223483), Sloan Foundation and the Division of Social Sciences at the University of Chicago is gratefully acknowledged.
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Cho, IK. Bounded rationality, neural network and folk theorem in repeated games with discounting. Econ Theory 4, 935–957 (1994). https://doi.org/10.1007/BF01213820
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DOI: https://doi.org/10.1007/BF01213820