This paper investigate the effect of various subsidy Schemes on Cournot duopoly with R＆D behaviors. Firms invest in 1st stage to reduce marginal cost and Compete noncooperatively in 2nd stage. Without subsidy, R＆D cooperation is more desirable than R＆D competitpn in the presence of sufficient R＆D spillover. Subsidy scheme that subsidies proportional to quantity and propotional to R＆D expenditure is not desirable. But Subsidy scheme that subsudies propotional to square of quantity and propotioal to R＆D expenditure is desirable. If firms compete in 1st stage, Regulator can accomplish social optimum with less subsidy than that in the R＆D cooperation. But more Information is required for regulator to accomplish social optimum in the R＆D competition.
