Compositional game theory

Neil Ghani, Julian Hedges, Viktor Winschel, Philipp Zahn

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

Abstract

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.
LanguageEnglish
Title of host publicationProceedings of the Symposium on Logic in Computer Science (LICS) 2018
Place of PublicationNew York
Number of pages10
DOIs
StatePublished - 12 Jul 2018

Fingerprint

Game theory
Economics
Computer science
Byproducts
Visualization
Chemical analysis

Keywords

  • game theory
  • open games
  • economic models
  • computation

Cite this

Ghani, N., Hedges, J., Winschel, V., & Zahn, P. (2018). Compositional game theory. In Proceedings of the Symposium on Logic in Computer Science (LICS) 2018 New York. DOI: 10.1145/3209108.3209165
Ghani, Neil ; Hedges, Julian ; Winschel, Viktor ; Zahn, Philipp. / Compositional game theory. Proceedings of the Symposium on Logic in Computer Science (LICS) 2018. New York, 2018.
@inproceedings{e257116a94ee4ab4b0ba2feac3ea36c5,
title = "Compositional game theory",
abstract = "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.",
keywords = "game theory, open games, economic models, computation",
author = "Neil Ghani and Julian Hedges and Viktor Winschel and Philipp Zahn",
year = "2018",
month = "7",
day = "12",
doi = "10.1145/3209108.3209165",
language = "English",
booktitle = "Proceedings of the Symposium on Logic in Computer Science (LICS) 2018",

}

Ghani, N, Hedges, J, Winschel, V & Zahn, P 2018, Compositional game theory. in Proceedings of the Symposium on Logic in Computer Science (LICS) 2018. New York. DOI: 10.1145/3209108.3209165

Compositional game theory. / Ghani, Neil; Hedges, Julian; Winschel, Viktor; Zahn, Philipp.

Proceedings of the Symposium on Logic in Computer Science (LICS) 2018. New York, 2018.

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

TY - GEN

T1 - Compositional game theory

AU - Ghani,Neil

AU - Hedges,Julian

AU - Winschel,Viktor

AU - Zahn,Philipp

PY - 2018/7/12

Y1 - 2018/7/12

N2 - 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.

AB - 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.

KW - game theory

KW - open games

KW - economic models

KW - computation

U2 - 10.1145/3209108.3209165

DO - 10.1145/3209108.3209165

M3 - Conference contribution

BT - Proceedings of the Symposium on Logic in Computer Science (LICS) 2018

CY - New York

ER -

Ghani N, Hedges J, Winschel V, Zahn P. Compositional game theory. In Proceedings of the Symposium on Logic in Computer Science (LICS) 2018. New York. 2018. Available from, DOI: 10.1145/3209108.3209165