Incentive-Driven Small-Cell Caching with Competing Mobile Operators: An Advanced Game-Theoretic and Stochastic Optimization Study

We conduct a detailed and advanced analysis of incentive-driven small-cell caching in multi-operator mobile networks. Building upon Stackelberg game theory and stochastic geometry, we extend the literature by integrating fairness, learning-based dynamics, time-varying popularity, multi-retailer competition, and spatial coupling. New theorems establish equilibrium existence, uniqueness, and efficiency bounds under uncertainty and asymmetric information. A novel iterative best-response algorithm is proposed, and extensive simulation studies on real-world urban topologies validate our framework. Results highlight significant improvements in efficiency, fairness, and operator sustainability when budget-aware, fairness-constrained mechanisms are applied.