Variable Demand and Multi-commodity Flow in Markovian Network Equilibrium.

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