Finite State Graphon Games with Applications to Epidemics

Aurell, Alexander; Carmona, René; Dayanıklı, Gökçe; Laurière, Mathieu

doi:10.1007/s13235-021-00410-2

Cited by 16 publications

(4 citation statements)

References 47 publications

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“…In addition, while sociality strategies are modeled here through the rate of well-mixed interactions that individuals have, it is also reasonable to consider how the benefits and costs of social interaction can impact how individuals choose neighbors in a network-structured population. Tools such as pair approximations [52,53] or graphons [54][55][56] can be used to model the spread of couple contagions on graph-structured populations, and evolutionary questions could also explore the evolution of modular network structure in the presence of infectious disease [57][58][59].…”

Section: Discussionmentioning

confidence: 99%

Social dilemmas of sociality due to beneficial and costly contagion

et al. 2022

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Levels of sociality in nature vary widely. Some species are solitary; others live in family groups; some form complex multi-family societies. Increased levels of social interaction can allow for the spread of useful innovations and beneficial information, but can also facilitate the spread of harmful contagions, such as infectious diseases. It is natural to assume that these contagion processes shape the evolution of complex social systems, but an explicit account of the dynamics of sociality under selection pressure imposed by contagion remains elusive. We consider a model for the evolution of sociality strategies in the presence of both a beneficial and costly contagion. We study the dynamics of this model at three timescales: using a susceptible-infectious-susceptible (SIS) model to describe contagion spread for given sociality strategies, a replicator equation to study the changing fractions of two different levels of sociality, and an adaptive dynamics approach to study the long-time evolution of the population level of sociality. For a wide range of assumptions about the benefits and costs of infection, we identify a social dilemma: the evolutionarily-stable sociality strategy (ESS) is distinct from the collective optimum—the level of sociality that would be best for all individuals. In particular, the ESS level of social interaction is greater (respectively less) than the social optimum when the good contagion spreads more (respectively less) readily than the bad contagion. Our results shed light on how contagion shapes the evolution of social interaction, but reveals that evolution may not necessarily lead populations to social structures that are good for any or all.

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Section: Discussionmentioning

confidence: 99%

Social dilemmas of sociality due to beneficial and costly contagion

et al. 2022

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“…A standard graphon W is formally defined as a symmetric, measurable function W : [0, 1] 2 → [0, 1] which yields the limit for sequences of undirected and unweighted graphs. Some papers such as [7] and [14] interpret the probability W (x, y) of an edge between nodes x and y as the "weight" of this edge. However, each realization of this random graph yields an unweighted graph.…”

Section: Colored Digraphonsmentioning

confidence: 99%

Mean Field Games on Weighted and Directed Graphs via Colored Digraphons

Fabian

Cui

Koeppl

2023

IEEE Control Syst. Lett.

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Multi-agent systems are in general hard to model and control due to their complex nature involving many individuals. Numerous approaches focus on empirical and algorithmic aspects of approximating outcomes and behavior in multi-agent systems and lack a rigorous theoretical foundation. Graphon mean field games (GMFGs) on the other hand provide a mathematically well-founded and numerically scalable framework for a large number of connected agents. In standard GMFGs, the connections between agents are undirected, unweighted and invariant over time. Our paper introduces colored digraphon mean field games (CDMFGs) which allow for weighted and directed links between agents that are also adaptive over time. Thus, CDMFGs are able to model more complex connections than standard GMFGs. Besides a rigorous theoretical analysis including both existence and convergence guarantees, we employ the online mirror descent algorithm to learn equilibria. To conclude, we illustrate our findings with an epidemics model and a model of the systemic risk in financial markets.

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“…Although we focus here on the continuous-state space setting, the same strategy can be applied to finite-state MFGs; see, e.g., [16,15].…”

Section: Deep Learning For Mckean-vlasov Fbsde Systemsmentioning

confidence: 99%

Recent Developments in Machine Learning Methods for Stochastic Control and Games

Hu¹,

Laurière²

2023

Preprint

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In this paper, we give an overview of recently developed machine learning methods for stochastic control problems and games. The main focus is on deep learning methods that have unlocked the possibility to solve such problems even when the structure is complex or the dimension is high, which is not feasible with traditional numerical methods. The new approaches build on recent breakthrough machine learning methods for high-dimensional partial differential equations or backward stochastic differential equations, or on model-free reinforcement learning for Markov decision processes. This review summarizes state-of-the-art works at the crossroad of machine learning and stochastic control and games. It also discusses connections with real applications and identifies unsolved challenges.

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Finite State Graphon Games with Applications to Epidemics

Cited by 16 publications

References 47 publications

Social dilemmas of sociality due to beneficial and costly contagion

Social dilemmas of sociality due to beneficial and costly contagion

Mean Field Games on Weighted and Directed Graphs via Colored Digraphons

Recent Developments in Machine Learning Methods for Stochastic Control and Games

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