Dynamic Vertical Pricing and Strategic Timing: Analytical and Numerical Evidence from the Thai Palm Oil Supply Chain

Abstract

This paper develops a dynamic game-theoretic model of a vertically decentralized agricultural supply chain with endogenous timing and three-layer pricing. Focusing on a factory–wholesaler–retailer structure, we derive closed-form subgame perfect Nash equilibria and establish existence and uniqueness under explicit economic conditions. Under linear demand and constant marginal costs, decentralized sequential pricing yields an exact efficiency ratio: total channel profit equals 7/16 of the integrated benchmark, implying a 56.25% structural profit loss. This loss admits a quadratic decomposition as a curvature-scaled squared retail-pricing wedge generated by uninternalized vertical pricing externalities. We further embed the pricing game in a continuous-time gradient adjustment system and establish global asymptotic stability using a Lyapunov argument. Spectral analysis links convergence speed to demand curvature, while computational sensitivity analysis illustrates robustness over economically admissible parameter regions. Calibration to Thai crude palm oil trade data (2015–2024) anchors demand at moderate inelasticity and indicates that the predicted distortion is quantitatively meaningful. Overall, the framework explains how vertically fragmented agricultural markets can be dynamically stable yet structurally inefficient.