Source note2 min read
Parametric Open Source Games
Source
arXiv
arxiv.org/abs/2606.27068v1
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 paper introduces 'parametric open-source games', a continuous version of program equilibria in which players choose parameter vectors for their behavior. The authors establish equilibrium existence results, derive a threshold for cooperation 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 change learning dynamics and equilibrium structure.
What the Document Says
- The authors introduce parametric open-source games, a continuous version of program equilibria where players choose parameter vectors for their behavior.
- In this framework, semantics maps convert the full parameter profile into mixed actions in an underlying finite game.
- Equilibrium existence results are established.
- A threshold is derived at which selfish gradient ascent in symmetric 2x2 games switches from defection toward cooperation.
- A one-dimensional boundary test for parametric program Nash equilibria is given.
- The framework is extended to a neural semantics class whose first-order cooperation condition is governed by the ratio of cross-player to self-player sensitivity.
- The paper shows how access to internal parameterizations can change learning dynamics and equilibrium structure.
Key Concepts Mentioned
- parametric open-source games
- program equilibria
- mixed actions
- selfish gradient ascent
- 2x2 games
- Nash equilibria
- neural semantics
- learning dynamics
- equilibrium structure
Claims Made by the Document
- Parametric open-source games provide a continuous analogue of program equilibria.
- Selfish gradient ascent in symmetric 2x2 games switches from defection to cooperation at a certain threshold.
- A one-dimensional boundary test exists for parametric program Nash equilibria.
Evidence Used
- The authors present the framework and its properties in detail.
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.
