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A mean field game model for COVID-19 with human capital accumulation

Author

Listed:
  • Daria Ghilli

    (Universitá di Pavia)

  • Cristiano Ricci

    (Universitá di Pisa)

  • Giovanni Zanco

    (Universitá di Siena)

Abstract

In this manuscript, we study a model of human capital accumulation during the spread of disease following an agent-based approach, where agents behave maximising their intertemporal utility. We assume that the agent interaction is of mean field type, yielding a mean field game description of the problem. We discuss how the analysis of a model including both the mechanism of change of species from one epidemiological state to the other and an optimisation problem for each agent leads to an aggregate behaviour that is not easy to describe, and that sometimes exhibits structural issues. Therefore we eventually propose and study numerically a SEIRD model in which the rate of infection depends on the distribution of the population, given exogenously as the solution to the mean field game system arising as the macroscopic description of the discrete multi-agent economic model for the accumulation of human capital. Such a model arises in fact as a simplified but tractable version of the initial one.

Suggested Citation

  • Daria Ghilli & Cristiano Ricci & Giovanni Zanco, 2024. "A mean field game model for COVID-19 with human capital accumulation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(1), pages 533-560, February.
    • Handle: RePEc:spr:joecth:v:77:y:2024:i:1:d:10.1007_s00199-023-01505-0
    DOI: 10.1007/s00199-023-01505-0
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    Keywords

    Spatial SIR type models; Mean field games; Spatial interactions;
    All these keywords.

    JEL classification:

    • E19 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Other
    • I10 - Health, Education, and Welfare - - Health - - - General
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • O11 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Macroeconomic Analyses of Economic Development
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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