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Publication# Border Games in Cellular Networks

Abstract

In each country today, cellular networks operate on carefully separated frequency bands. This separation is imposed by the regulators of the given country to avoid interference between these networks. But, the separation is only valid within the borders of a country, hence the operators are left on their own to resolve cross-border interference of their cellular networks. In this paper, we focus on the scenario of two operators, each located on one side of the border. We assume that they want to fine-tune the emitting power of the pilot signals (i.e., beacon signals) of their base stations. This operation is crucial, because the pilot signal power determines the number of users they can attract and hence the revenue they can obtain. In the case of no power costs, we show that there exists a motivation for the operators to be strategic, meaning to fine-tune the pilot signal powers of their base stations. In addition, we study Nash equilibrium conditions in an empirical model and investigate the efficiency of the Nash equilibria for different user densities. Finally, we modify our game model to take power costs into account. The game with power costs corresponds to the well-known Prisoner's Dilemma: The players are still motivated to adjust their pilot powers, but their strategic behavior leads to a sub-optimal Nash equilibrium.

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A cellular network or mobile network is a telecommunications network where the link to and from end nodes is wireless and the network is distributed over land areas called cells, each served by at

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In telecommunication, intersymbol interference (ISI) is a form of distortion of a signal in which one symbol interferes with subsequent symbols. This is an unwanted phenomenon as the previous symbo

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In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilib

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Mark Felegyhazi, Jean-Pierre Hubaux

So far, cellular networks have been operated in ``private" frequency bands. But recently, several researchers and legislators have argued in favor of a more flexible and more efficient management of the spectrum, leading to the possible coexistence of several network operators in a shared frequency band. In this paper, we study this situation in detail, assuming that mobile devices can freely roam among the various operators. Free roaming means that the mobile devices measure the signal strength of the pilot signals (i.e., beacon signals) of the base stations and attach to the base station with the strongest pilot signal. We model the behavior of the network operators in a game theoretic setting in which each operator decides about the power of the pilot signal of its base stations. We first identify possible Nash equilibria in the theoretical setting in which all base stations are located on the vertices of a two-dimensional lattice. We then prove that a socially optimal Nash equilibrium exists and that it can be enforced by using punishments. Finally, we relax the topological assumption and show that, in the more general case, finding the Nash equilibria is an NP-complete problem.

2005Mark Felegyhazi, Jean-Pierre Hubaux

So far, cellular networks have been operated in "private" frequency bands. But recently, several researchers and legislators have argued in favor of a more flexible and more efficient management of the spectrum, leading to the possible coexistence of several network operators in a shared frequency band. In our paper, we study this situation in detail, assuming that mobile devices can freely roam among the various operators. Free roaming means that the mobile devices measure the signal strength of the pilot signals (i.e., beacon signals) of the base stations and attach to the base station with the strongest pilot signal. We model the behavior of the network operators in a game theoretic setting in which each operator decides the power of the pilot signal of its base stations. We first identify possible Nash equilibria in the theoretical setting in which all base stations are located on the vertices of a two-dimensional lattice. We then relax this topological assumption and show that, in the more general case, finding the Nash equilibria is an NP-complete problem. Finally, we prove that a socially optimal Nash equilibrium exists and that it can be enforced by using punishments.

2005Mark Felegyhazi, Jean-Pierre Hubaux

So far, cellular networks have been operated in "private" frequency bands. But recently, several researchers and legislators have argued in favor of a more flexible and more efficient management of the spectrum, leading to the possible coexistence of several network operators in a shared frequency band. In this paper, we study this situation in detail, assuming that mobile devices can freely roam among the various operators. Free roaming means that the mobile devices measure the signal strength of the pilot signals (i.e., beacon signals) of the base stations and attach to the base station with the strongest pilot signal. We model the behavior of the network operators in a game theoretic setting in which each operator decides about the power of the pilot signal of its base stations. We first identify possible Nash equilibria in the theoretical setting in which all base stations are located on the vertices of a two-dimensional lattice. We then prove that a socially optimal Nash equilibrium exists and that it can be enforced by using punishments. Finally, we relax the topological assumption and show that, in the more general case, finding the Nash equilibria is an NP-complete problem.

2006