Flow Allocation Games: Pricing, Equilibria and Fast Convergence∗

We consider the distributed allocation problem of assigning rates to a set of network flows from a new game-theoretic standpoint. Our setting is a fixed capacitated network in which a set of long-lived flows is given and the routes these flows use are pre-ordained and fixed through the duration of the algorithm. Each flow is then given a set of tokens which it may place on the links that it intends to use. The flows then play an iterative game that runs in a sequence of distributed rounds. In each round, the flows place their tokens, then the links provide a tentative rate allocation in proportion to the number of tokens that it receives. Flows are then constrained to a rate that is the minima of the rates allocated to them by their incident links. The flows may then repeatedly reallocate their set of tokens across links to improve their allocation. We characterize the Nash equilibria of this game, relate them to the equilibria in the TCP Vegas analysis, and describe strategies which converge to the equilibria.