Compositional Game Theory, Compositionally - Archive ouverte HAL
Communication Dans Un Congrès Année : 2021

Compositional Game Theory, Compositionally

Résumé

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.
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hal-04470659 , version 1 (26-02-2024)

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Robert Atkey, Bruno Gavranović, Neil Ghani, Clemens Kupke, Jérémy Ledent, et al.. Compositional Game Theory, Compositionally. 3rd international Applied Category Theory Conference, Jul 2020, Online, United States. pp.198 - 214, ⟨10.4204/eptcs.333.14⟩. ⟨hal-04470659⟩
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