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Border Games in Cellular Networks. Márk Félegyházi*, Mario Čagalj†, Diego Dufour*, Jean-Pierre Hubaux* * Ecole Polytechnique Federale de Lausanne (EPFL), Lausanne, Switzerland † University of Split, Croatia. Infocom 2007. Problem.

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## Border Games in Cellular Networks

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**Border Games in Cellular Networks**Márk Félegyházi*, Mario Čagalj†, Diego Dufour*, Jean-Pierre Hubaux* * Ecole Polytechnique Federale de Lausanne (EPFL), Lausanne, Switzerland † University of Split, Croatia Infocom 2007**Problem**• spectrum licenses do not regulate access over national borders • adjust pilot power to attract more users Is there an incentive for operators to apply competitive pilot power control? Márk Félegyházi (EPFL)**Related Work**• Power control in cellular networks • up/downlink power control in CDMA [Hanly and Tse 1999, Baccelli et al. 2003, Catrein et al. 2004] • pilot power control in CDMA [Kim et al. 1999, Värbrand and Yuan 2003] • using game theory [Alpcan et al. 2002, Goodman and Mandayam 2001, Ji and Huang 1998, Meshkati et al. 2005, Lee et al. 2002] • Coexistence of service providers • wired [Shakkottai and Srikant 2005, He and Walrand 2006] • wireless [Shakkottai et al. 2006, Zemlianov and de Veciana 2005] Márk Félegyházi (EPFL)**System model (1/2)**Network: • cellular networks using CDMA • channels defined by orthogonal codes • two operators: A and B • one base station each • pilot signal power control Users: • roaming users • users uniformly distributed • select the best quality BS • selection based signal-to-interference-plus-noise ratio (SINR) Márk Félegyházi (EPFL)**System model (2/2)**TAw pilot signal SINR: TBw TAv PB PA v B A Pi – pilot power of i – processing gain for the pilot signal – channel gain between BS i and user v traffic signal SINR: – noise energy per symbol – available bandwidth – own-cell interference affecting the pilot signal – own-cell interference factor – traffic power between BS i and user v – set of users attached to BS i – other-to-own-cell interference factor Márk Félegyházi (EPFL)**Game-theoretic model**Power Control Game, GPC players → networks operators (BSs), A and B strategy → pilot signal power, 0W < Pi < 10W, i = {A, B} standard power, PS = 2W payoff → profit, where is the expected income serving user v normalized payoff difference: Márk Félegyházi (EPFL)**Simulation**Márk Félegyházi (EPFL)**Is there a game?**• only A is strategic (B uses PB = PS) • 10 data users • path loss exponent, α = 2 Δi Márk Félegyházi (EPFL)**Strategic advantage**• normalized payoff difference: Márk Félegyházi (EPFL)**Payoff of A**• Both operators are strategic • path loss exponent, α = 4 Márk Félegyházi (EPFL)**Nash equilibrium**• unique NE • NE power P* is higher than PS Márk Félegyházi (EPFL)**Efficiency**zero-sum game • 10 data users Márk Félegyházi (EPFL)**Convergence to NE (1/2)**• convergence based on better-response dynamics • convergence step: 2 W PA = 6.5 W Márk Félegyházi (EPFL)**Convergence to NE (2/2)**• convergence step: 0.1 W Márk Félegyházi (EPFL)**Summary**• two operators on a national border • single-cell model • pilot power control • roaming users • power control game, GPC • operators have an incentive to be strategic • NE are efficient, but they use high power • simple convergence algorithm • extended game with power cost • Prisoner’s Dilemma http://people.epfl.ch/mark.felegyhazi Márk Félegyházi (EPFL)**Future work**• multiple base stations • repeated game with power cost • strategic modeling of users • cooperative game of operators Márk Félegyházi (EPFL)

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