Optimal selling mechanisms under moment conditions

• Autor(a) principal: Carrasco, Vinicius
• Data de Publicação: 2017
• Outros Autores: Luz, Vitor Farinha, Kos, Nenad, Messner, Matthias, Monteiro, P. K., Moreira, Humberto Ataíde
• Tipo de documento: Artigo de conferência
• Idioma: eng
• Título da fonte: Repositório Institucional do FGV (FGV Repositório Digital)
• Texto Completo: https://hdl.handle.net/10438/27677
• topic: Optimal mechanism design; Robustness; Incentive compatibility; Individual rationality; Ambiguity aversion; Moment conditions; Economia; Mercado de capitais; Contratos administrativos

We study the revenue maximization problem of a seller who is partially informed about the distribution of buyer's valuations, only knowing its first N moments. The seller chooses the mechanism generating the best revenue guarantee based on the information available, that is, the optimal revenue is given by maxmin expected revenue. We show that the transfer function in the optimal mechanism is given by non-negative monotonic hull of a polynomial of degree N. This enables us to transform the seller's problem into a much simpler optimization problem over N variables. The optimal mechanism is found by choosing the coefficients of the polynomial subject to a resource constraint. We show that knowledge of the first moment does not guarantee strictly positive revenue for the seller, characterize the solution for the cases of two moments and derive some characteristics of the solution for the general case.