Optimal Routing Control: Game Theoretic Approach

Communication networks shared by sellsh users are considered and modeled as nonco-operative repeated games. Each user is interested only in optimizing its own performance by controlling the routing of its load. We investigate the existence of a Nash equilibrium point (NEP) that achieves the system-wide optimum cost. The existence of a subgame-perfect NEP that not only achieves the system-wide optimum cost but also yields a cost for each user no greater than its stage game NEP cost is shown for two-node multiple link networks. It is shown that more general networks where all users have the same source-destination pair have a subgame-perfect NEP that achieves the minimum total system cost, under a mild technical condition. It is shown that general networks with users having multiple source-destination pairs do not necessarily have such an NEP.