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# Growth of Strategy Sets, Entropy and Nonstationary Bounded Recall

## Author

Listed:
• Abraham Neyman Null

(Hebrew University)

() (Rutgers University)

## Abstract

This paper initiates the study of long term interactions where players' bounded rationality varies over time. Time dependent bounded rationality is reflected in part in the number $\psi(t)$ of distinct strategies in the first $t$-stages. We examine how the growth rate of $\psi_i(t)$ affects equilibrium outcomes of repeated games, and, as a special case, we study the repeated games with nonstationary bounded recall.

## Suggested Citation

• Abraham Neyman Null & Daijiro Okada, 2005. "Growth of Strategy Sets, Entropy and Nonstationary Bounded Recall," Departmental Working Papers 200514, Rutgers University, Department of Economics.
• Handle: RePEc:rut:rutres:200514
as

File URL: http://www.sas.rutgers.edu/virtual/snde/wp/2005-14.pdf

## References listed on IDEAS

as
1. Robert J. Aumann & Lloyd S. Shapley, 2013. "Long Term Competition -- A Game-Theoretic Analysis," Annals of Economics and Finance, Society for AEF, vol. 14(2), pages 627-640, November.
2. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
3. Olivier Gossner & Penélope Hernández & Abraham Neyman, 2006. "Optimal Use of Communication Resources," Econometrica, Econometric Society, vol. 74(6), pages 1603-1636, November.
4. Gossner, Olivier & Vieille, Nicolas, 2002. "How to play with a biased coin?," Games and Economic Behavior, Elsevier, vol. 41(2), pages 206-226, November.
5. Abraham Neyman & Daijiro Okada, 2000. "Two-person repeated games with finite automata," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(3), pages 309-325.
6. Neyman, Abraham & Okada, Daijiro, 2000. "Repeated Games with Bounded Entropy," Games and Economic Behavior, Elsevier, vol. 30(2), pages 228-247, February.
7. Ben-Porath Elchanan, 1993. "Repeated Games with Finite Automata," Journal of Economic Theory, Elsevier, vol. 59(1), pages 17-32, February.
8. Lehrer, Ehud, 1988. "Repeated games with stationary bounded recall strategies," Journal of Economic Theory, Elsevier, vol. 46(1), pages 130-144, October.
9. Aumann, Robert J., 1997. "Rationality and Bounded Rationality," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 2-14, October.
Full references (including those not matched with items on IDEAS)

## Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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Cited by:

1. Peretz, Ron, 2012. "The strategic value of recall," Games and Economic Behavior, Elsevier, vol. 74(1), pages 332-351.
2. Abraham Neyman, 2008. "Learning Effectiveness and Memory Size," Levine's Working Paper Archive 122247000000001945, David K. Levine.
3. Ron Peretz, 2011. "Correlation through Bounded Recall Strategies," Discussion Paper Series dp579, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
4. Ron Peretz, 2007. "The Strategic Value of Recall," Discussion Paper Series dp470, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
5. Olivier Gossner & Penélope Hernández & Ron Peretz, 2016. "The complexity of interacting automata," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 461-496, March.
6. Ron Peretz, 2013. "Correlation through bounded recall strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 867-890, November.
7. Ron Peretz, 2007. "The Strategic Value of Recall," Levine's Bibliography 122247000000001774, UCLA Department of Economics.

### Keywords

bounded rationality; strategy set growth; strategic complexity; nonstationary bounded recall; repeated games;

### JEL classification:

• C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
• C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

### NEP fields

This paper has been announced in the following NEP Reports:

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