# A Learning Framework for Distribution-Based Game-Theoretic Solution Concepts

## TL;DR

This paper introduces a unified learning-theoretic framework for understanding when and how various economic solution concepts can be learned from data, generalizing existing theories and applying to new economic notions.

## Contribution

It develops a general methodology based on graph dimension for analyzing the PAC learnability of economic solutions, extending prior work and introducing new concepts like PAC competitive equilibrium.

## Key findings

- Established conditions for PAC learnability of solution concepts
- Unified existing results within the new framework
- Introduced novel economic notions such as PAC competitive equilibrium

## Abstract

The past few years have seen several works on learning economic solutions from data; these include optimal auction design, function optimization, stable payoffs in cooperative games and more. In this work, we provide a unified learning-theoretic methodology for modeling such problems, and establish tools for determining whether a given economic solution concept can be learned from data. Our learning theoretic framework generalizes a notion of function space dimension -- the graph dimension -- adapting it to the solution concept learning domain. We identify sufficient conditions for the PAC learnability of solution concepts, and show that results in existing works can be immediately derived using our methodology. Finally, we apply our methods in other economic domains, yielding a novel notion of PAC competitive equilibrium and PAC Condorcet winners.