Data-Driven Estimation in Equilibrium Using Inverse Optimization

TL;DR

This paper introduces a data-driven method combining inverse optimization and variational inequalities to estimate equilibrium model parameters from observed data, supporting both parametric and nonparametric approaches.

Contribution

It develops an efficient estimation technique that leverages statistical learning for equilibrium models, applicable to game theory and transportation science, with improved out-of-sample performance.

Findings

Successfully estimates utility functions and congestion functions from observed data.

Regularization significantly enhances out-of-sample estimation accuracy.

Supports both parametric and nonparametric estimation methods.

Abstract

Equilibrium modeling is common in a variety of fields such as game theory and transportation science. The inputs for these models, however, are often difficult to estimate, while their outputs, i.e., the equilibria they are meant to describe, are often directly observable. By combining ideas from inverse optimization with the theory of variational inequalities, we develop an efficient, data-driven technique for estimating the parameters of these models from observed equilibria. We use this technique to estimate the utility functions of players in a game from their observed actions and to estimate the congestion function on a road network from traffic count data. A distinguishing feature of our approach is that it supports both parametric and \emph{nonparametric} estimation by leveraging ideas from statistical learning (kernel methods and regularization operators). In computational experiments involving Nash and Wardrop equilibria in a nonparametric setting, we find that a) we effectively estimate the unknown demand or congestion function, respectively, and b) our proposed regularization technique substantially improves the out-of-sample performance of our estimators.