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A quasi-variational approach to a competitive economic equilibrium problem without strong monotonicity assumption

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Abstract

This paper is focused on the investigation of the Walrasian economic equilibrium problem involving utility functions. The equilibrium problem is here reformulated by means of a quasi-variational inequality problem. Our goal is to give an existence result without assuming strong monotonicity conditions. To this end, we make use of a perturbation procedure. In particular, we will consider suitable perturbed utility functions whose gradient satisfies a strong monotonicity condition and whose associated equilibrium problem admits a solution. Then, we will prove that the limit solution solves the unperturbed problem. We stress out that our result allows us to consider a wide class of utility functions in which the Walrasian equilibrium problem may be solved.

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Authors and Affiliations

  1. Department of Mathematics, University of Messina, Contrada Papardo, Salita Sperone, 31, Messina, 98166, Italy

    G. Anello, M. B. Donato & M. Milasi

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  1. G. Anello
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  2. M. B. Donato
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  3. M. Milasi
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Correspondence to G. Anello.

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Anello, G., Donato, M.B. & Milasi, M. A quasi-variational approach to a competitive economic equilibrium problem without strong monotonicity assumption. J Glob Optim 48, 279–287 (2010). https://doi.org/10.1007/s10898-009-9492-1

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  • DOI: https://doi.org/10.1007/s10898-009-9492-1

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