Competition and Cooperation in Decentralized Distribution

Any decentralized retail or wholesale system of competing entities has a benefit sharing arrangement when collaborating with regards to demand realizations. We study a distribution system similar to the observed behavior of independent car dealerships. If a dealership does not have in stock the vehicle requested by a customer, it might consider acquiring it from a competing dealer. This raises questions about procurement strategies that achieve a system optimal (firstbest) outcome. We examine such a decentralized distribution system with respect to: (a) Does a unique first-best solution imply unique Nash equilibrium procurement strategies? (b) If some of the participants do not select Nash procurement strategies, what are the implications on the benefit sharing? (c) When demand parameters are not of common knowledge the system might not encourage truth revelation. (d) How are the above results affected if we relax the assumption of satisfying local demand first? We show that the profit sharing rules like the ones found in the literature will result in a stable collaborative outcome that achieves first-best only if (i) individual demand parameters satisfy a number of restrictive conditions, (ii) complete information assumption holds, and (iii) all the parties select Nash equilibrium strategy.