 
Summary: A GameTheoretic Framework for Congestion Control in General
Topology Networks 1
Tansu Alpcan2
, Tamer Bas¸ar2
(alpcan, tbasar)@control.csl.uiuc.edu
Abstract
We study control of congestion in general topology com
munication networks within a fairly general mathematical
framework that utilizes noncooperative game theory. We
consider a broad class of cost functions, composed of pric
ing and utility functions, which capture various pricing
schemes along with varying behavior and preferences for
individual users. We prove the existence and uniqueness of
a Nash equilibrium under mild convexity assumptions on
the cost function, and show that the Nash equilibrium is
the optimal solution of a particular "system problem". Fur
thermore, we prove the global stability of a simple gradi
ent algorithm and its convergence to the equilibrium point.
Thus, we obtain a distributed, marketbased, endtoend
framework that addresses congestion control, pricing and
