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The Mask Game with Multiple Populations

Author

Listed:
  • Eitan Altman

    (INRIA Sophia Antipolis – Méditerranée
    University of Avignon
    Laboratory of Information, Networking and Communication Sciences (LINCS))

  • Mandar Datar

    (INRIA Sophia Antipolis – Méditerranée
    University of Avignon)

  • Francesco Pellegrini

    (University of Avignon)

  • Samir Perlaza

    (INRIA Sophia Antipolis – Méditerranée)

  • Daniel Sadoc Menasché

    (Federal University of Rio de Janeiro)

Abstract

Masks save lives. Therefore, while the culture of wearing masks is promoted, it is critical to understand the various aspects of how that culture is adopted. The main contribution of this paper is in the modeling of the mask game. Wearing a mask provides partial protection against epidemics at some cost of comfort. Players can be differentiated according to both their risk state as well as their health state (susceptible, infected and removed). We formulate the problem as a Bayesian game in which players know their own risk state and ignore their own health state and the health and risk states of their counterparts. Using ideas from evolutionary games, we reduce the problem to a one-shot equivalent game and describe the structure of the symmetric equilibria. We prove that the policies adopted by the players at such equilibria admit a threshold structure. More specifically, players wear masks only if their risk state is equal to or bigger than a given threshold.

Suggested Citation

  • Eitan Altman & Mandar Datar & Francesco Pellegrini & Samir Perlaza & Daniel Sadoc Menasché, 2022. "The Mask Game with Multiple Populations," Dynamic Games and Applications, Springer, vol. 12(1), pages 147-167, March.
    • Handle: RePEc:spr:dyngam:v:12:y:2022:i:1:d:10.1007_s13235-022-00431-5
    DOI: 10.1007/s13235-022-00431-5
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    References listed on IDEAS

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    1. Mitze, Timo & Kosfeld, Reinhold & Rode, Johannes & Wälde, Klaus, 2020. "Face masks considerably reduce COVID-19 cases in Germany," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 124130, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    2. Mitze, Timo & Kosfeld, Reinhold & Rode, Johannes & Wälde, Klaus, 2020. "Face masks considerably reduce COVID-19 cases in Germany," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 124587, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    3. Nattavudh Powdthavee & Yohanes E Riyanto & Erwin C L Wong & Jonathan X W Yeo & Qi Yu Chan, 2021. "When face masks signal social identity: Explaining the deep face-mask divide during the COVID-19 pandemic," PLOS ONE, Public Library of Science, vol. 16(6), pages 1-15, June.
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    5. Chernozhukov, Victor & Kasahara, Hiroyuki & Schrimpf, Paul, 2021. "Causal impact of masks, policies, behavior on early covid-19 pandemic in the U.S," Journal of Econometrics, Elsevier, vol. 220(1), pages 23-62.
    6. Burridge, James & Gnacik, Michał, 2022. "Public efforts to reduce disease transmission implied from a spatial game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    7. Lynne Peeples, 2020. "Face masks: what the data say," Nature, Nature, vol. 586(7828), pages 186-189, October.
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    Cited by:

    1. Ashish R. Hota & Urmee Maitra & Ezzat Elokda & Saverio Bolognani, 2023. "Learning to Mitigate Epidemic Risks: A Dynamic Population Game Approach," Dynamic Games and Applications, Springer, vol. 13(4), pages 1106-1129, December.

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