Parametric Open Source Games

Source

• Source name: arXiv
• Source kind: paper
• Authors / organization: Aleksandar Todorov, Jesse ten Napel, Alexander Müller
• Venue: arXiv: cs.GT
• Published: 2026-06-25
• Collected: 2026-06-26
• URL: http://arxiv.org/abs/2606.27068v1
• PDF: https://arxiv.org/pdf/2606.27068v1
• DOI: UNKNOWN

Plain-Language Brief

The authors introduce a new concept called parametric open-source games, which are continuous versions of game equilibria where players choose parameter vectors to determine their actions in an underlying finite game. They provide theoretical results about the existence of equilibria, switching between defection and cooperation during learning, and a test for parametric program Nash equilibria.

What the Document Says

• The authors introduce parametric open-source games, which are continuous versions of program equilibria in game theory.
• In these games, players choose parameter vectors and semantics maps convert the full parameter profile into mixed actions in an underlying finite game.
• They establish equilibrium existence results for these games.
• The authors derive a coupling threshold at which selfish gradient ascent in symmetric 2x2 games switches from defection toward cooperation.
• They provide a one-dimensional boundary test for parametric program Nash equilibria.
• The framework also extends to a neural semantics class with first-order cooperation condition governed by the ratio of cross-player to self-player sensitivity.

Key Concepts Mentioned

• parametric open-source games
• game theory
• equilibrium existence results
• selfish gradient ascent
• 2x2 games
• neural semantics class

Claims Made by the Document

• Parametric open-source games offer a continuous analogue of program equilibria in game theory.
• Selfish gradient ascent switches from defection to cooperation at a certain coupling threshold in symmetric 2x2 games.
• There is a one-dimensional boundary test for parametric program Nash equilibria.

Evidence Used

• The text describes the introduction of the new concept and provides details about its properties.

Methods / Approach

• Mathematical modeling and analysis

Limitations Stated by the Authors

UNKNOWN

Limitations Noted by the Agent

Agent interpretation — not from the source.

The limitations or assumptions made by the authors are not explicitly stated in the provided text.

Open Questions

• What specific games does the authors test their framework on?

Notes for Future Q&A

May include interpretation. Labeled where it does.

The text provides theoretical results, but it is unclear if the authors tested their framework on specific games or scenarios.

Raw Abstract / Excerpt

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.