https://github.com/bmorphism/open-games-agda
A formalization of open games in Agda, building on lenses and Markov categories
https://github.com/bmorphism/open-games-agda
Last synced: 4 months ago
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A formalization of open games in Agda, building on lenses and Markov categories
- Host: GitHub
- URL: https://github.com/bmorphism/open-games-agda
- Owner: bmorphism
- Created: 2024-12-22T11:14:07.000Z (over 1 year ago)
- Default Branch: main
- Last Pushed: 2024-12-22T11:16:29.000Z (over 1 year ago)
- Last Synced: 2025-11-30T01:56:14.830Z (7 months ago)
- Language: Agda
- Size: 1.95 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Open Games in Agda
A formal development of compositional game theory using dependent types in Agda. This repository provides a categorical foundation for open games, building on lenses and Markov categories.
## Core Concepts
1. **Lenses and Optics** - Fundamental building blocks for composable state manipulation
2. **Markov Categories** - Categorical semantics for probabilistic computations
3. **Open Games** - Games as morphisms with composable strategies
4. **Equilibria** - Nash equilibria and best response maps in a categorical setting
## Project Structure
```
src/
Games/
Core/
Lens.agda -- Basic lens definitions
Optic.agda -- General optic framework
Category.agda -- Category theory foundations
Markov/
Core.agda -- Markov category definition
Composition.agda -- Composition of Markov kernels
OpenGames/
Definition.agda -- Core open game definition
Composition.agda -- Game composition
Examples/
Matching.agda -- Matching game examples
Bargaining.agda -- Bargaining game examples
Equilibrium/
Nash.agda -- Nash equilibrium definition
BestResponse.agda -- Best response maps
```
## Getting Started
This development requires:
- Agda 2.6.3 or later
- Standard library version 1.7.2 or later
To build:
```bash
agda --safe src/Games/OpenGames/Definition.agda
```
## References
1. Hedges, J. (2018). Morphisms of open games
2. Ghani, N., et al. (2018). Compositional game theory
3. Fritz, T. (2020). A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics
## Contributing
See CONTRIBUTING.md for guidelines on how to contribute to this formalization.