We consider a game theoretic model for two users communicating over an interference channel, in which each user can autonomously select its encoding and decoding strategy with the objective of maximizing its own rate. We give an information theoretic formulation for this game, which enables us to define a Nash equilibrium region that is a natural extension of the information theoretic capacity region of this channel. In previous work, we completely characterized this Nash equilibrium region for a deterministic interference channel model. Here, we show that certain properties of this analysis extend to a Gaussian channel model. In particular, we show that for a symmetric channel, the symmetric sum-rate point is always achieved as an approximate equilibrium.