Negotiations in Competing Supply Chains: The Kalai-Smorodinsky Bargaining Solution

Supply chain contract negotiation has gained increasing attention in recent years, and the studies involving negotiations in the operations literature almost exclusively apply the concept of the Nash bargaining (NB) solution. The NB solution, however, is derived based on the axiom of independence of irrelevant alternatives (IIA), an unrealistic assumption in many contexts. Indeed, our analysis suggests that the NB solution can lead to unreasonable negotiation outcomes in supply chains with horizontal competition. As an alternative, the Kalai-Smorodinsky (KS) solution has been applied in many fields but has not been introduced to the supply chain contexts. The KS solution is derived under the axiom of individual monotonicity in replacement of the IIA axiom. We perform a comprehensive comparison of contract negotiations under the KS and NB solutions in horizontally competing supply chains. Although the KS solution does not possess the flexibility of explicitly specifying the relative bargaining power as the NB solution does, the KS solution can appropriately capture the negotiation power shift induced by the decision ownership, the negotiation sequence, the vertical relationship, the competition intensity, the trade contingency, and the contract type. Our study sheds lights on the appropriate selection of solution concepts in studying negotiations in competing supply chains.