The first chapter studies how government should allocate R&D subsidies when firms interact through their R&D decisions. In practice, public agencies often distribute funding on a case-by-case (CbC) basis ignoring indirect effects that may arise due to firm interaction. The paper finds that when complementary knowledge spillovers occur among firms receiving support to research on independent products, knowledge spillovers induce complementary R&D interactions and CbC funding is socially excessive. By contrast, when no knowledge spillovers occur among firms receiving support to research on substitute products, product market rivalry induces substitutive R&D interactions and CbC funding is socially insufficient. An adjusted CbC rule is then proposed which corrects the inefficiency in CbC funding arising from a general pattern of bilateral influences. The second chapter presents a model of the agglomeration of an oligopolistic industry to study the effect of cluster size on firm performance and firms' incentives to cluster. The model captures a distinctive feature of agglomeration among firms which produce close substitutes: the interaction of agglomeration externalities and negative pecuniary externalities. The paper finds that i) the performance of cluster firms exhibits a rise-and-fall pattern with respect to cluster size; ii) neither complete agglomeration nor complete dispersion of firms is socially desirable; and iii) firms' unilateral incentives drive them to agglomerate completely. This suggests that the private incentives to agglomerate of competing firms may be socially excessive. The paper also compares the performance of cluster and isolated firms, which is relevant for situations where geography or government constrains firms' location decisions. The third chapter develops a model to study how government should subsidize investment, e.g. R&D, when firms are located in clusters and agglomeration externalities are present, e.g. local knowledge spillovers. The analysis focuses on industry spatial patterns characterized by a single core and peripheral cluster. The paper finds that asymmetries between core and peripheral cluster sizes create differential subsidy effects: i) the additionality effect of a subsidy on cluster firm investment is relatively stronger for a peripheral firm subsidy (expansion effect); and ii) the crowding-out effect of a subsidy on non-cluster firm investment is relatively stronger for a core firm subsidy (sitting-duck effect). We find the sitting-duck effect dominates the expansion effect. The main policy implication is that if government is justified in funding both core and peripheral firms then alongside core firm subsidies, government must provide adequate funding to peripheral firms to counteract the sitting-duck effect. The paper also finds that case-by-case subsidization is biased towards favouring firms in the core cluster.