Spectrum Sharing: How Much to Give

Spectrum holding per cellular telephony service provider in India is significantly lower than the world average. The spectrum is also severely fragmented across bands and the fragments also have different license conditions. Regulators in India have recently recognized that such spectrum fragmentation is a source of inefficiency for the service providers and have allowed sharing of spectrum among the providers. The genesis of this paper is this regulatory order and it has a three-fold objective. We first study an example spectrum allocation. By assuming GSM-like voice telephony service, we analyse the spectrum holding in one service area in some detail. Using simple calculations, we see that complete pooling of resources by the providers may not be stable-one provider may have a lower blocking probability if it does not form a coalition. This leads us to our second objective of developing analytically tractable partial sharing models where the providers do not pool all their resources. For a probabilistic spectrum sharing model, we analyse a simple system and obtain the partial sharing that will make the coalition stable and Pareto efficient. This model is then extended to a larger system and numerical results from the analytical model are used to obtain additional insights. We then consider a deterministic sharing model for which we also present a similar analysis for this system. We also show that the deterministic sharing system can be analysed via a suitably defined circuit multiplexed network that allows us to use Kelly's Erlang fixed point approximation which in turn provides economic insights. The final objective is to develop a game theoretic model for partial sharing. We provide a Nash bargaining framework for partial sharing. We also discuss some revenue sharing mechanisms when the providers' benefits from partial sharing are asymmetric.