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Players With Limited Memory

Author Info

  • Huck Steffen

    ()

    (University College London)

  • Sarin Rajiv

    ()

    (Texas A&M)

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.

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Article provided by De Gruyter in its journal The B.E. Journal of Theoretical Economics.

Volume (Year): 4 (2004)
Issue (Month): 1 (September)
Pages: 1-27

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Handle: RePEc:bpj:bejtec:v:contributions.4:y:2004:i:1:n:6
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Find related papers by 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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  1. Lehrer, Ehud, 1988. "Repeated games with stationary bounded recall strategies," Journal of Economic Theory, Elsevier, vol. 46(1), pages 130-144, October.
  2. Martin J. Osborne & Ariel Rubinstein, 1997. "Games with Procedurally Rational Players," Department of Economics Working Papers 1997-02, McMaster University.
  3. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  4. J. Bergin & B. Lipman, 2010. "Evolution with State-Dependent Mutations," Levine's Working Paper Archive 486, David K. Levine.
  5. 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.
  6. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
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  8. 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.
  9. 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.
  10. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  11. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
  12. James Dow, 1991. "Search Decisions with Limited Memory," Review of Economic Studies, Oxford University Press, vol. 58(1), pages 1-14.
  13. Eric Friedman & Scott Shenker, 1998. "Learning and Implementation on the Internet," Departmental Working Papers 199821, Rutgers University, Department of Economics.
  14. 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.
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  19. Rubinstein, Ariel, 1995. "On the Interpretation of Decision Problems with Imperfect Recall," Mathematical Social Sciences, Elsevier, vol. 30(3), pages 324-324, December.
  20. Eric Friedman & Scott Shenker & Amy Greenwald, 1998. "Learning in Networks Contexts: Experimental Results from Simulations," Departmental Working Papers 199825, Rutgers University, Department of Economics.
  21. Sabourian, Hamid, 1998. "Repeated games with M-period bounded memory (pure strategies)," Journal of Mathematical Economics, Elsevier, vol. 30(1), pages 1-35, August.
  22. Chen, Yan, 1992. "Asynchrony and Learning in Serial and Average Cost Pricing Mechanisms: An Experimental Study," Discussion Paper Serie A 592, University of Bonn, Germany.
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Cited by:

  1. Jörg Oechssler & Burkhard C. Schipper, 2000. "Can You Guess the Game You're Playing?," Bonn Econ Discussion Papers bgse11_2000, University of Bonn, Germany.
  2. Yilmaz Kocer, 2010. "Endogenous Learning with Bounded Memory," Working Papers 1290, Princeton University, Department of Economics, Econometric Research Program..
  3. Sherstyuk, Katerina & Tarui, Nori & Wengrin, Melinda Podor & Viloria, Jay & Saijo, Tatsuyoshi, 2014. "Other-regarding behavior under collective action," CEI Working Paper Series 2014-2, Center for Economic Institutions, Institute of Economic Research, Hitotsubashi University.
  4. Vostroknutov, Alexander, 2012. "Non-probabilistic decision making with memory constraints," Economics Letters, Elsevier, vol. 117(1), pages 303-305.
  5. Yan Chen & Laura Razzolini & Theodore Turocy, 2007. "Congestion allocation for distributed networks: an experimental study," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(1), pages 121-143, October.
  6. Vostroknutov, Alexander, 2005. "Non-Probabilistic Decision Making with Memory Constraints," MPRA Paper 2653, University Library of Munich, Germany, revised Jul 2007.

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