Prior research has mainly emphasized the strategic importance of a collaborative green innovation (CGI) between the manufacturer and supplier in a supply chain, leading to an overlook at the decision-making mechanism and determinants of CGI. Guided by the transaction cost economics and social exchange theory, our study constructs a mathematical game model to incorporate the key dimensions of an effective inter-firm collaboration for green innovation. Applying the Nash game bargaining principles, our evolutionary game model analysis provides an analytic system to understand the mechanisms of forming and operating a collaboration partnership between the manufacturer and supplier for green innovation. Based on various scenarios from the numerical simulation parameters for the involved influencing factors, our simulation has produced the Nash equilibrium solutions and identified the major determining factors for successfully forming and operating CGI. They are the trust level between the manufacturer and supplier as the CGI partners, value/profit sharing ratio between the partners, knowledge complementarity of the partners, and product type for the green innovation.