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Foundation and identification of multi-attribute Shannon entropy

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  • Walker-Jones, David

Abstract

By weakening Shannon's original axioms to allow for attributes of the choice environment to differ in their associated learning costs, this paper provides an axiomatic foundation for Multi-Attribute Shannon Entropy, a natural multi-parameter generalization of Shannon Entropy. Sufficient conditions are also provided for a simple dataset that provides a closed-form solution for the Multi-Attribute Shannon Entropy cost function for information by analyzing stochastic choice data produced by a rationally inattentive agent that is picking between pairs of options when relatively few states of the world have a positive probability of being realized.

Suggested Citation

  • Walker-Jones, David, 2025. "Foundation and identification of multi-attribute Shannon entropy," Games and Economic Behavior, Elsevier, vol. 150(C), pages 334-355.
    • Handle: RePEc:eee:gamebe:v:150:y:2025:i:c:p:334-355
    DOI: 10.1016/j.geb.2025.01.006
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    References listed on IDEAS

    as
    1. Luciano Pomatto & Philipp Strack & Omer Tamuz, 2018. "The Cost of Information: The Case of Constant Marginal Costs," Papers 1812.04211, arXiv.org, revised Feb 2023.
    2. Luciano Pomatto & Philipp Strack & Omer Tamuz, 2023. "The Cost of Information: The Case of Constant Marginal Costs," American Economic Review, American Economic Association, vol. 113(5), pages 1360-1393, May.
    3. Filip Matêjka & Alisdair McKay, 2015. "Rational Inattention to Discrete Choices: A New Foundation for the Multinomial Logit Model," American Economic Review, American Economic Association, vol. 105(1), pages 272-298, January.
    4. Ellis, Andrew, 2018. "Foundations for optimal inattention," Journal of Economic Theory, Elsevier, vol. 173(C), pages 56-94.
    5. Walker-Jones, David, 2023. "Rational inattention with multiple attributes," Journal of Economic Theory, Elsevier, vol. 212(C).
    6. Andrew Caplin & Mark Dean & John Leahy, 2022. "Rationally Inattentive Behavior: Characterizing and Generalizing Shannon Entropy," Journal of Political Economy, University of Chicago Press, vol. 130(6), pages 1676-1715.
    7. de Oliveira, Henrique & Denti, Tommaso & Mihm, Maximilian & Ozbek, Kemal, 2017. "Rationally inattentive preferences and hidden information costs," Theoretical Economics, Econometric Society, vol. 12(2), May.
    8. Bartosz Maćkowiak & Filip Matějka & Mirko Wiederholt, 2023. "Rational Inattention: A Review," Journal of Economic Literature, American Economic Association, vol. 61(1), pages 226-273, March.
    9. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
    10. Tommaso Denti, 2022. "Posterior Separable Cost of Information," American Economic Review, American Economic Association, vol. 112(10), pages 3215-3259, October.
    11. Mark Dean & Nathaniel Neligh, 2023. "Experimental Tests of Rational Inattention," Journal of Political Economy, University of Chicago Press, vol. 131(12), pages 3415-3461.
    12. Benjamin Hébert & Michael Woodford, 2021. "Neighborhood-Based Information Costs," American Economic Review, American Economic Association, vol. 111(10), pages 3225-3255, October.
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    Keywords

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    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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