Abstract
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.
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© 2012 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering
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Su, Y., van der Schaar, M. (2012). Additively Coupled Sum Constrained Games. In: Jain, R., Kannan, R. (eds) Game Theory for Networks. GameNets 2011. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 75. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30373-9_6
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DOI: https://doi.org/10.1007/978-3-642-30373-9_6
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