Partition-form Cooperative Games in Two-Echelon Supply Chains

Competition and cooperation are inherent features of any multi-echelon supply chain. The interactions among the agents across the same echelon and that across various echelons influence the percolation of market demand across echelons. The agents may want to collaborate with others in pursuit of attracting higher demand and thereby improving their own revenue. We consider one supplier (at a higher echelon) and two manufacturers (at a lower echelon and facing the customers) and study the collaborations that are `stable'; the main differentiator from the existing studies in supply chain literature is the consideration of the following crucial aspect -- the revenue of any collaborative unit also depends upon the way the opponents collaborate. Such competitive scenarios can be modeled using what is known as partition form games. Our study reveals that the grand coalition is not stable when the product is essential and the customers buy it from any of the manufacturers without a preference. The supplier prefers to collaborate with only one manufacturer, the one stronger in terms of market power; further, such collaboration is stable only when the stronger manufacturer is significantly stronger. Interestingly, no stable collaborative arrangements exist when the two manufacturers are nearly equal in market power.