A new biform game-based investment incentive mechanism for eco-efficient innovation in supply chain

In supply chain, when a visionary focal firm makes direct investment in his partners' upfront cost of eco-efficient innovation, he would want more innovation efforts without sacrificing too many self-interests. To this end, we use a new biform-game model to develop an investment incentive mechanism for eco-efficient innovation in a supply chain consisting of two competing manufactures who are accountable for their respective eco-efficient innovations and a supplier who provides them with investments. Our proposed biform-game model can be regarded as a nested combination of noncooperative and cooperative games: In the noncooperative part, we construct a noncooperative game between the two manufacturers under their profit maximizing strategies, defining the competitive environment in the cooperative part. For three players in the cooperative part, we use Minimax and Maximin principles to construct their cooperative game of the investment cooperation strategy, which is proven to be convex. Subsequently, Shapley value is employed to derive the solution (profits) of the cooperative game, which is used to deduce the pay-off functions of the noncooperative part, thereby obtaining the optimal profit-maximizing strategies and investment cooperation strategies of the biform game. Next, we conduct analytical and numerical studies to verify the validity of our developed model by comparing with the model without applying the biform coordination mechanism.