A Game-Theoretic Load-Aware Pricing and User Association Scheme for Proximal Spectrum Sharing in Multi-Operator Cellular Networks

Proximal spectrum sharing allows users to connect to nearby base stations (BSs) of other operators based on SINR, improving spectral efficiency and user experience. However, it raises challenges in load balancing and fair revenue distribution. To address this, we propose a game-theoretic framework for joint user association and dynamic pricing. Users choose BSs by maximizing a utility that considers SINR and price, while operators adjust prices based on load to optimize revenue. The interaction is modeled as a two-stage game: an ordinal potential game for user association and a concave optimization for pricing. We prove convergence to a Nash Equilibrium, ensuring stability and fairness. Our framework ensures fair, stable, and efficient coexistence—maximizing throughput while preserving operator incentives. Extensive simulations validate its effectiveness across throughput, load distribution, user satisfaction, and operator revenue.