Theoretical analysis uncovers a mathematical error in supply function models, indicating that symmetric Nash equilibria under demand uncertainty are consistently linear.
Turnbull (Econ Lett 13: 253–258, 1983) describes unique symmetric Nash equilibria for supply function competition under demand uncertainty which consist of affine strategies that are nonlinear. For the same economy Klemperer and Meyer (Econometrica 79: 1919–1966, 1989) derive unique Nash equilibria that are linear. This note shows that the friction between both results comes from a mathematical error in Turnbull (Econ Lett 13: 253–258, 1983). Correcting this error establishes the same linear Nash equilibria for both models.
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Alexander Zimper (2026) studied this question.
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