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

2. Infocom 2007Márk Félegyházi (EPFL) 2 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?

3. Infocom 2007Márk Félegyházi (EPFL) 3 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]

4. Infocom 2007Márk Félegyházi (EPFL) 4 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)

5. Infocom 2007Márk Félegyházi (EPFL) 5 System model (2/2) A B v PAPA PBPB T Av T Bw T Aw pilot signal SINR: traffic signal SINR: P i – pilot power of i – processing gain for the pilot signal – noise energy per symbol – channel gain between BS i and user v – available bandwidth – own-cell interference affecting the pilot signal – own-cell interference factor – traffic power between BS i and user v – other-to-own-cell interference factor – set of users attached to BS i

6. Infocom 2007Márk Félegyházi (EPFL) 6 Game-theoretic model ► Power Control Game, G PC – players → networks operators (BSs), A and B – strategy → pilot signal power, 0W < P i < 10W, i = {A, B} – standard power, P S = 2W – payoff → profit, where is the expected income serving user v – normalized payoff difference:

7. Infocom 2007Márk Félegyházi (EPFL) 7 Simulation

8. Infocom 2007Márk Félegyházi (EPFL) 8 Is there a game? ► only A is strategic (B uses P B = P S ) ► 10 data users ► path loss exponent, α = 2 ΔiΔi

9. Infocom 2007Márk Félegyházi (EPFL) 9 Strategic advantage ► normalized payoff difference:

10. Infocom 2007Márk Félegyházi (EPFL) 10 Payoff of A ► Both operators are strategic ► path loss exponent, α = 4

11. Infocom 2007Márk Félegyházi (EPFL) 11 Nash equilibrium ► unique NE ► NE power P * is higher than P S

12. Infocom 2007Márk Félegyházi (EPFL) 12 Efficiency ► 10 data users zero-sum game

13. Infocom 2007Márk Félegyházi (EPFL) 13 ► convergence based on better-response dynamics ► convergence step: 2 W Convergence to NE (1/2) P A = 6.5 W

14. Infocom 2007Márk Félegyházi (EPFL) 14 Convergence to NE (2/2) ► convergence step: 0.1 W

15. Infocom 2007Márk Félegyházi (EPFL) 15 Summary ► two operators on a national border ► single-cell model ► pilot power control ► roaming users ► power control game, G PC – 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

16. Infocom 2007Márk Félegyházi (EPFL) 16 Future work ► multiple base stations ► repeated game with power cost ► strategic modeling of users ► cooperative game of operators