Negotiation mechanisms for an order subcontracting and scheduling problem

We consider a decentralized decision-making environment in which a firm and its subcontractor make decisions on subcontracting heterogeneous orders for processing with private information. We design two market-like negotiation mechanisms that adopt the multi-round ascending pricing framework under two negotiation protocols, labeled as Protocols 1 and 2. Applying game-theoretic and combinatorial optimization approaches, we analyze the decision behaviors of both players and derive the final negotiation outcomes. We find that the negotiation mechanism under Protocol 1 cannot guarantee the existence of the equilibrium price, while the negotiation mechanism under Protocol 2 result in equilibrium solutions. For some special cases, we investigate the system performance bounds under the two negotiation mechanisms and find that the performance bounds under the former are better than those under the latter.