Modeling Presymptomatic Spread in Epidemics via Mean-Field Games

Coordinating communication and control is a key component in the stability and performance of networked multi-agent systems. While single user networked control systems have gained a lot of attention within this domain, in this work, we address the more challenging problem of large population multi-team dynamic games. In particular, each team constitutes two decision makers (namely, the sensor and the controller) who coordinate over a shared network to control a dynamically evolving state of interest under costs on both actuation and sensing/communication. Due to the shared nature of the wireless channel, the overall cost of each team depends on other teams' policies, thereby leading to a noncooperative game setup. Due to the presence of a large number of teams, we compute approximate decentralized Nash equilibrium policies for each team using the paradigm of (extended) mean-field games, which is governed by (1) the mean traffic flowing over the channel, and (2) the value of information at the sensor, which highlights the semantic nature of the ensuing communication. In the process, we compute optimal controller policies and approximately optimal sensor policies for each representative team of the mean-field system to alleviate the problem of general non-contractivity of the mean-field fixed point operator associated with the finite cardinality of the sensor action space.Consequently, we also prove the ǫ-Nash property of the mean-field equilibrium solution which essentially characterizes how well the solution derived using mean-field analysis performs on the finite-team system.Finally, we provide extensive numerical simulations, which corroborate the theoretical findings and lead to additional insights on the properties of the results presented.

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“…where the last inequality follows by using Lemma 2. Then, by substituting ( 40) in (39), we arrive at…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Large Population Games with Timely Scheduling over Constrained Networks

Aggarwal

Zaman

Bastopcu

et al. 2023

2023 American Control Conference (ACC)

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

2023

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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.

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