This paper examines R&D contests where prizes and costs are affected by the number of firms. There are two groups of firms. The government allocates a fixed prize among the two groups. Then firms in each group engage in R&D contest. Examining the effect of prize allocation in such R&D contests, the paper derives the following results. The aggregate efforts increase in the prize share of the larger group. In R&D contests with cost externalities, the aggregate payoffs increase in the prize share of the smaller group. The paper derives the neutrality result in R&D contests with cost externalities that the aggregate payoffs are independent of firm distribution across groups if the prize is allocated in proportion to group size. Also, the groups tend to be of equal size if inter-group mobility of firms is allowed. In contests with externalities in prizes, integration of contests can yield higher aggregate payoffs than the decentralized contests. Moreover, an increase in the number of firms makes it more likely that the payoffs in the integrated R&D contest are greater than in the decentralized R&D contests. Abstract 1. Introduction 2 2. R&D contests with cost externalities 5 3. R&D contests with externalities in prizes 15 4. Concluding Remarks 22 References 24