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Recent empirical evidence about innovation shows that established firms rarely invest in radical innovation but incrementally improve the existing technology. Revolutionary breakthroughs are more likely to be introduced by new entrants. These stylized facts motivate a renewed attention of the debate on incentives to innovate. In this stream of the literature our paper emphasizes the importance of distinguishing between degrees of innovativeness when comparing an incumbent’s and an entrant’s incentives to invest in innovation. The model presented captures the peculiarity of a radical innovation with respect of an incremental one along three dimension: risk, impact on the existing market and capability of opening up a new market. The results reflect the empirical evidence and emphasize the role of substitutability between markets in determining the strength of this effect. We thank L. Zirulia for helpful comments.