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 a continuous version of program equilibria in game theory. In these games, players choose parameter vectors that determine their actions. The authors establish equilibrium existence results, derive a threshold for cooperation vs defection in symmetric 2x2 games, and provide a test for parametric program Nash equilibria. They also extend the framework to neural semantics and show how it can reshape learning dynamics and equilibrium structure.

What the Document Says

• Parametric open-source games are introduced as a continuous version of program equilibria in game theory.
• In these games, players choose parameter vectors which determine their mixed actions in an underlying finite game through semantics maps.
• Equilibrium existence results are established for parametric open-source games.
• A coupling threshold is derived at which selfish gradient ascent in symmetric 2x2 games switches from defection towards cooperation.
• A one-dimensional boundary test for parametric program Nash equilibria is given.

Key Concepts Mentioned

• parametric open-source games
• game theory
• parameter vectors
• semantics maps
• equilibrium existence results
• coupling threshold
• selfish gradient ascent
• one-dimensional boundary test

Claims Made by the Document

• Parametric open-source games reshape learning dynamics and equilibrium structure.
• Sufficiently strong open-source coupling can steer selfish optimization towards cooperative outcomes.

Evidence Used

• Across canonical games, the framework shows how access to internal parameterizations can qualitatively reshape learning dynamics and equilibrium structure.
• The framework further demonstrates how sufficiently strong open-source coupling can steer selfish optimization toward cooperative outcomes.

Methods / Approach

UNKNOWN

Limitations Stated by the Authors

UNKNOWN

Limitations Noted by the Agent

Agent interpretation — not from the source.

UNKNOWN

Open Questions

UNKNOWN

Notes for Future Q&A

May include interpretation. Labeled where it does.

UNKNOWN

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.