On Stability and Learning of Competitive Equilibrium in Generalized Fisher Market Models: A Variational Inequality Approach
Mandar Datar
TL;DR
This paper addresses equilibrium computation in generalized Fisher markets where buyers' utilities depend on rivals' allocations (social influence). It reframes the CE problem as a generalized Nash equilibrium problem and derives a novel variational inequality formulation whose solution coincides with CE, enabling tractable analysis of monotonicity, stability, and uniqueness. Two decentralized learning algorithms are proposed: a two-time-scale stochastic-approximation-based tâtonnement and a trading-post mechanism with replicator-like dynamics, both provably convergent under standard assumptions and validated through numerical experiments. By linking CE in generalized settings to existing EG results and variational-equilibrium theory, the work broadens the applicability of Fisher-market analysis to interdependent utilities and provides practical, scalable mechanisms for decentralized CE attainment.
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{â}tonnement method and a trading-post mechanism-based learning method. Finally, we validate the proposed algorithms through numerical simulations.