alexlyzhov / n-player-games

Experiments from "The Mechanics of n-Player Differentiable Games" and beyond

A course project by S. Pozdniakov, E. Trofimova, I. Bulygin, A. Lyzhov, K. Botashev

Introduction

The project is inspired by new approach for tackling the problem of finding game equilibriums, presented in The Mechanics of n−Player Differentiable Games [1].

We (1) reproduce multiple experiments from this paper, (2) develop techniques that are useful in the problem of finding equilibria when just a stochastic gradient approximation can be computed and (3) conduct a theoretical convergence analysis in case of games with quadratic loss functions

Code description

four_player_SGA.ipynb - convergence analysis of optimization methods on a simple four-player game from Appendix D in [1]

rock_paper_scissors.ipynb - analysis of dynamics of a rock-paper-scissors game

four_player_*.ipynb - reproduction of experiment in appendix D of [1]

reconstruction.py - reproduction of some experiments from main part of the paper

gan_experiments.ipynb - the effect of game dynamics on behavior of generator and beyond

final_distribution_numerical_experiments - some numerical experiments related to quadratic losses.

References

[1] The Mechanics of n−Player Differentiable Games