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Compositionality and String Diagrams for Game Theory
[article]
2016
arXiv
pre-print
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We introduce string diagrams as a formal mathematical, graphical language to represent, compose, program and reason about games. ...
We apply this language to the game theoretical setting and show examples how to use it for some economic games where we highlight the compositional nature of our higher-order game theory. ...
We establish a close connection between the formal theory and the computer code: The string diagrams are directly translatable into the functional programming language Haskell. 4. ...
arXiv:1604.06061v1
fatcat:kdgsbheltfekfmxcux65s5iuve
Compositional game theory
[article]
2018
arXiv
pre-print
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Open games can be represented by string diagrams which provide an intuitive but formal visualisation of the information flows. ...
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. ...
STRING DIAGRAMS We will now informally present the string diagram language for open games. ...
arXiv:1603.04641v3
fatcat:bwojrkwqejhrhnybd6hozyh4ui
Compositional Game Theory
2018
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '18
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Open games can be represented by string diagrams which provide an intuitive but formal visualisation of the information lows. ...
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. ...
String diagrams We will now informally present the string diagram language for open games. ...
doi:10.1145/3209108.3209165
dblp:conf/lics/GhaniHWZ18
fatcat:hikh4nmqijfmrmsjtjafcro2bm
The algebra of predicting agents
[article]
2018
arXiv
pre-print
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The category of open games, which provides a strongly compositional foundation of economic game theory, is intermediate between symmetric monoidal and compact closed. ...
We explore the algebraic properties of these agents via the symmetric monoidal bicategory whose 2-cells are morphisms between open games, and show how the resulting structure approximates a compact closed ...
A general open game G : (X, S) → (Y, R) is denoted by a string diagram of the form X Y R S G In the string diagram language, a set on the left of a pair always labels a wire pointing forwards, and a set ...
arXiv:1803.10131v1
fatcat:s7qnn4l4vbbonamsm544rg2eya
Composing games into complex institutions
[article]
2021
arXiv
pre-print
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Game theory is used by all behavioral sciences, but its development has long centered around tools for relatively simple games and toy systems, such as the economic interpretation of equilibrium outcomes ...
Our contribution, compositional game theory, permits another approach of equally general appeal: the high-level design of large games for expressing complex architectures and representing real-world institutions ...
JT acknowledges members of the Morgenstern workshop at the Mercatus Center, especially Katherine Wright and Ginny Choi, for their feedback and support. ...
arXiv:2108.05318v1
fatcat:73rqnprdwvf6jdq3eyxfbzdfwm
The game semantics of game theory
[article]
2020
arXiv
pre-print
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We use a reformulation of compositional game theory to reunite game theory with game semantics, by viewing an open game as the System and its choice of contexts as the Environment. ...
The goal of the system is to play a Nash equilibrium, and the goal of the environment is to prevent it. ...
Compositional game theory [Hed16, GHWZ18] , as its name suggests, is an attempt to introduce the principle of compositionality into game theory, motivated by practical concerns about modelling large ( ...
arXiv:1904.11287v2
fatcat:chm2th4sfrfq3fin6sgvzhgn6i
Compositional Abstraction Error and a Category of Causal Models
[article]
2021
arXiv
pre-print
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We introduce a category of finite interventional causal models and, leveraging theory of enriched categories, prove the desired compositionality properties for our framework. ...
Here, we argue that compositionality is a desideratum for such model transformations and the associated errors: When abstracting a reference model M iteratively, first obtaining M' and then further simplifying ...
Acknowledgements We thank the anonymous reviewers for their constructive comments that helped improve the interdisciplinary presentation. SW was supported by the Carlsberg Foundation. ...
arXiv:2103.15758v2
fatcat:v72erh5skbe47bl7jy6o4awdi4
Towards Functorial Language-Games
[article]
2018
arXiv
pre-print
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We illustrate the theory using simple examples of Wittgenstein's language-games. ...
We compositionally build game-theoretic semantics of sentences by taking the semantic category to be the category whose morphisms are open games. ...
