Abstract
The goal of this work is to generalize closed form approach suggested by Altman, Avrachenkov and Garnaev for a water-filling problem in game-theoretical frameworks for the case of a general allocation of users. Also we take into account power cost which can produce essential impact on users behaviour. The equilibrium strategies for the extended model are found in closed form. Uniqueness of the equilibrium is proved. Explicit criteria showing when the users prefer to apply all the power they have in disposition, or they would like to reduce it or even to cancel transmission at all are supplied. Algorithm based on a generalization of bisection method is produced and numerical modelling is performed.
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Garnaev, A., Toritsyn, A. (2010). A Two-Users Transmission Game in OFDM Wireless Networks with Resource Cost. In: Vinel, A., Bellalta, B., Sacchi, C., Lyakhov, A., Telek, M., Oliver, M. (eds) Multiple Access Communications. MACOM 2010. Lecture Notes in Computer Science, vol 6235. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15428-7_22
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DOI: https://doi.org/10.1007/978-3-642-15428-7_22
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