[2101.12045v1] Compositional Game Theory, Compositionally
Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Computer Science > Logic in Computer Science

arXiv:2101.12045v1 (cs)
[Submitted on 26 Jan 2021]

Title:Compositional Game Theory, Compositionally

Authors:Robert Atkey, Bruno Gavranović, Neil Ghani, Clemens Kupke, Jérémy Ledent, Fredrik Nordvall Forsberg
View PDF
Abstract: We present a new compositional approach to compositional game theory (CGT) based upon Arrows, a concept originally from functional programming, closely related to Tambara modules, and operators to build new Arrows from old. We model equilibria as a bimodule over an Arrow and define an operator to build a new Arrow from such a bimodule over an existing Arrow. We also model strategies as graded Arrows and define an operator which builds a new Arrow by taking the colimit of a graded Arrow. A final operator builds a graded Arrow from a graded bimodule. We use this compositional approach to CGT to show how known and previously unknown variants of open games can be proven to form symmetric monoidal categories.
Comments: In Proceedings ACT 2020, arXiv:2101.07888
Subjects: Logic in Computer Science (cs.LO); Category Theory (math.CT)
ACM classes: F.3.m
Cite as: arXiv:2101.12045 [cs.LO]
  (or arXiv:2101.12045v1 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.2101.12045
Journal reference: EPTCS 333, 2021, pp. 198-214
Related DOI: https://doi.org/10.4204/EPTCS.333.14

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Tue, 26 Jan 2021 00:06:15 UTC (37 KB)
Full-text links:

Access Paper:

view license
Current browse context:
cs.LO
< prev   |   next >
new | recent | 2021-01
Change to browse by:
cs
math
math.CT

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)