Variable demand and multi-commodity flow in Markovian network equilibrium

Markovian network equilibrium generalizes the classical Wardrop in games. At a equilibrium, each player of game solves Markov decision process instead shortest path problem. We propose two novel extensions by considering (1) variable demand, which offers players quitting option, and (2) multi-commodity flow, allows to have heterogeneous ending time. further develop dynamic-programming-based iterative algorithms for proposed problems, together with their arithmetic complexity analysis. Finally, we illustrate our model via ride-sharing example, compare computational efficiency against state-of-the-art optimization software MOSEK over extensive numerical experiments.