We introduce heterogeneous R&D productivities into an endogenous R&D network formation model, generalizing the framework of Goyal and Moraga-González (2001). Heterogeneous productivities endogenously create asymmetric gains from collaboration: less productive firms benefit disproportionately from links, while more productive firms exert greater R&D effort and incur higher costs. When productivity gaps are sufficiently large, more productive firms experience lower profits from collaborating with less productive partners. As a result, the complete network -- stable under homogeneity -- becomes unstable, and the positive assortative (PA) network, in which firms cluster by R&D productivity, emerges as pairwise stable. Using simulations, we show that the clustered structure delivers higher welfare than the complete network; nevertheless, welfare under this formation follows an inverted U-shape as the fraction of high-productivity firms increases, reflecting crowding-out effects at high fractions. Altogether, we uncover an R&D productivity puzzle: economies with higher average R&D productivity may exhibit lower welfare through (i) the formation of alternative stable networks, or (ii) a crowding-out effect of high-productivity firms. Our findings show that productivity gaps shape the organization of innovation by altering equilibrium R&D alliances and effort. Productivity-enhancing policies must therefore account for these endogenous responses, as they may reverse intended welfare gains.