Theory of Linear Games with Constraints and Its Application to Power Control of Optical Networks

In this paper, we introduce a class of linear non- cooperative games with linearly coupled constraints. It bears striking connections with classical linear systems theory and finds itself pervasively used in network engineering applications. In the second part of the paper, we will illustrate this type of games by an application from OSNR-based power control in optical networks, where we can view the slack variables as fictitious players. This powerful interpretation allows us to bridge over the theory and the issue of implementation in engineering.