In this work we address the problem of optimizing collective profitability in semi-competitive intermediation networks defined as augmented directed acyclic graphs. Network participants are modeled as autonomous agents endowed with private utility functions. We introduce a mathematical optimization model for defining pricing strategies of network participants. We employ welfare economics aiming to maximize the Nash social welfare of the intermediation network. The paper contains mathematical results that theoretically prove the existence of such optimal strategies. We also discuss computational results that we obtained using a nonlinear convex numerical optimization package.