Mark Felegyhazi, Jean-Pierre Hubaux

1. Mobicom ’05 Mark Felegyhazi, Jean-Pierre Hubaux 2005.08.31 Wireless Operators in a Shared Spectrum Motivation Simplified network model • better utilization of the spectrum • shift towards unlicensed frequency bands (Wi-Fi) • interference is an important issue • mobiles attach to the BS with the strongest signal where Assumptions • two operators (H and L) • base stations (BS) on the grid • each BS of a given operator has the same radio range rL or rH (0 < rL, rH < RMAX) • service coverage everywhere: RMIN is the smallest uniform range that ensures full coverage • simplified radio model (additive power diagram) • perfect roaming of users Power control game • two players (H and L) • strategy: set the radio ranges rL and rH coverage area Oi:set of points where users attach to BSi interference area Yi: set of points in the radio range, but not in the coverage area Results – single stage game Pareto-optimal strategies: V(i) is the Voronoi region of BSi utility Ui: γ(i) is the sensitivity parameter Result – repeated game • Punisher strategy: Plays RMIN in the first time step. For any further steps it plays: • RMIN, if the other player played RMIN in the previous time step • RMAX for the next ki time steps, if the other player played anything else. General topologies: Result 1: Finding Nash equilibria in the power control game for general topologies of base stations is NP-complete. Result 2: A cooperative Nash equilibrium based on RMIN can be enforced by using the Punisher strategy if and • where: • Gi is the utility of player i if its cheats, while player j plays RMIN • Di is the utility of the players by playing RMAX • Ci is the utility of the players by playing RMIN {mark.felegyhazi,jean-pierre.hubaux}@epfl.ch MICS – Mobile Communication and Information Systems http://www.mics.org LCA – Laboratory for Computer Communications and Applications http://lcawww.epfl.ch