Platform Promotional Subsidy Strategies Under Price Regulation: A Tripartite Interactive Game Analysis of Regulator, Platform and Consumers

Abstract

This paper investigates platform promotional subsidy strategies under price regulation. We construct a dynamic game model of incomplete information. The model involves a regulator, a monopoly platform, and heterogeneous consumers. The regulator sets a subsidy cap. The platform chooses the price and subsidy after observing its cost type. Consumers decide whether to purchase based on their valuation and the perceived subsidy value. We solve the game by backward induction. We characterize the perfect Bayesian equilibria. We derive closed-form solutions for the critical subsidy threshold, separating/self-selection equilibrium conditions, and optimal regulatory policies. The analysis yields three main findings. First, the sign of the net social benefit of the promotional subsidy determines the optimal policy. A positive sign calls for a high subsidy cap. This induces full market coverage. A negative sign calls for a ban on subsidies. Second, when the subsidy cap lies between the two platform types’ critical thresholds, a natural separating/self-selection equilibrium emerges. It operates at no cost. The feasible interval widens linearly in the cost gap. Third, diseconomies of scale have a stronger marginal effect on the critical subsidy than marginal cost. There exists an endogenously determined critical proportion of high-value consumers, which depends on the model parameters, such as vH,vL,cI,ηI. This proportion divides the policy space into two regimes. These results provide a basis for low-cost information screening and differentiated regulation.