Shareholding Strategies in Dual-Channel Supply Chains with Parallel Imports

Parallel imports, where genuine products are sold through unauthorized channels at lower prices, create significant channel conflicts in modern supply chains. This study develops a game-theoretic model to examine how equity-based coordination mechanisms—specifically forward, backward, and cross-shareholding strategies—can mitigate these conflicts between manufacturers and authorized retailers. Using a three-party Stackelberg game framework with numerical analysis, we find that: (1) cross-shareholding achieves Pareto improvements when the forward shareholding ratio $$k\in [\text{0.3,0.5}]$$ k ∈ [ 0.3,0.5 ] and backward ratio $$j\in [\text{0.2,0.4}]$$ j ∈ [ 0.2,0.4 ] ; (2) this bilateral equity arrangement simultaneously increases manufacturer profits by 18%, retailer profits by 21%, and quality assurance investments by 31%; (3) consumer trust levels and parallel import costs significantly influence optimal shareholding configurations. Our findings provide strategic guidance for brand manufacturers managing gray market challenges through equity-based channel coordination.