Compositional Game Theory, Compositionally
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.
Keywords
Cite
@article{arxiv.2101.12045,
title = {Compositional Game Theory, Compositionally},
author = {Robert Atkey and Bruno Gavranović and Neil Ghani and Clemens Kupke and Jérémy Ledent and Fredrik Nordvall Forsberg},
journal= {arXiv preprint arXiv:2101.12045},
year = {2021}
}
Comments
In Proceedings ACT 2020, arXiv:2101.07888