Understanding Nash epidemics

Simon K. Schnyder (), John J. Molina, Ryoichi Yamamoto and Matthew S. Turner ()
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Simon K. Schnyder: a Institute of Industrial Science , The University of Tokyo , Tokyo 153-8505 , Japan
John J. Molina: b Department of Chemical Engineering , Kyoto University , Kyoto 615-8510 , Japan
Ryoichi Yamamoto: b Department of Chemical Engineering , Kyoto University , Kyoto 615-8510 , Japan
Matthew S. Turner: d Institute for Global Pandemic Planning , University of Warwick , Coventry CV4 7AL , United Kingdom

Proceedings of the National Academy of Sciences, 2025, vol. 122, issue 9, e2409362122

Abstract:

Faced with a dangerous epidemic humans will spontaneously social distance to reduce their risk of infection at a socioeconomic cost. Compartmentalized epidemic models have been extended to include this endogenous decision making: Individuals choose their behavior to optimize a utility function, self-consistently giving rise to population behavior. Here, we study the properties of the resulting Nash equilibria, in which no member of the population can gain an advantage by unilaterally adopting different behavior. We leverage an analytic solution that yields fully time-dependent rational population behavior to obtain, 1) a simple relationship between rational social distancing behavior and the current number of infections; 2) scaling results for how the infection peak and number of total cases depend on the cost of contracting the disease; 3) characteristic infection costs that divide regimes of strong and weak behavioral response; 4) a closed form expression for the value of the utility. We discuss how these analytic results provide a deep and intuitive understanding of the disease dynamics, useful for both individuals and policymakers. In particular, the relationship between social distancing and infections represents a heuristic that could be communicated to the population to encourage, or “bootstrap,†rational behavior.

Keywords: epidemiology; control theory; mean-field games; game theory; mathematical modeling (search for similar items in EconPapers)
Date: 2025
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