EE (energy efficiency) level, an indispensable index reflecting the environmental performance of products, can be improved by the EE innovating effort of the producer. Considering both the evolution of EE level and market differentiation, we develop a Stackelberg differential game between a policy maker who sets the EE standard and multiple competing producers with different initial EE levels who decide the EE innovation simultaneously. As there exist numerous possible reactions for each producer under a given EE standard about whether to meet the EE standard or not, whether there exists an equilibrium is what we pay special attention to. We find that, under a given EE standard, there indeed exists a unique optimal reaction for each producer, and there exists an equilibrium. Moreover, we find that as green awareness or initial EE level increases, both the EE standard and EE innovation increase. Additionally, if policy maker pays more attention to consumer welfare and environmental performance rather than profit of producer, a more strict EE standard would be set. Also, both less information about the initial EE level and more competition among producers induce lower EE standard and social welfare.
A survey of stackelberg differential game models in supply and marketing channels
