# Myerson–Satterthwaite theorem

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Formally, the theorem applies if a prospective buyer A has a valuation $v_A \in [x_a,y_a]$, and the prospective seller B has an independent valuation $v_B \in [x_b,y_b]$, such that the intervals $[x_a,y_a]$ and $[x_b,y_b]$ overlap, and the probability densities for the valuations are strictly positive on those intervals. Under those conditions, there is no Bayesian incentive compatible social choice function that is guaranteed in advance to produce efficient outcomes and guarantees buyers and sellers non-negative returns regardless of $v_a$ and $v_b$.