Compositional game theory

Neil Ghani, Julian Hedges, Viktor Winschel, Philipp Zahn

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

41 Citations (Scopus)
81 Downloads (Pure)


We introduce open games as a compositional foundation of economic game theory. A compositional approach potentially allows methods of game theory and theoretical computer science to be applied to large-scale economic models for which standard economic tools are not practical. An open game represents a game played relative to an arbitrary environment and to this end we introduce the concept of coutility, which is the utility generated by an open game and returned to its environment. Open games are the morphisms of a symmetric monoidal category and can therefore be composed by categorical composition into sequential move games and by monoidal products into simultaneous move games. Open games can be represented by string diagrams which provide an intuitive but formal visualisation of the information flows.We show that a variety of games can be faithfully represented as open games in the sense of having the same Nash equilibria and off-equilibrium best responses.
Original languageEnglish
Title of host publicationLICS '18
Subtitle of host publicationProceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science
Place of PublicationNew York
Number of pages10
Publication statusPublished - 12 Jul 2018


  • game theory
  • open games
  • economic models
  • computation


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