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.

翻译：近年来，随着前沿人工智能的发展，我们观察到开源与闭源决策中呈现出特定动态。本文提出一个博弈论模型，用于分析当前人工智能竞赛格局下的这些动态。我们的模型建立在赢家通吃环境下的研发竞赛框架之上，并涵盖了参与者采取离散或连续行动（例如部分开源，如开放权重）的情形。研究表明，判定离散纯非平凡纳什均衡的存在性在一般情况下是NP难的，但我们可以将离散纳什存在性计算转化为混合整数规划（MIP）问题，从而使得使用标准MIP求解器处理小规模实例变得可行。接着，我们证明了问题连续版本中纯纳什均衡的存在性与可解性，并借助标准凸分析结果构建了等价的MIP公式。在整个研究过程中，我们利用主要技术成果及相关技术分析，得出了具有社会意义的见解。我们认为这些见解既有助于理解已有的决策与动态，也可能为制定新政策提供参考。