Game Theory for Networks. 2nd International ICST Conference, GAMENETS 2011, Shanghai, China, April 16-18, 2011, Revised Selected Papers

Research Article

Additively Coupled Sum Constrained Games

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  • @INPROCEEDINGS{10.1007/978-3-642-30373-9_6,
        author={Yi Su and Mihaela Schaar},
        title={Additively Coupled Sum Constrained Games},
        proceedings={Game Theory for Networks. 2nd International ICST Conference, GAMENETS 2011, Shanghai, China, April 16-18, 2011, Revised Selected Papers},
        proceedings_a={GAMENETS},
        year={2012},
        month={10},
        keywords={},
        doi={10.1007/978-3-642-30373-9_6}
    }
    
  • Yi Su
    Mihaela Schaar
    Year: 2012
    Additively Coupled Sum Constrained Games
    GAMENETS
    Springer
    DOI: 10.1007/978-3-642-30373-9_6
Yi Su1, Mihaela Schaar1
  • 1: UCLA

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.