# Overview

In empirical game theoretic analysis (EGTA), the goal is to analyze or estimate various properties of a game, given only noisy blackbox (simulator) access to it. In particular, this means that we do not know the *utility function* of the game, and can only access samples of (per-player) utility values at any strategy profile (configuration of all player strategies) that, *in expectation*, match the utility of said profile.

Over the last several years, alongside my collaborators Amy Greenwald, and Enrique Areyan Viqueira, I have worked to bound the sample complexity of estimating equilibria and other properties of games in this setting. Furthermore, we have extended these ideas to *mechanism design*, wherein the goal is not just to estimate the properties of a game, but to modify a game or select its parameters in order to incentivize various types of strategic behavior and other desiderata.

# Computational and Data Requirements for Learning Generic Properties of Simulation-Based Games

## Cyrus Cousins, Bhaskar Mishra, Enrique Areyan Viqueira, and Amy Greenwald

### Cyrus Cousins

## Abstract

Empirical game-theoretic analysis (EGTA) is primarily focused on learning the equilibria of simulation-based games. Recent approaches have tackled this problem by learning a uniform approximation of the game’s utilities, and then applying precision-recall theorems: i.e., all equilibria of the true game are approximate equilibria in the estimated game, and vice-versa. In this work, we generalize this approach to all game properties that are well behaved (i.e., Lipschitz continuous in utilities), including regret (which defines Nash and correlated equilibria), adversarial values, and power-mean and Gini social welfare. Further, we introduce a novel algorithm—progressive sampling with pruning (PSP)—for learning a uniform approximation and thus any well-behaved property of a game, which prunes strategy profiles once the corresponding players’ utilities are well-estimated, and we analyze its data and query complexities in terms of the a priori unknown utility variances. We experiment with our algorithm extensively, showing that 1) the number of queries that PSP saves is highly sensitive to the utility variance distribution, and 2) PSP consistently outperforms theoretical upper bounds, achieving significantly lower query complexities than natural baselines. We conclude with experiments that uncover some of the remaining difficulties with learning properties of simulation-based games, in spite of recent advances in statistical EGTA methodology, including those developed herein.

Empirical game-theoretic analysis (EGTA) ♦ Sample Complexity ♣ Lipschitz Analysis ♥ Equilibria Estimation ♠ Price of Anarchy

Read the full paper on arXiv