Compositional game theory with mixed strategies : probabilistic open games using a distributive law

Ghani, Neil and Kupke, Clemens and Lambert, Alasdair and Nordvall Forsberg, Fredrik (2019) Compositional game theory with mixed strategies : probabilistic open games using a distributive law. In: Applied category theory conference 2019, 2019-07-15 - 2019-07-19.

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    Abstract

    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.