On Stability and Learning of Competitive Equilibrium in Generalized Fisher Market Models: A Variational Inequality Approach

TL;DR

This paper extends Fisher market models to include social influence, proposing a variational inequality framework to analyze stability, uniqueness, and decentralized algorithms for learning competitive equilibrium.

Contribution

It introduces a novel variational inequality formulation for generalized Fisher markets with social influence and develops decentralized algorithms for equilibrium learning.

Findings

The variational inequality framework captures market stability and uniqueness.

Decentralized algorithms effectively achieve competitive equilibrium.

Numerical simulations validate the proposed methods.

Abstract

In this work, we study a generalized Fisher market model that incorporates social influence. In this extended model, a buyer's utility depends not only on their own resource allocation but also on the allocations received by their competitors. We propose a novel competitive equilibrium formulation for this generalized Fisher market using a variational inequality approach. This framework effectively captures competitive equilibrium in markets that extend beyond the traditional assumption of homogeneous utility functions. We analyze key structural properties of the proposed variational inequality problem, including monotonicity, stability, and uniqueness. Additionally, we present two decentralized learning algorithms for buyers to achieve competitive equilibrium: a two-timescale stochastic approximation-based t{\^a}tonnement method and a trading-post mechanism-based learning method. Finally, we validate the proposed algorithms through numerical simulations.