Multi-Dimensional Continuous Type Population Potential Games

We consider an extension of continuous population potential games where the population mass is represented by a distribution over a multi-dimensional continuous type space. Each dimension of the type space corresponds to a subset of strategies in the potential game. The difference between two elements in each population member's type vector encodes their relative preference for strategies in each subset. We define an extension of a Wardrop equilibrium for this type based model and show how to compute the equilibrium by means of optimizing a specific potential function.