Vertical Cooperative Advertising in a Dual-Channel Supply Chain Under the Premium Effect of Animal Welfare Labels

To investigate the marketing cooperation and decision equilibrium mechanism of a dual-channel supply chain under the premium effect of animal welfare labels, this paper constructs a dual-channel supply chain model consisting of one manufacturer and one retailer. The manufacturer invests in animal welfare and adopts animal welfare certification labels to obtain product premiums, and the retailer implements local advertising campaigns to boost offline market demand. Within this framework, we study equilibrium outcomes under two decentralized decision modes, including the Nash non-cooperative game and the Stackelberg leader–follower game, as well as the centralized decision mode corresponding to the fully cooperative game. We compare the optimal advertising investment, animal welfare investment and supply chain members’ profits in different scenarios. The findings indicate that the manufacturer offers no advertising cost-sharing under the Nash non-cooperative equilibrium. Under the Stackelberg leader–follower game, the manufacturer is willing to cover part of the retailer’s advertising cost if the manufacturer’s marginal profit ρ1 satisfies 2ρ1 > ρ2, and both firms achieve higher profits than those under the Nash equilibrium. When 2ρ1 ≤ ρ2, the optimal sharing ratio equals zero, and the Stackelberg equilibrium degenerates into the Nash equilibrium. The total supply chain profit under centralized decision-making is consistently higher than that under the two decentralized decision modes. Serving as a theoretical benchmark, centralized decision-making reveals the boundary of efficiency loss arising from decentralized decisions. Numerical simulations further validate the above findings and uncover how the advertising cost-sharing ratio and channel preference influence the profits of all participants.