Dynamic Reward Optimization for Sharing Economies: A Stochastic Control Framework for the Smart World

This paper proposes a dynamic and game-theoretic framework for optimizing reward policies in the sharing economy. Moving beyond static incentive schemes, we design a platform-wide control system that dynamically selects which shoppers to incentivize using real-time data, probability-driven models, and Nash equilibrium assumptions. Our approach integrates a dynamic programming algorithm and a continuous-time stochastic control formulation to determine optimal incentive allocations under budget constraints. Furthermore, we develop a novel methodology to estimate the optimal value of α, which represents the marginal value of a successful order (OTP). Simulated scenarios confirm the robustness of our framework across varying market dynamics, shopper behaviors, and budget scales. The results provide theoretical and practical foundations for deploying intelligent, adaptive, and cost-efficient reward policies at scale for the smart world.