A bilevel optiization based algorithm for solving a class of price equilibrium problems

TL;DR

This paper introduces a bilevel optimization algorithm to solve ill-posed equilibrium models, including Walras supply-demand and competitive models, by regularizing the problem and finding the nearest equilibrium point.

Contribution

The paper formulates a class of equilibrium problems as variational inequalities and develops a bilevel optimization algorithm to address ill-posedness and compute approximate equilibria.

Findings

Algorithm effectively finds equilibrium points in complex models.

Computational results demonstrate robustness across various data sets.

Method improves stability and convergence in equilibrium computation.

Abstract

We consider class of equilibrium models including the implicit Walras supply-demand and competitive models. Such a model in this class, in general, is ill-posed. We formulate such a model in the form a variational inequality having certain monotonicity property which allow us to describe a regularization algorithm avoiding the ill-posedness based upon the bilevel optimization for fnding a point that is nearest to the given guessed or desired equilibrium price for the model. The obtained computational results with many randomly generated data show that the proposed algorithm works well for this class of the equilibrium models.