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In the spirit of Arrow (The Rate and Direction of Inventive Activity, Princeton, NJ, Princeton University Press, 1962), we examine, in an oligopoly model with horizontally differentiated products, how much a firm is willing to pay for a process innovation that it would be the only one to use. We show that different measures of competition (number of firms, degree of product differentiation, Cournot vs. Bertrand) affect incentives to innovate in non-monotonic, different and potentially opposite ways.