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

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.