New 'Parametric Open Source Games' Framework Enables AI Cooperation via Continuous Parameters

Traditional open-source game theory models agents whose strategies depend on each other's decision procedures, but these typically rely on discrete or symbolic programs — limiting scalability and analytical tractability. In a new paper from ICML's NExT-Game workshop, Todorov, ten Napel, and Müller propose parametric open-source games, a continuous framework where each player selects a real-valued parameter vector. A semantics map converts the full parameter profile into a mixed strategy in an underlying finite game, enabling smooth optimization and gradient-based learning.

The authors establish equilibrium existence results and derive a precise coupling threshold for symmetric 2×2 games: below this threshold, selfish gradient ascent leads to mutual defection; above it, the dynamics naturally converge toward cooperation. They also provide a one-dimensional boundary test for identifying parametric program Nash equilibria. Extending to neural network semantics, they show that the first-order cooperation condition depends on the ratio of cross-player to self-player sensitivity — i.e., how much each agent's parameters influence others versus themselves. These results demonstrate that controlled access to internal parameterizations can fundamentally reshape multi-agent learning dynamics, steering otherwise self-interested optimization toward cooperative outcomes without explicit reward engineering. The work has implications for AI safety, multi-agent systems, and the design of cooperative artificial intelligence.