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Foguen-Tchuendom, Rinel; Gao, Shuang; Caines, Peter E.; Huang, Minyi

Infinite horizon LQG graphon mean field games: explicit Nash values and local minima. (English) Zbl 07878491

Syst. Control Lett. 187, Article ID 105780, 9 p. (2024).
Summary: In this study, we generalize the analysis of infinite horizon linear quadratic Gaussian (LQG) mean field games within the framework of graphon mean field games (GMFGs) introduced in P. E. Caines and M. Huang [SIAM J. Control Optim. 59, No. 6, 4373–4399 (2021; Zbl 1479.91035)] over finite horizons. GMFGs are non-uniform generalizations of mean field games where the non-uniformity of agents is characterized by the nodes on which they are located in a network. Under mild assumptions on the structure of the network and parameters of the game, we obtain for almost every node, an explicit analytical expression for the Nash values (i.e. the cost at equilibrium). With additional assumptions, we provide sufficient conditions for nodes to have locally minimal Nash values. We illustrate the results for the uniform attachment network.

MSC:

91A16 Mean field games (aspects of game theory)
49N80 Mean field games and control

Keywords:

graphons; mean field games; Nash values; infinite horizon

Citations:

Zbl 1479.91035
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Full Text: DOI

References:

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