We denote ε X by the string diagram X X Given a set X , we write X for X 1 and X for 1 X . ...
arXiv:1807.07828v1
fatcat:nbnwd5rjmfawbl3dujmuunikky
Categorial Compositionality III: F-(co)algebras and the Systematicity of Recursive Capacities in Human Cognition
2012
PLoS ONE
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Thus, many species (and infants) can employ recursive processes without having a full-blown capacity for number and language. ...
Citation: Phillips S, Wilson WH (2012) Categorial Compositionality III: F-(co)algebras and the Systematicity of Recursive Capacities in Human Cognition. PLoS ONE 7(4): e35028. ...
eDabS for tailembedded sentences, and S?eDaSb for center-embedded sentences, where e is the symbol for the empty string. ...
doi:10.1371/journal.pone.0035028
pmid:22514704
pmcid:PMC3325926
fatcat:b47temdl5bejlb57o4mhgp75de
The Emergence of Compositional Languages for Numeric Concepts Through Iterated Learning in Neural Agents
[article]
2019
arXiv
pre-print
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In this work, we explore the emergence of compositional languages for numeric concepts in multi-agent communication systems. ...
We demonstrate that compositional language for encoding numeric concepts can emerge through iterated learning in populations of deep neural network agents. ...
Figure 1 : Sketch diagram of the Bag-Select game. The speaker observes a bag of objects of distinct types. ...
arXiv:1910.05291v1
fatcat:ugmj2ddqkzgatcqx66ojuls6gu
How to make qubits speak
[article]
2021
arXiv
pre-print
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landscape, including our account on the notion of compositionality. ...
We also provide some guidance for the actual execution, so that the reader can give it a go as well. ...
game theory [38, 30] , and even in cognition [65, 61] . ...
arXiv:2107.06776v1
fatcat:lfkqyncqvbewva675pv5gshy3i
Coherence for lenses and open games
[article]
2017
arXiv
pre-print
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Categories of polymorphic lenses in computer science, and of open games in compositional game theory, have a curious structure that is reminiscent of compact closed categories, but differs in some crucial ...
We precisely define a diagrammatic language suitable for these categories, and prove a coherence theorem for them. ...
Circuit diagrams and string diagrams In this paper we following the naming convention of Coecke, using the term 'string diagram' to refer specifically to diagrams for compact closed categories, and refer ...
arXiv:1704.02230v3
fatcat:qmpxatvex5g5lddkjuxhh3x4ci
Games on graphs: a compositional approach
[article]
2020
arXiv
pre-print
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As well as being relevant in computer science, mathematical analysis and computer simulations of such distributed games are vital methodologies in economics, politics and epidemiology, amongst other fields ...
As well as introducing the theoretical framework, we identify some applications of compositionality. ...
This is also more clearly seen with the string diagrams. ...
arXiv:2006.03493v1
fatcat:shlh3cdhibap3lc2twnlepmguy
Coalgebraic Semantics of Reflexive Economics (Dagstuhl Seminar 15042)
2015
Dagstuhl Reports
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This report documents the program and the outcomes of Dagstuhl Seminar 15042 "Coalgebraic ...
a category whose morphisms are suitably generalised games) and a graphical notation based on string diagrams in quantum information theory. ...
The tools of compositionality that lend themselves into suitable approaches to network theory do also allow for a unified approach to the theory of optimal currency areas and money theory. ...
doi:10.4230/dagrep.5.1.197
dblp:journals/dagstuhl-reports/AbramskyKLW15
fatcat:bfot4e2lbjh5tarbfps4qzrsmy
The Structure of First-Order Causality (extended version)
[article]
2011
arXiv
pre-print
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Here, we present an original methodology to achieve this task, which requires to combine advanced tools from game semantics, rewriting theory and categorical algebra. ...
This work thus bridges algebra and denotational semantics in order to reveal the structure of dependencies induced by first-order quantifiers, and lays the foundations for a mechanized analysis of causality ...
I would like to thank Martin Hyland and Paul-André Melliès, as well as John Baez, Albert Burroni, Jonas Frey, Yves Guiraud, Yves Lafont, François Métayer and Luke Ong, for the lively discussion we had, ...
arXiv:1101.4813v1
fatcat:qgb6vjs7gbdurfh3aq6iwinh3u
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