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Journal of Applied Mathematics
Volume 2014, Article ID 268427, 11 pages
Research Article

Existence of an Equilibrium for Lower Semicontinuous Information Acquisition Functions

1ENS de Lyon, 15 Parvis René Descartes, BP 7000, 69342 Lyon Cedex 07, France
2ENSAE, 3 Avenue Pierre Larousse, 92245 Malakoff Cedex, France
3CEREMADE, Université Paris Dauphine, Place du Marechal de Lattre de Tassigny, 75016 Paris, France

Received 24 July 2013; Accepted 13 March 2014; Published 22 April 2014

Academic Editor: Takashi Matsuhisa

Copyright © 2014 Agnès Bialecki et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider a two-period model in which a continuum of agents trade in a context of costly information acquisition and systematic heterogeneous expectations biases. Because of systematic biases agents are supposed not to learn from others' decisions. In a previous work under somehow strong technical assumptions a market equilibrium was proved to exist and the supply and demand functions were proved to be strictly monotonic with respect to the price. Here we extend these results under very weak technical assumptions. We also prove that the equilibrium price maximizes the trading volume and further additional properties (such as the antimonotonicity of the trading volume with respect to the marginal information price).