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Published in: Dynamic Games and Applications 1/2022

02-12-2021

Mobility Choices and Strategic Interactions in a Two-Group Macroeconomic–Epidemiological Model

Authors: Davide La Torre, Danilo Liuzzi, Rosario Maggistro, Simone Marsiglio

Published in: Dynamic Games and Applications | Issue 1/2022

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Abstract

We analyze the implications of strategic interactions between two heterogeneous groups (i.e., young and old, men and women) in a macroeconomic–epidemiological framework. The interactions between groups determine the overall prevalence of a communicable disease, which in turn affects the level of economic activity. Individuals may lower their disease exposure by reducing their mobility, but since changing mobility patterns is costly, each group has an incentive to free ride negatively affecting the chances of disease containment at the aggregate level. By focusing on an early epidemic setting, we explicitly characterize the cooperative and noncooperative equilibria, determining how the inefficiency induced by noncooperation (i.e., failure to internalize epidemic externalities) depends both on economic and epidemiological parameters. We show that long-run eradication may be possible even in the absence of coordination, but coordination leads to a faster reduction in the number of infectives in finite time. Moreover, the inefficiency induced by noncooperation increases (decreases) with the factors increasing (decreasing) the pace of the disease spread.

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Appendix
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Footnotes
1
In the absence of a linear-quadratic structure and of \(C^1\)-regularity of the function satisfying the Hamilton–Jacobi–Bellman equation (HJB), obtaining closed-form solutions would not be possible. If this is the case, we might rely either on a numerical approach or on the notion of viscosity solution. Different from numerical approaches, the viscosity solutions theory permits to guarantee existence and uniqueness (via comparison principle) of the solution for problems which do not allow for classical closed-form solutions [1214].
 
