Why Open Source? A Game-Theoretic Analysis of the AI Race

TL;DR

This paper models the open-source versus closed-source decisions in AI development as a game-theoretic problem, analyzing equilibrium existence and computational tractability to inform policy and strategic choices.

Contribution

It introduces a novel game-theoretic framework for AI open-sourcing decisions, analyzing equilibrium existence and computational methods for both discrete and continuous actions.

Findings

Discrete pure Nash equilibrium existence is NP-hard but can be approximated with MIP.

Pure Nash equilibria in the continuous case are tractable and can be formulated as MIP.

Insights derived can inform policy and strategic decisions in AI development.

Abstract

In recent years, with the advancement of frontier AI, we have observed certain dynamics in open-sourcing and closed-sourcing decisions. We propose a game-theoretic model to analyze these dynamics in the current landscape of the AI race. Our model builds on an R&D race framework under a winner-takes-all setting, and it accounts for the cases where the players' actions can be either discrete or continuous (i.e., partial open-sourcing, such as open weights). We show that determining the existence of a discrete pure non-trivial Nash equilibrium is NP-hard in general but that we can transform the discrete Nash existence computation into a MIP (Mixed-Integer Programming) problem, making it tractable for small instances using a standard MIP solver. Next, we show the existence and tractability of pure Nash equilibria in the continuous version of our problem, leveraging standard convex analysis results, and constructing an equivalent MIP formulation. Throughout this work, we leverage both our main technical results as well as surrounding technical analysis, to derive socially relevant insights that we believe can serve both to understand already existing decisions and dynamics and to potentially inform new policies.