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We propose and analyze a broad family of games played by resource-constrainedplayers, which are characterized by the following central features: 1) eachuser has a multi-dimensional action space, subject to a single sum resourceconstraint; 2) each user's utility in a particular dimension depends on anadditive coupling between the user's action in the same dimension and theactions of the other users; and 3) each user's total utility is the sum of theutilities obtained in each dimension. Familiar examples of such multi-userenvironments in communication systems include power control overfrequency-selective Gaussian interference channels and flow control in Jacksonnetworks. In settings where users cannot exchange messages in real-time, westudy how users can adjust their actions based on their local observations. Wederive sufficient conditions under which a unique Nash equilibrium exists andthe best-response algorithm converges globally and linearly to the Nashequilibrium. In settings where users can exchange messages in real-time, wefocus on user choices that optimize the overall utility. We provide theconvergence conditions of two distributed action update mechanisms, gradientplay and Jacobi update.

Structural Solutions For Additively Coupled Sum Constrained Games