Non-Computable Strategies and Discounted Repeated Games
AbstractA 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.
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Bibliographic InfoPaper provided by UCLA Department of Economics in its series UCLA Economics Working Papers with number 735.
Date of creation: 01 Apr 1995
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Other versions of this item:
- William R. Zame & John H. Nachbar, 1996. "Non-computable strategies and discounted repeated games," Economic Theory, Springer, vol. 8(1), pages 103-122.
- Nachbar, John H & Zame, William R, 1996. "Non-computable Strategies and Discounted Repeated Games," Economic Theory, Springer, vol. 8(1), pages 103-22, June.
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
- E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
- O11 - Economic Development, Technological Change, and Growth - - Economic Development - - - Macroeconomic Analyses of Economic Development
- O47 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Measurement of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence
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