Literature
1.
go back to reference Acemoglu D, Chernozhukov V, Werning I, Whinston MD (2020) A multi-risk SIR model with optimally targeted lockdown, Am Econ Rev: Insights ( Forthcoming) Acemoglu D, Chernozhukov V, Werning I, Whinston MD (2020) A multi-risk SIR model with optimally targeted lockdown, Am Econ Rev: Insights ( Forthcoming)
2.
go back to reference Alon T, Doepke M, Olmstead-Rumsey J, Tertilt M (2020) This time it’s different: the role of women’s employment in a pandemic recession. CEPR Discussion Paper 15149 Alon T, Doepke M, Olmstead-Rumsey J, Tertilt M (2020) This time it’s different: the role of women’s employment in a pandemic recession. CEPR Discussion Paper 15149
3.
go back to reference Alvarez FE, Argente D, Lippi F (2020) A simple planning problem for COVID-19 lockdown. Am Econ Rev: Insights ( Forthcoming) Alvarez FE, Argente D, Lippi F (2020) A simple planning problem for COVID-19 lockdown. Am Econ Rev: Insights ( Forthcoming)
4.
go back to reference Angelucci M, Angrisani M, Bennett DM, Kapteyn A, Schaner SG (2020) Remote work and the heterogeneous impact of COVID-19 on employment and health. NBER Working Paper 27749 Angelucci M, Angrisani M, Bennett DM, Kapteyn A, Schaner SG (2020) Remote work and the heterogeneous impact of COVID-19 on employment and health. NBER Working Paper 27749
5.
go back to reference Atkeson A (2020) What will be the economic impact of COVID-19 in the US? Rough estimates of disease scenarios. NBER Working Paper 26867 Atkeson A (2020) What will be the economic impact of COVID-19 in the US? Rough estimates of disease scenarios. NBER Working Paper 26867
6.
go back to reference Belot M, Choi S, Tripodi E, van den Broek-Altenburg E, Jamison JC, Papageorge NW (2020) Unequal consequences of COVID-19 across age and income: representative evidence from six countries. IZA Discussion Paper 13366 Belot M, Choi S, Tripodi E, van den Broek-Altenburg E, Jamison JC, Papageorge NW (2020) Unequal consequences of COVID-19 across age and income: representative evidence from six countries. IZA Discussion Paper 13366
7.
go back to reference Caselli FG, Grigoli F, Sandri D, Spilimbergo A (2020) Mobility under the COVID-19 pandemic: asymmetric effects across gender and Age. IMF Working Paper 2020/282 Caselli FG, Grigoli F, Sandri D, Spilimbergo A (2020) Mobility under the COVID-19 pandemic: asymmetric effects across gender and Age. IMF Working Paper 2020/282
8.
go back to reference Chakraborty S, Papageorgiou C, Pérez Sebastián F (2010) Diseases, infection dynamics and development. J Monet Econ 57:859–872 CrossRef Chakraborty S, Papageorgiou C, Pérez Sebastián F (2010) Diseases, infection dynamics and development. J Monet Econ 57:859–872 CrossRef
9.
go back to reference Chetty R, Friedman JN, Hendren N, Stepner M (2020) How did COVID-19 and stabilization policies affect spending and employment? A new real-time economic tracker based on private sector data. NBER Working Paper 27431 Chetty R, Friedman JN, Hendren N, Stepner M (2020) How did COVID-19 and stabilization policies affect spending and employment? A new real-time economic tracker based on private sector data. NBER Working Paper 27431
10.
go back to reference Chowell G, Sattenspiel L, Bansal S, Viboud C (2016) Mathematical models to characterize early epidemic growth: a review. Phys Life Rev 18:66–97 CrossRef Chowell G, Sattenspiel L, Bansal S, Viboud C (2016) Mathematical models to characterize early epidemic growth: a review. Phys Life Rev 18:66–97 CrossRef
11.
go back to reference Codagnone C, Bogliacino F, Gomez C, Charris R, Montealegre F, Liva G, Lupianez-Villanueva F, Folkvord F, Veltri GA (2020) Assessing concerns for the economic consequence of the COVID-19 response and mental health problems associated with economic vulnerability and negative economic shock in Italy, Spain, and the United Kingdom. PLoS ONE 15:e0240876 CrossRef Codagnone C, Bogliacino F, Gomez C, Charris R, Montealegre F, Liva G, Lupianez-Villanueva F, Folkvord F, Veltri GA (2020) Assessing concerns for the economic consequence of the COVID-19 response and mental health problems associated with economic vulnerability and negative economic shock in Italy, Spain, and the United Kingdom. PLoS ONE 15:e0240876 CrossRef
12.
13.
go back to reference Crandall MG, Evans LC, Lions P-L (1984) Some properties of viscosity solutions of Hamilton–Jacobi equations. Trans Am Math Soc 282:487–502 MathSciNetCrossRef Crandall MG, Evans LC, Lions P-L (1984) Some properties of viscosity solutions of Hamilton–Jacobi equations. Trans Am Math Soc 282:487–502 MathSciNetCrossRef
14.
go back to reference Crandall MG, Ishii H, Lions P-L (1987) Uniqueness of viscosity solutions of Hamilton–Jacobi equations revisited. J Math Soc Jpn 39:581–596 MathSciNetCrossRef Crandall MG, Ishii H, Lions P-L (1987) Uniqueness of viscosity solutions of Hamilton–Jacobi equations revisited. J Math Soc Jpn 39:581–596 MathSciNetCrossRef
15.
go back to reference Crossley TF, Fisher P, Low H (2021) The heterogeneous and regressive consequences of COVID-19: evidence from high quality panel data. J Public Econ 193:104334 CrossRef Crossley TF, Fisher P, Low H (2021) The heterogeneous and regressive consequences of COVID-19: evidence from high quality panel data. J Public Econ 193:104334 CrossRef
