Variational inequalities and economic equilibrium

• 成果类型: Article
• 署名作者: Jofre, Alejandro; Rockafellar, R. Terry; Wets, Roger J-B.
• 署名单位: Universidad de Chile; Universidad de Chile; University of Washington; University of Washington Seattle; University of California System; University of California Davis
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1060.0233
• 发表日期: 2007
• 页码: 32-50
• 关键词: complementarity-problems; monotone operators; sequence; approximation; CONVERGENCE; EXISTENCE; algorithm; models

摘要

Variational inequality representations are set up for a general Walrasian model of consumption and production with trading in a market. The variational inequalities are of functional rather than geometric type and therefore are able to accommodate a wider range of utility functions than has been covered satisfactorily in the past. They incorporate Lagrange multipliers for budget constraints, which are shown to lead to an enhanced equilibrium framework with features of collective optimization. Existence of such an enhanced equilibrium is confirmed through a new result about solutions to nonmonotone variational inequalities over bounded domains. Truncation arguments with specific estimates, based on the data in one economic model, are devised to transform the unbounded variational inequality that naturally comes up into a bounded one having the same solutions.