We consider the interaction of several transmit-receive pairs coexisting in the same area and communicating using the same portion of the spectrum. Using a game theoretic framework, each pair is regarded as a player whose payoff function is the individual link rate and power is allocated using the iterative water-filling algorithm. We find properties of the resulting Nash equilibria and derive conditions for when various operating points are achievable. The analysis presented herein extends previous work by characterizing the set of stable solutions for a multi-user system. Also, we show how the game can be modified to obtain better operating points in terms of sum rate compared to the iterative water-filling algorithm. The increase in performance corresponding to one such modification is evaluated and compared to the iterative water-filling algorithm by numerical simulations.