Towards behavioral control in multi-player network games

Congestion in the routers as well as certain types of resource-exhaustion DoS attacks at the servers can be treated by differentiating packet processing according to previous history of its source. Since it is often difficult to correctly classify packets as legitimate or attack traffic, the scheduling algorithm should tolerate imprecise labeling of packets as long as on the average it punishes misbehaving sources. In this paper, we propose a game-theoretic model based on player rating and formulate the problem in terms of optimal control theory. Applying the Pontryagin maximum principle, we derive necessary control functions to encourage good behavior of network players. As an application of results, we suggest two algorithms for differentiating packet treatment in congested servers and routers.