Optimal incentives to mitigate epidemics: a Stackelberg mean field game approach

Principal agent games are a growing area of research which focuses on the optimal behaviour of a principal and an agent, with the former contracting work from the latter, in return for providing a monetary award. While this field canonically considers a single agent, the situation where multiple agents, or even an infinite amount of agents are contracted by a principal are growing in prominence and pose interesting and realistic problems. Here, agents form a Nash equilibrium among themselves, and a Stackelberg equilibrium between themselves as a collective and the principal. We apply this framework to the problem of implementing emissions markets. We do so while incorporating market clearing as well as agent heterogeneity, and distinguish ourselves from extant literature by incorporating the probabilistic approach to MFGs as opposed to the analytic approach, with the former lending itself more naturally for our problem. For a given market design, we find the Nash equilibrium among agents using techniques from mean field games. We then provide preliminary results for the optimal market design from the perspective of the regulator, who aims to maximize revenue and overall environmental benefit.

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“…Other possible extensions include using deep learning methods to numerically solve for the PA game (as in [9] or [5]).…”

Section: Discussionmentioning

confidence: 99%

Optimal Behaviour in Solar Renewable Energy Certificate (SREC) Markets

Shrivats

Jaimungal

2019

SSRN Journal

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“…In such models, the members in the populations are taking actions based on policies issued by the regulator, while the regulator anticipates the population's reaction and optimizes the policy. The case of a cooperative population has been studied in [37], while in [3], a population of selfish agents with contact factor control has been studied.…”

Section: Mean Field Games and Related Models For Epidemicsmentioning

confidence: 99%

“…The set of susceptible agents is not necessarily the whole non-infected population, depending on the disease immunity can be gained after exposure. The evidence suggests that the COVID-19 virus mainly spreads through close contact 3 . Fortunately, the disease transmission probability can be decreased by the efforts of the individual.…”

Section: Introductionmentioning

confidence: 99%

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Finite State Graphon Games with Applications to Epidemics

Aurell¹,

Carmona²,

Dayanıklı³

et al. 2021

Preprint

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We consider a game for a continuum of non-identical players evolving on a finite state space. Their heterogeneous interactions are represented by a graphon, which can be viewed as the limit of a dense random graph. The player's transition rates between the states depend on their own control and the interaction strengths with the other players. We develop a rigorous mathematical framework for this game and analyze Nash equilibria. We provide a sufficient condition for a Nash equilibrium and prove existence of solutions to a continuum of fully coupled forward-backward ordinary differential equations characterizing equilibria. Moreover, we propose a numerical approach based on machine learning tools and show experimental results on different applications to compartmental models in epidemiology.

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“…Mean-field game (control), introduced by [17,23], describes the deterministic (stochastic) differential games as the number of players tends to infinity, where a given player interacts through the distribution of all players in the state-space. It is a thriving research direction with applications in economics, crowd motion, industrial engineering, and more, including epidemics [12,3,22]. Numerical methods are also invented to obtaining quantitative information of such mean-field game(control) models, especially when the state-space is in high dimensions [1,2,5,29].…”

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confidence: 99%

Mean field control problems for vaccine distribution

Lee¹,

Liu²,

Li³

et al. 2021

Preprint

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With the invention of the COVID-19 vaccine, shipping and distributing are crucial in controlling the pandemic. In this paper, we build a mean-field variational problem in a spatial domain, which controls the propagation of pandemic by the optimal transportation strategy of vaccine distribution. Here we integrate the vaccine distribution into the mean-field SIR model designed in [25]. Numerical examples demonstrate that the proposed model provides practical strategies in vaccine distribution on a spatial domain.

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Optimal incentives to mitigate epidemics: a Stackelberg mean field game approach

Cited by 6 publications

References 0 publications

Optimal Behaviour in Solar Renewable Energy Certificate (SREC) Markets

Optimal Behaviour in Solar Renewable Energy Certificate (SREC) Markets

Finite State Graphon Games with Applications to Epidemics

Mean field control problems for vaccine distribution

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