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Information Theory and Observational Limitations in Decision Making

Author

Listed:
  • Wolpert David

    () (NASA Ames Research Center, Santa Fe Institute, and Los Alamos National Laboratory)

  • Leslie David S.

    () (University of Bristol)

Abstract

We introduce a general framework for formalizing and analyzing the problem faced by a Decision Maker (DM) working under information-theoretic constraints on their observational ability. The random utility model and the "hedonic utility" model of Netzer and Robson (NR) are special cases of this framework. We begin by applying information theory to our framework to derive general results concerning the expected regret of DM under observational limitations. We then turn our attention to the effects of observational limitations on choice behavior (rather than their effects on the regret values induced by that behavior). We focus on the special case of NR. First we derive two postulates assumed by NR. We then provide a simple derivation of the result of NR that a particular hedonic utility function satisfies certain optimality principles. Next we extend NR to allow a countable, rather than uncountable, set of states of the world. In particular we show how to use dynamic programming to solve for the optimal preference order of DM in this extension. We also extend NR by considering the case where more than two options are presented to DM. In particular, we show that the results of NR change in such a case, implying that the number of options being presented is a crucial aspect of choice problems.

Suggested Citation

  • Wolpert David & Leslie David S., 2012. "Information Theory and Observational Limitations in Decision Making," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-43, January.
  • Handle: RePEc:bpj:bejtec:v:12:y:2012:i:1:n:5
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    References listed on IDEAS

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    1. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, January.
    2. Sergiu Hart, 2013. "Adaptive Heuristics," World Scientific Book Chapters,in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 11, pages 253-287 World Scientific Publishing Co. Pte. Ltd..
    3. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555.
    4. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, January.
    5. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
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    Cited by:

    1. Michael Woodford, 2014. "An Optimizing Neuroeconomic Model of Discrete Choice," NBER Working Papers 19897, National Bureau of Economic Research, Inc.

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