Non-Computable Strategies and Discounted Repeated Games
A number of authors have used formal models of computation to capture the idea of "bounded rationality" in repeated games. Most of this literature has used computability by a finite automaton as the standard. A conceptual difficulty with this standard is that the decision problem is not "closed." That is, for every strategy implementable by an automaton, there is some best response implementable by an automaton, but there may not exist any algorithm for finding such a best response that can be implemented by an automaton. However, such algorithms can always be implemented by a Turing machine, the most powerful formal model of computation. In this paper, we investigate whether the decision problem can be closed by adopting Turing machines as the standard of computability. The answer we offer is negative. Indeed, for a large class of discounted repeated games (including the repeated Prisoner's Dilemma) there exist strategies implementable by a Turing machine for which no best response is implementable by a Turing machine.
(This abstract was borrowed from another version of this item.)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Gilboa, Itzhak & Samet, Dov, 1989.
"Bounded versus unbounded rationality: The tyranny of the weak,"
Games and Economic Behavior,
Elsevier, vol. 1(3), pages 213-221, September.
- Itzhak Gilboa & Dov Samet, 1989. "Bounded Versus Unbounded Rationality: The Tyranny of the Weak," Post-Print hal-00753239, HAL.
- Ehud Kalai & William Stanford, 1986.
"Finite Rationality and Interpersonal Complexity in Repeated Games,"
679, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March.
- Canning, David, 1992. "Rationality, Computability, and Nash Equilibrium," Econometrica, Econometric Society, vol. 60(4), pages 877-88, July.
- Stanford, William, 1989. "Symmetric paths and evolution to equilibrium in the discounted prisoners' dilemma," Economics Letters, Elsevier, vol. 31(2), pages 139-143, December.
- Binmore, Ken, 1987. "Modeling Rational Players: Part I," Economics and Philosophy, Cambridge University Press, vol. 3(02), pages 179-214, October.
- Anderlini, Luca & Sabourian, Hamid, 1995.
"Cooperation and Effective Computability,"
Econometric Society, vol. 63(6), pages 1337-69, November.
- Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-81, November.
- John H. Nachbar, 1995.
"Prediction, Optimization, and Learning in Repeated Games,"
Game Theory and Information
9504001, EconWPA, revised 14 Feb 1996.
- John H. Nachbar, 1997. "Prediction, Optimization, and Learning in Repeated Games," Econometrica, Econometric Society, vol. 65(2), pages 275-310, March.
- John Nachbar, 2010. "Prediction, Optimization and Learning in Repeated Games," Levine's Working Paper Archive 576, David K. Levine.
- Knoblauch Vicki, 1994. "Computable Strategies for Repeated Prisoner's Dilemma," Games and Economic Behavior, Elsevier, vol. 7(3), pages 381-389, November.
- Rubinstein, Ariel, 1986.
"Finite automata play the repeated prisoner's dilemma,"
Journal of Economic Theory,
Elsevier, vol. 39(1), pages 83-96, June.
- Ariel Rubinstein, 1997. "Finite automata play the repeated prisioners dilemma," Levine's Working Paper Archive 1639, David K. Levine.
When requesting a correction, please mention this item's handle: RePEc:cla:uclawp:735. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Tim Kwok)
If references are entirely missing, you can add them using this form.