Graphon Games: A Statistical Framework for Network Games and Interventions

Parise, Francesca; Ozdaglar, Asuman

doi:10.2139/ssrn.3437293

Cited by 9 publications

(6 citation statements)

References 78 publications

(133 reference statements)

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“…We should point out that the use of graphons to analyze heterogeneous interaction in game theory emerged recently (see e.g. [11,12,26]). Among these, [26] analyzes static graphon games and the convergence of the n-player game with interaction network sampled from a given graphon.…”

Section: Introductionmentioning

confidence: 99%

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Graphon mean field systems

Bayraktar¹,

Chakraborty²,

Wu³

2020

Preprint

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We consider heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. A law of large numbers result is established as the system size increases and the underlying graphons converge. The limit is given by a graphon mean field system consisting of independent but heterogeneous nonlinear diffusions whose probability distributions are fully coupled. Well-posedness, continuity and stability of such systems are provided. We also consider a not-so-dense analogue of the finite particle system, obtained by percolation with vanishing rates and suitable scaling of interactions. A law of large numbers result is proved for the convergence of such systems to the corresponding graphon mean field system.

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Section: Introductionmentioning

confidence: 99%

“…[11,12,26]). Among these, [26] analyzes static graphon games and the convergence of the n-player game with interaction network sampled from a given graphon. Static graphon games are considered in [12] and the convergence of the nplayer game with general interaction network that converges to a given graphon is obtained.…”

Section: Introductionmentioning

confidence: 99%

Graphon mean field systems

Bayraktar¹,

Chakraborty²,

Wu³

2020

Preprint

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“…Further, finite state mean field control, risk-sensitive control, and zero-sum games are treated in [20,18,19] which cover cases of unbounded jump intensities. Graphon games [24,9,8,50,10,31,4] have recently been receiving an increasing research interest. The motivation is the study of strategic decision making in the face of a large non-complete but dense networks of distinguishable agents.…”

Section: Graphon Games and Finite State Space Mean Field Gamesmentioning

confidence: 99%

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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“…Moreover, mean field games on Erdős-Rényi random graphs are analyzed in [12], and graphon mean field games on static graphs with possibly uncountable players have recently been studied (see e.g. [9,10,24]).…”

Section: Introductionmentioning

confidence: 99%

Mean field interaction on random graphs with dynamically changing multi-color edges

Bayraktar

2019

Preprint

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We consider weakly interacting jump processes on time-varying random graphs with dynamically changing multi-color edges. The system consists of a large number of nodes in which the node dynamics depends on the joint empirical distribution of all the other nodes and the edges connected to it, while the edge dynamics depends only on the corresponding nodes it connects. Asymptotic results, including law of large numbers, propagation of chaos, and central limit theorems, are established. In contrast to the classic McKean-Vlasov limit, the limiting system exhibits a path-dependent feature in that the evolution of a given particle depends on its own conditional distribution given its past trajectory. We also analyze the asymptotic behavior of the system when the edge dynamics is accelerated. A law of large number and a propagation of chaos result is established, and the limiting system is given as independent McKean-Vlasov processes. Error between the two limiting systems, with and without acceleration in edge dynamics, is also analyzed.

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Graphon Games: A Statistical Framework for Network Games and Interventions

Cited by 9 publications

References 78 publications

Graphon mean field systems

Graphon mean field systems

Finite State Graphon Games with Applications to Epidemics

Mean field interaction on random graphs with dynamically changing multi-color edges

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