Compositional Game Theory with Mixed Strategies: Probabilistic Open Games Using a Distributive Law

Neil Ghani
(University of Strathclyde)
Clemens Kupke
(University of Strathclyde)
Alasdair Lambert
(University of Strathclyde)
Fredrik Nordvall Forsberg
(University of Strathclyde)

We extend the open games framework for compositional game theory to encompass also mixed strategies, making essential use of the discrete probability distribution monad. We show that the resulting games form a symmetric monoidal category, which can be used to compose probabilistic games in parallel and sequentially. We also consider morphisms between games, and show that intuitive constructions give rise to functors and adjunctions between pure and probabilistic open games.

In John Baez and Bob Coecke: Proceedings Applied Category Theory 2019 (ACT 2019), University of Oxford, UK, 15-19 July 2019, Electronic Proceedings in Theoretical Computer Science 323, pp. 95–105.
Published: 15th September 2020.

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