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

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

Research output: Contribution to conference › Paper

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.
LanguageEnglish
Pages1-12
Number of pages12
Publication statusPublished - 15 Jul 2019
EventApplied category theory conference 2019 - Oxford, United Kingdom
Duration: 15 Jul 2019 → 19 Jul 2019
http://www.cs.ox.ac.uk/ACT2019/

Conference

ConferenceApplied category theory conference 2019
Abbreviated titleACT
CountryUnited Kingdom
CityOxford
Period15/07/19 → 19/07/19
Internet address

Fingerprint

Game theory
Probability distributions

Keywords

  • game theory
  • strategy
  • open games

Cite this

Ghani, Neil ; Kupke, Clemens ; Lambert, Alasdair ; Nordvall Forsberg, Fredrik. / Compositional game theory with mixed strategies : probabilistic open games using a distributive law. Paper presented at Applied category theory conference 2019, Oxford, United Kingdom.12 p.
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Ghani, N, Kupke, C, Lambert, A & Nordvall Forsberg, F 2019, 'Compositional game theory with mixed strategies: probabilistic open games using a distributive law' Paper presented at Applied category theory conference 2019, Oxford, United Kingdom, 15/07/19 - 19/07/19, pp. 1-12.

Compositional game theory with mixed strategies : probabilistic open games using a distributive law. / Ghani, Neil; Kupke, Clemens; Lambert, Alasdair; Nordvall Forsberg, Fredrik.

2019. 1-12 Paper presented at Applied category theory conference 2019, Oxford, United Kingdom.

Research output: Contribution to conference › Paper

TY - CONF

T1 - Compositional game theory with mixed strategies

T2 - probabilistic open games using a distributive law

AU - Ghani, Neil

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

SP - 1

EP - 12

ER -

Ghani N, Kupke C, Lambert A, Nordvall Forsberg F. Compositional game theory with mixed strategies: probabilistic open games using a distributive law. 2019. Paper presented at Applied category theory conference 2019, Oxford, United Kingdom.

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