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We consider the optimal subsidy policy under different assumptions on the firms' and government's behaviors: precommitment equilibrium and sequential equilibrium. In the presence of spillover learning-by-doing, positive subsidies may not be justified when the home firm behaves strategically against the foreign firm and the home government. The home firm Ins additional incentives to increase output in the first period: through the pure learning-by-doing effect, strategic effect against the foreign firm, strategic effect against the home government. and inward spillover effect. This implies that the home firm has an incentive to utilize pure learning-by-doing to improve the home firm's future strategic position in competition with the foreign firm, to increase the subsidy, and to benefit from the inward spillovers. On the other lund, the home government has an incentive to offset the strategic behaviors by the home firm: to offset the home firm in the first period to restrain home firm from over-producing strategically against the foreign firm and against the home government, and to reduce inward spillover effect.
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