用连续参数建模开源游戏，揭示合作与背叛的临界条件。
Parametric Open Source Games
- 玩家选择参数向量，通过语义映射生成混合策略
- 对称2×2游戏中存在合作转向的精确耦合阈值
- 神经语义下合作由跨玩家敏感度决定，适合博弈学习研究
开源博弈论研究行为相互依赖的智能体，但现有模型多采用离散或符号程序。本文提出参数化开源博弈，作为程序均衡的连续类比：玩家选择参数向量，语义映射将完整参数配置转换为底层有限博弈中的混合行动。我们建立了均衡存在性结果，推导出对称2×2博弈中自私梯度上升从背叛转向合作的精确耦合阈值，并给出一维边界检验法判定参数化程序纳什均衡。进一步扩展至神经语义类，其一阶合作条件由跨玩家敏感度与自玩家敏感度之比决定。在典型博弈中，该框架揭示内部参数化可质变学习动态与均衡结构，且足够强的开源耦合能引导自私优化走向合作结果。
原文摘要 · Abstract (English)
Open-source game theory studies agents whose behavior may depend on one another's decision procedures, but most existing models use discrete or symbolic programs. We introduce parametric open-source games, a continuous analogue of program equilibria in which players choose parameter vectors and semantics maps convert the full parameter profile into mixed actions in an underlying finite game. We establish equilibrium existence results, derive an exact coupling threshold at which selfish gradient ascent in symmetric $2\times2$ games switches from defection toward cooperation, and give a one-dimensional boundary test for parametric program Nash equilibria. We further extend the framework to a neural semantics class whose first-order cooperation condition is governed by the ratio of cross-player to self-player sensitivity. Across canonical games, the framework shows how access to internal parameterizations can qualitatively reshape learning dynamics and equilibrium structure, and how sufficiently strong open-source coupling can steer selfish optimization toward cooperative outcomes.
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