1\begin{tabular}{lrrrrr}2\toprule3sellers & $\theta$ decentralised & $\theta$ planner & welfare decentralised & welfare planner & gain (\%) \\4\midrule5heterogeneous & 4.391 & 3.802 & 0.15820 & 0.15867 & 0.299 \\6homogeneous & 4.460 & 3.850 & 0.15799 & 0.15838 & 0.243 \\7\bottomrule8\end{tabular}9