# A Consumer-Theoretic Characterization of Fisher Market Equilibria

arXiv: https://arxiv.org/abs/2107.08153 · HTML: https://mlsanity.com/paper/2107.08153/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jul 2021.

## Built on by (most cited first, 2 of 2)

- [Convex-Concave Min-Max Stackelberg Games](https://mlsanity.com/paper/2110.05192/) (2021)
- [Robust No-Regret Learning in Min-Max Stackelberg Games](https://mlsanity.com/paper/2203.14126/) (2022)

## Abstract (arXiv)

In this paper, we bring consumer theory to bear in the analysis of Fisher markets whose buyers have arbitrary continuous, concave, homogeneous (CCH) utility functions representing locally non-satiated preferences. The main tools we use are the dual concepts of expenditure minimization and indirect utility maximization. First, we use expenditure functions to construct a new convex program whose dual, like the dual of the Eisenberg-Gale program, characterizes the equilibrium prices of CCH Fisher markets. We then prove that the subdifferential of the dual of our convex program is equal to the negative excess demand in the associated market, which makes generalized gradient descent equivalent to computing equilibrium prices via tatonnement. Finally, we run a series of experiments which suggest that tatonnement may converge at a rate of Oleft(frac(1+E)t2right) in CCH Fisher markets that comprise buyers with elasticity of demand bounded by E. Our novel characterization of equilibrium prices may provide a path to proving the convergence of tatonnement in Fisher markets beyond those in which buyers utilities exhibit constant elasticity of substitution.