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Consider a supply chain consisting of a common manufacturer and two asymmetric retailers, a dominant retailer and a weak one. This article develops a differential game in which the manufacturer sets the wholesale price for the weak retailer and invests advertising to improve goodwill, while both retailers compete for market demand by setting their respective retail prices. We study two market structures: a no-alliance scenario and an alliance scenario to answer a key question that the dominant retailer is facing: Can the dominant retailer benefit from the alliance between the manufacturer and the weak retailer? Our results show that the dominant retailer can take advantage from the alliance when the marginal contribution of goodwill on market demand is relatively high. The weak channel always benefits from alliance because of the strengthened channel power. Under the no-alliance scenario, the dominant retailer with a relatively small market share will set a lower steady-state price than that of the weak retailer, while the opposite situation occurs for the dominant retailer with a relatively large market share. Under the alliance scenario, the dominant retailer’s steady-state price is always higher than that of the weak channel, and both the dominant retailer and the weak channel charge higher steady-state prices compared to the no-alliance scenario when the effect of goodwill on demand is large, while lower prices of the dominant retailer and the weak channel arise for a small effect of goodwill on demand.
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