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Yilankaya, Okan (1999), “A note on the seller’s optimal mechanism in bilateral trade with two-sided incomplete information.†Journal of Economic Theory, 87, 267–271. B Supplementary material B.1 Equilibrium payoffs in the motivating example This section characterizes the set of equilibrium interim payoff vectors for the seller in the motivating example of Section 2. Assume that X = Y = {1, 2}, v1 1(x) + v2 1(y) = 100x, v1 2(x) + v2 2(y) = 100(x + y), p1 ≡ 1/2, and p2 ≡ 1/2. Let g = (q, t) be an equilibrium allocation. We show that the set of equilibrium interim payoff vectors is characterized by the following system of linear inequalities (i.e., the red triangle in Figure B.1): Ug 1 (2) ≥ 800/3 (B.1) Ug 1 (2) ≤ Ug 1 (1)/3 + 200 (B.2) Ug 1 (2) ≤ 500 − Ug 1 (1) (B.3)