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Modeling large societies: Why countable additivity is necessary

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  • Khan, M. Ali
  • Qiao, Lei
  • Rath, Kali P.
  • Sun, Yeneng

Abstract

The economic literature with an atomless countably additive measure space to model the interaction of agents in a large society is enormous. However, there have been a number of attempts to relax the countable additivity assumption by working with a finitely (but non-countably) additive measure space (such as the set of natural numbers with a density charge). The main purpose of this paper is to demonstrate the necessity of countable additivity in modeling a large society in terms of the existence of equilibrium and its idealized limit property in both general equilibrium and game theory as illustrations. In addition, we point out that in the setting of atomless finitely additive agent spaces, even approximate equilibria may not exist in general, but do so only with additional assumptions.

Suggested Citation

  • Khan, M. Ali & Qiao, Lei & Rath, Kali P. & Sun, Yeneng, 2020. "Modeling large societies: Why countable additivity is necessary," Journal of Economic Theory, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:jetheo:v:189:y:2020:i:c:s0022053120300958
    DOI: 10.1016/j.jet.2020.105102
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    More about this item

    Keywords

    Countable additivity; Finite additivity; Competitive equilibrium; Nash equilibrium; Existence of equilibrium; Idealized limit property;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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