Abstract: Because recycling the EOL products can both diminish environmental pollution and save useful social resources, widespread importance is attached to research of closed-loop supply chain by the academia. Six types of non-game closed-loop supply chain models of two levels are built based on innovation study and cooperation by the production function against backgrounds of stable and risk market and the existence of the optimal solution of the models and and the corresponding approaches is proved by using multi-mathematics methods. Information asymmetry is an important characteristic of supply chain and an increase in the share of imformation is a fundamental trend of supply chain development in times to come. Firstly, according to the following assumptions: innovation input can decrease the unit cost of remake and advertisements input, models proposed in this paper can increase the recyleing rate of EOL products and sales volume of remake. Secondly, collaboration is stressed in the course of finding the optimal solution of the models and supply chain management idea of making two sets of rules is put forward, for internal profit distribution and allied decision-making. Each member should abjure (or diminish at least) the internal fight. The amount of investment by each member is determined by the principle of ensuring the maximal profit of the whole supply chain. Finally, an emulational analysis of the model is made and by case study show that cooperation often brings much more profit to the supply chain than game in the same market and under the same innovation condition.Besides, the total profit of equal cooperation and subordinative cooperation remains the same wether under stable or risk-market conditions. Thus, host enterprises should try their best to support weaker enterprises to increase competitiveness of the whole supply chain.

Key words: supply chain, cooperation, innovation, investment, approximation