Nash equilibria as a fundamental issue concerning network-switches design

We view the ´packet-switching problem´ (from N inputs towards N outputs) from the perspective of game theory and we prove that, if the rates of flows are weighed then ´weighed max-min fair service rates´ are the unique Nash equilibrium point of a natural strategic game in which throughput is granted on a ´least-demanding first-served´ principle. We prove that a crossbar switching device with suitably randomized schedulers converges to this equilibrium point without pre-computing it.