  The use of game theoretic models has been quite successful in describing
various cooperative and non-cooperative optimization problems in networks and
other domains of computer systems. In this paper, we study an application of
game theoretic models in the domain of distributed system, where nodes play a
game to balance the total processing loads among themselves. We have used
congestion gaming model, a model of game theory where many agents compete for
allocating resources, and studied the existence of Nash Equilibrium for such
types of games. As the classical congestion game is known to be PLS-Complete,
we use an approximation, called the \epsilon-Congestion game, which converges
to \epsilon-Nash equilibrium within finite number of steps under selected
conditions. Our focus is to define the load balancing problem using the model
of \epsilon-congestion games, and finally provide a greedy algorithm for load
balancing in distributed systems. We have simulated our proposed system to show
the effect of \epsilon-congestion game, and the distribution of load at
equilibrium state.
