Managing decentralized inventory and transshipment

Any decentralized retail or wholesale system of competing entities requires a benefit sharing arrangement when competing entities collaborate after their demands are realized. For instance, consider a distribution system similar to the observed behavior of independent car dealerships. If a dealership does not have in stock the car requested by a customer, it might consider acquiring it from a competing dealer. Such behavior raises questions about procurement strategies that achieve system optimal (first-best) outcomes. In this paper, we examine the existence and uniqueness of pure strategy Nash equilibrium (PSNE) for a decentralized system that adopts a transfer payment approach proposed by Anupindi et al. (Manuf. Serv. Oper. Manag. 4(3):349-368, 2001). In particular, we state a set of conditions on cost parameters and distributions that guarantee uniqueness of PSNE and discuss its consequences. We also examine a situation with incomplete information and expand the scope of the earlier models by relaxing the assumption of satisfying local demand first. That is, we allow the retailers to transship their inventory regardless of the local demand status if such transshipment increases retailer's profit, and observe that this model extension does not affect our results relative to the more restrictive case. In short, our results provide important insights, clarifications, and strategic limitations regarding collaborations in decentralized distribution system.