An Optimal Auction with Externalities

• Autores: Héctor Chade
• Localización: Abstracts of the Fifth Spanish Meeting on Game Theory and Applications / coord. por Jesús Mario Bilbao Arrese, Francisco Ramón Fernández García, 2002, ISBN 84-472-0733-1, pág. 127
• Idioma: inglés
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• Resumen

  • This paper analyzes the problem of a seller who wants to design an optimal mechanism to sell multiple units of a good to a set of potential buyers who have single-unit demands. A buyer�s valuation for the good is determined by two factors: (i) a taste parameter that is private information; (ii) a positve externality parameter determined by the identities of the other buyers who also obtain a unit of the good.

    We characterize the optimal (profit maximizing) selling mechanism in the presence of private information and identity-dependent externalities, which clearly illustrates how the existence of external effects alters the allocation and payment rules with respect to the case with just private information. We provide several examples that shed light on the main properties of the optimal mechanism; in particular, we show that it leads sometimes to an ex-post inefficient allocation, and also that a buyer�s payment for a unit of the good is a decreasing function of the positive externalities he generates.

    As an application of the model, we consider the case of the owner of a shopping center who wants to allocate retail space to a set of potential firms; the value for a firm of locating there depends on the size of the inter-store externalities, which determines the flow of customers. We show that, when interstore externalities are sufficiently large, then the following sequential mechanism which is commonly used in practice is optimal: first, allocate retail space to the firms that generate the largest external effects at a deep discount; second, auction the remaining space among the rest of the firms. However, for intermediate values of inter-store externalities, we show the sequential mechanism allocates space to the firms that generate the largest external effects too often compared to the optimal mechanism.