  We propose and analyze a broad family of games played by resource-constrained
players, which are characterized by the following central features: 1) each
user has a multi-dimensional action space, subject to a single sum resource
constraint; 2) each user's utility in a particular dimension depends on an
additive coupling between the user's action in the same dimension and the
actions of the other users; and 3) each user's total utility is the sum of the
utilities obtained in each dimension. Familiar examples of such multi-user
environments in communication systems include power control over
frequency-selective Gaussian interference channels and flow control in Jackson
networks. In settings where users cannot exchange messages in real-time, we
study how users can adjust their actions based on their local observations. We
derive sufficient conditions under which a unique Nash equilibrium exists and
the best-response algorithm converges globally and linearly to the Nash
equilibrium. In settings where users can exchange messages in real-time, we
focus on user choices that optimize the overall utility. We provide the
convergence conditions of two distributed action update mechanisms, gradient
play and Jacobi update.
