О задаче монополиста и двойственной к ней

Математические заметки. 2023. Т. 114. № 2. С. 181–194.

Bogachev T., Kolesnikov A.

In this paper, we study the functional ΦΦ that arises in numerous economic applications, in particular, in the monopolist problem. A special feature of these problems is that the domains of such functionals are nonclassical (in our case, increasing convex functions). We use an appropriate minimax theorem to prove the duality relation for ΦΦ. In particular, an important corollary is obtained stating that the dual functional (defined on a space of measures and known as the “Beckmann functional) attains its minimum. The present approach also provides simpler proofs of some previously known results.

Keywords: Linear programming, линейное программирование, Дизайн аукционов, auction design, monopolist problem, Задача монополиста

Publication based on the results of: Stochastic Algorithms in Machine Learning (2022)