Scattering equations for tree-level amplitudes are viewed in the context of string theory. As a result of the comparison we are led to define a new dual model which coincides with string theory in both the small and large $��'$ limit, and whose solution is found algebraically on the surface of solutions to the scattering equations. Because it has support only on the scattering equations, it can be solved exactly, yielding a simple resummed model for $��'$-corrections to all orders. We use the same idea to generalize scattering equations to amplitudes with fermions and any mixture of scalars, gluons and fermions. In all cases checked we find exact agreement with known results.

v2: 18 pp, 1 figure, added clarifications and comments. Version to be published in PRD