An existence and uniqueness result for mean field games with congestion effect on graphs

Details An existence and uniqueness result for mean field games with congestion effect on graphs An existence and uniqueness result for mean field games with congestion effect on graphs

2011-10-15

arxiv.org/abs/1110.3442v2

Mathematics

Optimization and Control

Scientific paper

This paper presents a general existence and uniqueness result for the mean field games equations on a graph ($\mathcal{G}$-MFG). In particular, our setting allows to take into account congestion effects as those initially evoked in a continuous framework or even non-local forms of congestion. These general congestion effects are particularly relevant in graphs in which the cost to move from on node to another may for instance depend on the proportion of players in both the source node and the target node. Existence is proved using a priori estimates. Uniqueness is obtained through the usual algebraic manipulations proposed in other articles and we propose a new criterion to ensure uniqueness that allows for hamiltonian functions with a more complex structure.

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