Dynamic Data Pricing: A Mean Field Stackelberg Game Approach

Abstract: This paper studies the dynamic pricing mechanism for data products in demand-driven markets through a game-theoretic framework. We develop a three-tier Stackelberg game model to capture the hierarchical strategic interactions among key market entities: a single data buyer, an intermediary broker, and a competitive seller group. To characterize the temporal dynamics of data quality evolution, we establish a coupled system of stochastic differential equations (SDEs) where sellers' quality investments interact through mean field effects. Given exogenous pricing policies, we derive approximate Nash equilibrium adjustment strategies for competitive sellers using the mean field game (MFG) approach. The broker's optimal pricing strategy is subsequently established by solving a Stackelberg leadership problem, while the buyer's procurement policy is determined through an optimal control formulation involving conditional mean field forward-backward SDEs (FBSDEs). Under some regularity conditions, the proposed strategies are shown to collectively form an $(ε_1,ε_2,ε_3)$-Stackelberg equilibrium.