Optimal Type Count for HMFG Given Fleet Size N

Determine the optimal number of agent types K to use for a heterogeneous vehicle fleet of size N in heterogeneous mean field games for LEO satellite-assisted V2X networks, by characterizing K as a function of N that minimizes the ε-Nash approximation error (including its asymptotic scaling).

Background

The paper studies coordination of large, heterogeneous vehicle fleets using heterogeneous mean field games (HMFG). A key modeling choice is how many agent types K to use when partitioning a fleet of size N. Using more types better captures heterogeneity but reduces per-type sample sizes, weakening mean-field approximations. Prior HMFG and MARL works typically fixed K heuristically without a principled selection rule.

The authors make the type-granularity question central, deriving an error decomposition and a scaling law. They motivate this by explicitly stating that the fundamental design question of how many agent types to use for a given fleet size N had remained open, particularly in the LEO-assisted V2X setting with stringent latency and dynamic backhaul. The open problem asks for a principled determination of K as a function of N that optimally balances discretization and sampling errors.