Non-Probabilistic Decision Making with Memory Constraints

Vostroknutov, Alexander (2005): Non-Probabilistic Decision Making with Memory Constraints. Unpublished.

Abstract

In the model of choice, studied in this paper, the decision maker chooses the actions non-probabilistically in each period (Sarin and Vahid, 1999; Sarin, 2000). The action is chosen if it yields the biggest payoff according to the decision maker’s subjective assessment. Decision maker knows nothing about the process that generates the payoffs. If the decision maker remembers only recent payoffs, she converges to the maximin action. If she remembers all past payoffs, the maximal expected payoff action is chosen. These results hold for any possible dynamics of weights and are robust against the mistakes. The estimates of the rate of convergence reveal that in some important cases the convergence to the asymptotic behavior can take extremely long time. The model suggests simple experimental test of the way people memorize past experiences: if any weighted procedure is actually involved, it can possibly generate only two distinct modes of behavior.

• Item Type: MPRA Paper
• Institution: University of Minnesota
• Language: English
• Keywords: Adaptive learning; constrained memory; bandit problem; non-probabilistic choice
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D83 - Search; Learning; Information and Knowledge; Communication; Belief; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty

References

Fristedt, B., and L. Gray (1997): A modern approach to probability theory. Boston: Birkhauser. Huck, S., and R. Sarin (2004): “Players with limited memory,” Contributions to Theoretical Economics, 4(1). Loeve, M. M. (1978): Probability Theory. New York, NY: Springer-Verlag. Sarin, R. (2000): “Decision Rules with Bounded Memory,” Journal of Economic Theory, 90(1), 151–160. Sarin, R., and F. Vahid (1999): “Payoff Assessments without Probabilities: A Simple Dynamic Model of Choice,” Games and Economic Behavior, 28(2), 294–309. Sarin, R., and F. Vahid (2001): “Predicting How People Play Games: A Simple Dynamic Model of Choice,” Games and Economic Behavior, 34(1), 104–122. Sutton, R. S., and A. G. Barto (1998): Reinforcement Learning: An Introduction. Cambridge, Mass.: MIT Press. Young, H. P. (1998): Individual strategy and social structure: an evolutionary theory of institutions. Princeton, N.J.: Princeton University Press. Young, H. P. (2007): “Learning by Trial and Error,” mimeo, University of Oxford, The Brookings Institution.