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A characterization of Cesàro average utility

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  • Pivato, Marcus

Abstract

Let X be a connected metric space, and let ⪰ be a weak order defined on a suitable subset of XN. We characterize when ⪰ has a Cesàro average utility representation. This means that there is a continuous real-valued function u on X such that, for all sequences x=(xn)n=1∞ and y=(yn)n=1∞ in the domain of ⪰, we have x⪰y if and only if the limit as N→∞ of the average value of u(x1),…,u(xN) is higher than limit as N→∞ of the average value of u(y1),…,u(yN). This has applications to decision theory, game theory, and intergenerational social choice.

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  • Pivato, Marcus, 2022. "A characterization of Cesàro average utility," Journal of Economic Theory, Elsevier, vol. 201(C).
    • Handle: RePEc:eee:jetheo:v:201:y:2022:i:c:s0022053122000308
    DOI: 10.1016/j.jet.2022.105440
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    Cited by:

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    3. Adam Jonsson, 2023. "An axiomatic approach to Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(1), pages 117-133, February.

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    More about this item

    Keywords

    Subjective expected utility; Insufficient reason; Intertemporal choice; Infinite patience; Intergenerational social choice; Cesàro mean;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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