Abstract: Faced with severe challenges resulting from gray markets, multinational corporations have to develop a new strategy of response. This paper analytically investigates the advertising strategies of authorized channels and their effects in centralized and decentralized supply chains where a gray market exists. Two-stage and three-stage Stackelberg game models for centralized and decentralized supply chains are developed respectively to investigate different advertising strategies such as no advertising, advertising only in the highprice market, advertising in both high-and low-price markets, and use of cooperative advertising under both structures. The results show that: (1) The advertising level is negatively correlated with consumers’ relative perception of gray market products, but stabilizes eventually. (2) In the centralized supply chain, advertising in the high-price market is a “ win-win” strategy for both the manufacturer and the gray market speculator. (3) In the centralized supply chain, advertising in both high-price and low-price markets not only benefits the manufacturer, but also plays a role in weakening the speculator during the maturity of the gray market. (4) In the decentralized supply chain, the advertising level will decline, and the profit of the authorized channel will shrink, but the profit of the gray market speculator may rise. (5) Cooperative advertising can increase prices of both channels in both markets and stimulate advertising, which benefits the manufacturer and the gray market speculator, but harms the retailer.

Key words: gray market, advertising strategy, cooperative advertising, Stackelberg model