Optimizing Marketing Budgets for Social Influence: A Generalized Fractional Incentives Framework

Marketing managers routinely allocate limited budgets across individuals in social networks whose responsiveness and influence vary substantially. We study the problem of Budgeted Generalized Fractional Influence Maximization (BGFIM), which captures the allocation of continuous levels of marketing spend across users in the presence of heterogeneous response and network spillovers. In this framework, adoption probabilities are governed by user-specific response functions that capture both baseline propensity and marginal responsiveness, while incentive costs vary across users. We propose a scalable solution approach based on a discrete greedy procedure with provable approximation guarantees, enabling tractable optimization under realistic budget constraints. Our formulation generalizes prior influence maximization models by allowing heterogeneous response and cost structures, providing a more flexible representation of targeted marketing interventions. Using experiments on multiple large-scale networks, we show that continuous allocation strategies can outperform standard heuristics and improve influence outcomes under heterogeneous conditions, and we illustrate how the framework can support profit-oriented decision making by identifying budget levels that balance marginal returns and costs. Overall, our results highlight the value of fine-grained budget allocation in networked marketing environments and offer a scalable approach for data-driven marketing resource allocation.