A Cellular Market Model for Social Welfare Maximization through a Subsidization Scheme

Abstract

In cellular communications markets, various stakeholders interact while considering regulatory policies enacted by governments to maximize social welfare. However, there remains an opportunity to develop new tools that support countries in making informed decisions regarding the adoption of strategies aimed at enhancing societal well-being. Accordingly, network economics and game theory offer a relevant framework for analyzing such policies. In this regard, the state-of-the-art lacks a market model for cellular communications that incorporates stakeholder interactions under a subsidization scheme designed to maximize the system’s social welfare. This paper introduces a novel subsidization scheme, formulated as a constrained optimization problem involving three stakeholders: the central planner, the cellular network operator, and the aggregate cellular data users. In this context, the central planner and the cellular network operator, acting as strategic players, optimize their respective payoff functions by incorporating benefit factors that represent their interactions, accounting for both attributes and behavioral aspects. Their decision variables include the subsidization factor, bandwidth allocation across the spectrum license, perceived service quality, and data plan pricing. Meanwhile, the aggregate cellular data users consume cellular data based on optimal pricing and perceived service quality. To capture the interactions among these players, a two-stage dynamic game is proposed, employing the backward induction method in combination with an algorithm to derive the subgame perfect equilibrium from the Nash equilibrium. A case study demonstrates a 46.35% increase in social welfare and a 24.10% in cellular network operator’s profit margin by comparing the results associated with the subsidization factor at its optimal value and when it is not optimal. Furthermore, the proposed model incorporates additional elements beyond those typically considered in the literature such as network infrastructure costs, the number of base stations, and the users-to-base-station ratio resulting in a more realistic and practically relevant model for decision-making in cellular communications markets.