16.
go back to reference Eichenbaum M, Rebelo S, Trabandt M (2020) The macroeconomics of epidemics. NBER Working Paper 26882 Eichenbaum M, Rebelo S, Trabandt M (2020) The macroeconomics of epidemics. NBER Working Paper 26882
17.
go back to reference Gersovitz M, Hammer JS (2004) The economical control of infectious diseases. Econ J 114:1–27 Gersovitz M, Hammer JS (2004) The economical control of infectious diseases. Econ J 114:1–27
18.
go back to reference Glaeser EL, Gorback CS, Redding SJ (2020) How much does COVID-19 increase with mobility? Evidence from New York and four other US cities. NBER, Working Paper 27519 Glaeser EL, Gorback CS, Redding SJ (2020) How much does COVID-19 increase with mobility? Evidence from New York and four other US cities. NBER, Working Paper 27519
19.
go back to reference Glover A, Heathcote J, Krueger D, Rios-Rull J-V (2020) Health versus wealth: on the distributional effects of controlling a pandemic. CEPR Discussion Paper 14606 Glover A, Heathcote J, Krueger D, Rios-Rull J-V (2020) Health versus wealth: on the distributional effects of controlling a pandemic. CEPR Discussion Paper 14606
21.
go back to reference Hupkau C, Petrangolo B (2020) Work, care and gender during the COVID-19 crisis. CEPR Discussion Paper 15358 Hupkau C, Petrangolo B (2020) Work, care and gender during the COVID-19 crisis. CEPR Discussion Paper 15358
22.
go back to reference Jorgensen S, Zaccour G (2019) Optimal pricing and advertising policies for a one-time entertainment event. J Econ Dyn Control 100:395–416 MathSciNetCrossRef Jorgensen S, Zaccour G (2019) Optimal pricing and advertising policies for a one-time entertainment event. J Econ Dyn Control 100:395–416 MathSciNetCrossRef
23.
go back to reference Kermack WO, McKendrick AG (1927) A contribution to the mathematical theory of epidemics. Proc R Soc Lond Ser A 115:700–721 CrossRef Kermack WO, McKendrick AG (1927) A contribution to the mathematical theory of epidemics. Proc R Soc Lond Ser A 115:700–721 CrossRef
24.
go back to reference La Torre D, Liuzzi D, Marsiglio S (2021) Epidemics and macroeconomic outcomes: social distancing intensity and duration. J Math Econ 93:102473 MathSciNetCrossRef La Torre D, Liuzzi D, Marsiglio S (2021) Epidemics and macroeconomic outcomes: social distancing intensity and duration. J Math Econ 93:102473 MathSciNetCrossRef
25.
go back to reference La Torre D, Malik T, Marsiglio S (2020) Optimal control of prevention and treatment in a basic macroeconomic-epidemiological model. Math Soc Sci 108:100–108 MathSciNetCrossRef La Torre D, Malik T, Marsiglio S (2020) Optimal control of prevention and treatment in a basic macroeconomic-epidemiological model. Math Soc Sci 108:100–108 MathSciNetCrossRef
26.
go back to reference Liu S, Yang L, Zhang C, Xiang Y-T, Liu Z, Hu S, Zhang B (2020) Online mental health services in China during the COVID-19 outbreak. Lancet 7:e17–e18 Liu S, Yang L, Zhang C, Xiang Y-T, Liu Z, Hu S, Zhang B (2020) Online mental health services in China during the COVID-19 outbreak. Lancet 7:e17–e18
27.
go back to reference Lopez AD, Mathers CD, Ezzati M, Jamison DT, Murray CJL (2006) Global burden of disease and risk factors. New York, Oxford University Press CrossRef Lopez AD, Mathers CD, Ezzati M, Jamison DT, Murray CJL (2006) Global burden of disease and risk factors. New York, Oxford University Press CrossRef
28.
go back to reference Ma J (2020) Estimating epidemic exponential growth rate and basic reproduction number. Infect Disease Model 5:129–141 CrossRef Ma J (2020) Estimating epidemic exponential growth rate and basic reproduction number. Infect Disease Model 5:129–141 CrossRef
29.
go back to reference Marsiglio S, Masoudi N (2021) Transboundary pollution control and competitiveness concerns in a two-country differential game. Environ Model Assess ( Forthcoming) Marsiglio S, Masoudi N (2021) Transboundary pollution control and competitiveness concerns in a two-country differential game. Environ Model Assess ( Forthcoming)
30.
go back to reference Philipson T (2000) Economic epidemiology and infectious disease. In: Cuyler AJ, Newhouse JP (eds) Handbook of health economics, vol 1B. Amsterdam, North Holland, pp 1761–1799 Philipson T (2000) Economic epidemiology and infectious disease. In: Cuyler AJ, Newhouse JP (eds) Handbook of health economics, vol 1B. Amsterdam, North Holland, pp 1761–1799
31.
33.
go back to reference Remuzzi A, Remuzzi G (2020) COVID-19 and Italy: what next? Lancet 395:1225–1228 Remuzzi A, Remuzzi G (2020) COVID-19 and Italy: what next? Lancet 395:1225–1228
Metadata
Title
Mobility Choices and Strategic Interactions in a Two-Group Macroeconomic–Epidemiological Model
Authors
Davide La Torre
Danilo Liuzzi
Rosario Maggistro
Simone Marsiglio
Publication date
02-12-2021
Publisher
Springer US
Published in
Dynamic Games and Applications / Issue 1/2022
Print ISSN: 2153-0785
Electronic ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-021-00413-z

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