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

Neil Ghani; Clemens Kupke; Alasdair Lambert; Fredrik Nordvall Forsberg

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

Neil Ghani, Clemens Kupke, Alasdair Lambert, Fredrik Nordvall Forsberg

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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.

Original language	English
Pages	1-12
Number of pages	12
Publication status	Published - 15 Jul 2019
Event	Applied category theory conference 2019 - Oxford, United Kingdom Duration: 15 Jul 2019 → 19 Jul 2019 http://www.cs.ox.ac.uk/ACT2019/

Conference

Conference	Applied category theory conference 2019
Abbreviated title	ACT
Country/Territory	United Kingdom
City	Oxford
Period	15/07/19 → 19/07/19
Internet address	http://www.cs.ox.ac.uk/ACT2019/

Keywords

game theory
strategy
open games

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Ghani-etal-ACT2019-Compositional-game-theory-with-mixed-strategiesAccepted author manuscript, 438 KB

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title = "Compositional game theory with mixed strategies: probabilistic open games using a distributive law",

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.",

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AU - Kupke, Clemens

AU - Lambert, Alasdair

AU - Nordvall Forsberg, Fredrik

PY - 2019/7/15

Y1 - 2019/7/15

N2 - 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.

AB - 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.

KW - game theory

KW - strategy

KW - open games

UR - http://www.cs.ox.ac.uk/ACT2019/

M3 - Paper

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EP - 12

Y2 - 15 July 2019 through 19 July 2019

ER -

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

Abstract

Conference

Keywords

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