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Players With Limited Memory

Author

Listed:
  • Huck Steffen

    (University College London, s.huck@ucl.ac.uk)

  • Sarin Rajiv

    (Texas A&M, rsarin@econmail.tamu.edu)

Abstract

This paper studies a model of memory. The model takes into account that memory capacity is limited and imperfect. We study how agents with such memory limitations, who have very little information about their choice environment, play games. We introduce the notion of a Limited Memory Equilibrium (LME) and show that play converges to an LME in every generic normal form game. Our characterization of the set of LME suggests that players with limited memory do (weakly) better in games than in decision problems. We also show that agents can do quite well even with severely limited memory, although severe limitations tend to make them behave cautiously.

Suggested Citation

  • Huck Steffen & Sarin Rajiv, 2004. "Players With Limited Memory," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 4(1), pages 1-27, September.
    • Handle: RePEc:bpj:bejtec:v:contributions.4:y:2004:i:1:n:6
    DOI: 10.2202/1534-5971.1109
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    1. Sethi, Rajiv, 2000. "Stability of Equilibria in Games with Procedurally Rational Players," Games and Economic Behavior, Elsevier, vol. 32(1), pages 85-104, July.
    2. John Conlisk, 1996. "Why Bounded Rationality?," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 669-700, June.
    3. Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-956, July.
    4. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, vol. 1(1), pages 5-39, March.
    5. Piccione, Michele & Rubinstein, Ariel, 1997. "On the Interpretation of Decision Problems with Imperfect Recall," Games and Economic Behavior, Elsevier, vol. 20(1), pages 3-24, July.
    6. Eric Friedman & Scott Shenker & Amy Greenwald, 1998. "Learning in Networks Contexts: Experimental Results from Simulations," Departmental Working Papers 199825, Rutgers University, Department of Economics.
    7. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    8. Gilboa, Itzhak & Schmeidler, David, 1996. "Case-Based Optimization," Games and Economic Behavior, Elsevier, vol. 15(1), pages 1-26, July.
    9. Eric Friedman & Scott Shenker, 1998. "Learning and Implementation on the Internet," Departmental Working Papers 199821, Rutgers University, Department of Economics.
    10. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    11. James Dow, 1991. "Search Decisions with Limited Memory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(1), pages 1-14.
    12. Osborne, Martin J & Rubinstein, Ariel, 1998. "Games with Procedurally Rational Players," American Economic Review, American Economic Association, vol. 88(4), pages 834-847, September.
    13. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
    14. Sabourian, Hamid, 1998. "Repeated games with M-period bounded memory (pure strategies)," Journal of Mathematical Economics, Elsevier, vol. 30(1), pages 1-35, August.
    15. Sendhil Mullainathan, 2002. "A Memory-Based Model of Bounded Rationality," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(3), pages 735-774.
    16. Lehrer Ehud, 1994. "Finitely Many Players with Bounded Recall in Infinitely Repeated Games," Games and Economic Behavior, Elsevier, vol. 7(3), pages 390-405, November.
    17. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    18. Ellison, Glenn, 1997. "Learning from Personal Experience: One Rational Guy and the Justification of Myopia," Games and Economic Behavior, Elsevier, vol. 19(2), pages 180-210, May.
    19. Lehrer, Ehud, 1988. "Repeated games with stationary bounded recall strategies," Journal of Economic Theory, Elsevier, vol. 46(1), pages 130-144, October.
    20. Aner Sela & Dorothea Herreiner, 1999. "Fictitious play in coordination games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 189-197.
    21. Sarin, Rajiv & Vahid, Farshid, 1999. "Payoff Assessments without Probabilities: A Simple Dynamic Model of Choice," Games and Economic Behavior, Elsevier, vol. 28(2), pages 294-309, August.
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    2. Katerina Sherstyuk & Nori Tarui & Melinda Podor Wengrin & Jay Viloria & Tatsuyoshi Saijo, 2014. "Other-regarding behavior under collective action," Working Papers 201404, University of Hawaii at Manoa, Department of Economics.
    3. Vostroknutov, Alexander, 2005. "Non-Probabilistic Decision Making with Memory Constraints," MPRA Paper 2653, University Library of Munich, Germany, revised Jul 2007.
    4. Yilmaz Kocer, 2010. "Endogenous Learning with Bounded Memory," Working Papers 1290, Princeton University, Department of Economics, Econometric Research Program..
    5. Vostroknutov, Alexander, 2012. "Non-probabilistic decision making with memory constraints," Economics Letters, Elsevier, vol. 117(1), pages 303-305.

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    More about this item

    Keywords

    bounded rationality; games; memory; maxmin;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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