Efficiently characterizing games consistent with perturbed equilibrium observations

TL;DR

This paper introduces a convex optimization-based method to efficiently characterize the set of games consistent with observed equilibrium behavior, enabling better understanding of game structures from data.

Contribution

It presents a novel, computationally efficient approach for characterizing game sets based on observations, applicable to various game classes and observation models.

Findings

Provides sharp, efficient game characterization

Quantifies how observations constrain game space

Demonstrates approach with numerical simulations

Abstract

We study the problem of characterizing the set of games that are consistent with observed equilibrium play. Our contribution is to develop and analyze a new methodology based on convex optimization to address this problem for many classes of games and observation models of interest. Our approach provides a sharp, computationally efficient characterization of the extent to which a particular set of observations constrains the space of games that could have generated them. This allows us to solve a number of variants of this problem as well as to quantify the power of games from particular classes (e.g., zero-sum, potential, linearly parameterized) to explain player behavior. We illustrate our approach with numerical simulations.