Variational Inequality Type Formulations of General Market Equilibrium Problems with Local Information

TL;DR

This paper introduces a novel quasi-variational inequality framework for modeling general market equilibria with agents having local, partial information, and proposes an iterative solution method with proven convergence.

Contribution

It formulates market equilibrium as a quasi-variational inequality accommodating local information and develops a convergent iterative solution method.

Findings

Existence results for the market model under various conditions

An iterative solution method based on local information evaluations

Proof of convergence for the proposed algorithm

Abstract

We suggest a new approach to creation of general market equilibrium models involving economic agents with local and partial knowledge about the system and under different restrictions. The market equilibrium problem is then formulated as a quasi-variational inequality that enables us to establish existence results for the model in different settings. We also describe dynamic processes, which fall into information exchange schemes of the proposed market model. In particular, we propose an iterative solution method for quasi-variational inequalities, which is based on evaluations of the proper market information only in a neighborhood of the current market state without knowledge of the whole feasible set and prove its convergence.