We discuss an extension of a scheme recently proposed for multi-agent control of large-scale networks, like power networks, road traffic networks, water networks, etc. The original scheme uses serial sequences of agent interactions that under some assumptions make agents locally choose actions that are globally optimal. However, some weaknesses of the approach appear when applied to large-scale networks. We identify these weaknesses and propose, for problems with a tree-structured problem topology, an improvement based on parallelization of the serial scheme. With an example we illustrate and compare the schemes.