Inducing coordination in supply chains through linear reward schemes

Decentralized decision-making in supply chain management is quite common, and often inevitable due to the magnitude of the chain, its geographical dispersion, and the number of agents that play a role in it. But, decentralized decision-making is known to result in inefficient Nash equilibrium outcomes, and optimal outcomes that maximize the sum of the utilities of all agents need not be Nash equilibria. In this paper we demonstrate through several examples of supply chain models how linear reward/penalty schemes can be implemented so that a given optimal solution becomes a Nash equilibrium. The examples represent both vertical and horizontal coordination issues. The techniques we employ build on a general framework for the use of linear reward/penalty schemes to induce stability in given optimal solutions and should be useful to other multi-agent operations management settings.