The Massachusetts Institute of Technology (MIT) Commission on Industrial Productivity, in their report Made in America, found that six recurring weaknesses were hampering American manufacturing industries. The two weaknesses most relevant to product development were 1) technological weakness in development and production, and 2) failures in cooperation. The remedies to these weaknesses are considered the essential twin pillars of CE: 1) improved development process, and 2) closer cooperation. In the MIT report, it is recognized that total cooperation among teams in a CE environment is rare in American industry, while the majority of the design research in mathematically modeling CE has assumed total cooperation. In this paper, we present mathematical constructs, based on game theoretic principles, to model degrees of collaboration characterized by approximate cooperation, sequential decision making and isolation. The design of a pressure vessel and a passenger aircraft are included as illustrative examples.