Parametric Open Source Games

2026-06-25

AI Summary

This work addresses the limitations of traditional open-source game models in capturing strategic interactions among agents with continuous parameterizations. It introduces the first continuous-parameter open-source game framework, wherein players’ parameter vectors are semantically mapped to mixed strategies in finite games, enabling analysis of equilibria and learning dynamics. Key contributions include deriving an exact coupling threshold at which selfish gradient ascent transitions to cooperation in symmetric 2×2 games, proposing a one-dimensional boundary test for efficiently identifying Nash equilibria, and introducing the ratio of cross-player to self-player sensitivity as a first-order condition for cooperation. Experiments demonstrate that internal parameterization substantially alters learning dynamics, and strong open-source coupling can steer selfish optimization toward cooperative equilibria.

Abstract

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.

Problem

• open-source games
• program equilibria
• parameterized agents
• cooperation
• game theory

Innovation

• parametric open-source games
• program equilibrium
• gradient ascent
• neural semantics
• cooperation threshold