Taking absorptive capacity effects on research spillovers into consideration, this paper focuses on the R＆D investment decisions and the output decisions of labor-managed firms. Based on the general model of the cost-reducing R＆D, the strategic interactions of output and R＆D investment between labor-managed firms in a duopoly are analyzed. Moreover, the impact of absorptive capacity effects on optimal output in the production stage is discussed. In the R＆D stage, the impacts of absorptive capacity effects on the equilibrium R＆D investment in cooperative and non-cooperative R＆D are analyzed. Finally, the R＆D strategy of labor-managed firms is compared with the behavior of profit-maximizing firms. The results show that equilibrium R＆D investment is always higher than that in the exogenous spillover rate, which is similar to the behavior of the profit-maximizing firms. However, unlike the profit-maximizing firms, the impact of the absorptive capacity that affects the relationship between the optimal output and its own（rival＇ s）R＆D is shown to be dependent upon a return-to-scale of the production.
The proximal-based decomposition method was originally proposed by Chen and Teboulle （Math. Programming, 1994, 64：81-101 for solving corrvex minimization problems. This paper extends it to solving monotone variational inequalities associated with separable structures with the improvements that the restrictive assumptions on the involved parameters are much relaxed, and thus makes it practical to solve the subproblems easily. Without additional assumptions, global convergence of the new method is proved under the same mild assumptions on the problem＇s data as the original method.
