 Multiplicative resource-price dynamics

For route prices $p=A^T\mu$, logarithmic users demand $x_r=w_r/p_r$, while resource prices adjust asThis model raises prices under excess demand and lowers them under spare capacity. Positive capacities and nonempty routes are standard well-definedness assumptions. Positive initial prices approach the dual optimum; zero prices are invariant and can create boundary equilibria of multiplicative price dynamics that overload a resource.