A communication network routing problem: Modeling and optimization using non-cooperative game theory

We consider a communication network routing problem wherein a number of users need to efficiently transmit their throughput demand in the form of data packets (incurring less cost and less delay) through one or more links. Using the game theoretic perspective, we propose a dynamic model which ensures unhindered transmission of data even in the case where the capacity of the link is exceeded. The model incorporates a mechanism in which users are appropriately punished (with additional cost) when the total data to be transmitted exceeds the capacity of the link. The model has multiple Nash equilibrium points. To arrive at rational strategies, we introduce the concept of focal points and get what is termed focal Nash equilibrium (FNE) points for the model. We further introduce the concept of preferred focal Nash equilibrium (PFNE) points and find their relation with the Pareto optimal solution for the model.