The new perspective emerging from strategy's value-capture stream is that the effects of competition are two-fold: competition for an agent bounds its performance from below, while that for its transaction partners bounds from above. Thus, assessing the intensity of competition on either side is essential to understanding firm performance. Yet, the literature provides no formal notion of "competitive intensity" with which to make such assessments. Rather, some authors use added value as their central analytic concept, others the core. Added value is simple, but misses the crucial, for-an-agent side of competition. The core is theoretically complete, but difficult to interpret and empirically intractable. This paper formalizes three, increasingly general notions of competitive intensity, all of which improve upon added value while avoiding the complexity of the core. We analyze markets characterized by disjoint networks of agents (e.g., supply chains), providing several insights into competition and new tools for empirical work.