Additively Coupled Sum Constrained Games

  • Yi Su
  • Mihaela van der Schaar
Conference paper
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 75)


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.


Nash Equilibrium Convergence Condition Pure Nash Equilibrium Strategic Substitute Unique Nash Equilibrium 
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Copyright information

© ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering 2012

Authors and Affiliations

  • Yi Su
    • 1
  • Mihaela van der Schaar
    • 1
  1. 1.Department of Electrical EngineeringUCLAUSA

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