What question did this study set out to answer?

Establish the existence and analytical properties of solutions for finite horizon deterministic mean field games defined on network domains with edge-dependent costs.

October 1, 2024SIAM Journal on Mathematical Analysis

Deterministic Mean Field Games on Networks: A Lagrangian Approach

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Authors

YAYves AchdouSupélec PMPaola MannucciUniversità di Camerino CMClaudio MarchiUniversity of Padua

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Implication

Theoretical analysis establishes the existence of relaxed equilibria in network-constrained agent systems, providing rigorous foundations for mean field control problems.

Key Points

Establish the existence and analytical properties of solutions for finite horizon deterministic mean field games defined on network domains with edge-dependent costs.
Formulated a Lagrangian framework defining relaxed equilibria as probability distributions over admissible paths on a network.
Evaluated optimal trajectory sets and established closed graph properties for trajectory mapping from network coordinates.
Characterized mild solutions by coupling optimal control value functions with time-dependent spatial probability measures.
Proved the existence of relaxed equilibria when running and terminal costs are continuous along edges but discontinuous across network vertices.
Demonstrated that the optimal control value function corresponds to a viscosity solution of a Hamilton–Jacobi problem on the network.
Established regularity properties for the value function alongside a weak continuity equation governing probability measure evolution.

Cite This Study

Achdou et al. (2024) studied this question.

synapsesocial.com/papers/6aafa2a2cf0423585676fb49 https://doi.org/10.1137/23m1615073

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Implication

Theoretical analysis establishes the existence of relaxed equilibria in network-constrained agent systems, providing rigorous foundations for mean field control problems.

Deterministic Mean Field Games on Networks: A Lagrangian Approach

Discussion

Member takes

Implication

Key Points

Cite This Study

Deterministic Mean Field Games on Networks: A Lagrangian Approach

Discussion

Member takes

Implication

Key Points

Cite This Study

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