Compositional Game Theory, compositionally

Atkey, Robert and Gavranović, Bruno and Ghani, Neil and Kupke, Clemens and Ledent, Jérémy and Nordvall Forsberg, Fredrik (2020) Compositional Game Theory, compositionally. In: Applied Category Theory 2020, 2020-07-06 - 2020-07-10.

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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 module over an Arrow and define an operator to build a new Arrow from such a module 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.

ORCID iDs

Atkey, Robert ORCID logoORCID: https://orcid.org/0000-0002-4414-5047, Gavranović, Bruno, Ghani, Neil ORCID logoORCID: https://orcid.org/0000-0002-3988-2560, Kupke, Clemens, Ledent, Jérémy ORCID logoORCID: https://orcid.org/0000-0001-7375-4725 and Nordvall Forsberg, Fredrik ORCID logoORCID: https://orcid.org/0000-0001-6157-9288;
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