Define each router or link as a player, assign a cost function that captures delay or bandwidth usage, and make sure the game is a potential game so a global objective exists. Then use best‑response dynamics or a gradient‑based descent on the potential to converge to a Nash equilibrium. In practice, that’s just solving a convex optimisation with Lagrange multipliers – the algorithm runs in parallel, each node updates its allocation using only local information. The key is to keep the payoff simple so the distributed updates are fast and the equilibrium is efficient.

A small damping factor will bound the multipliers and prevent runaway back‑offs. Just add a modest step‑size limit to the update rule; the system will still converge while staying in the feasible region.