Compositional Game Theory, compositionally

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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.
Original languageEnglish
Number of pages27
Publication statusPublished - 6 Jul 2020
EventApplied Category Theory 2020 -
Duration: 6 Jul 202010 Jul 2020


ConferenceApplied Category Theory 2020
Abbreviated titleACT 2020
Internet address


  • compositional game theory (CGT)
  • equilibria
  • Arrow
  • compositional approach


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