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Compositional Modelling of Network Games

Authors Elena Di Lavore , Jules Hedges, Paweł Sobociński

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Subject Classification

ACM Subject Classification
  • Theory of computation → Categorical semantics
Keywords
  • game theory
  • category theory
  • network games
  • open games
  • open graphs
  • compositionality

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Abstract

The analysis of games played on graph-like structures is of increasing importance due to the prevalence of social networks, both virtual and physical, in our daily life. 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. Our contribution is to give compositional semantics of a family of such games as a well-behaved mapping, a strict monoidal functor, from a category of open graphs (syntax) to a category of open games (semantics). As well as introducing the theoretical framework, we identify some applications of compositionality.

Cite As Get BibTex

Elena Di Lavore, Jules Hedges, and Paweł Sobociński. Compositional Modelling of Network Games. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 30:1-30:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.CSL.2021.30

Author Details

Elena Di Lavore
  • Department of Software Science, Tallinn University of Technology, Estonia
Jules Hedges
  • Department of Computer and Information Sciences, University of Strathclyde, Glasgow, UK
Paweł Sobociński
  • Department of Software Science, Tallinn University of Technology, Estonia

Funding

Elena Di Lavore and Paweł Sobociński are supported by the ESF funded Estonian IT Academy research measure (project 2014-2020.4.05.19-0001).

References

  1. John C Baez and Brendan Fong. A compositional framework for passive linear networks, 2015. arXiv preprint: URL: https://arxiv.org/abs/1504.05625.
  2. Joe Bolt, Jules Hedges, and Philipp Zahn. Bayesian open games, 2019. arXiv preprint: URL: https://arxiv.org/abs/1910.03656.
  3. Filippo Bonchi, Fabio Gadducci, Aleks Kissinger, Pawel Sobocinski, and Fabio Zanasi. Rewriting modulo symmetric monoidal structure. In Martin Grohe, Eric Koskinen, and Natarajan Shankar, editors, Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS '16, New York, NY, USA, July 5-8, 2016, pages 710-719. ACM, 2016. URL: https://doi.org/10.1145/2933575.2935316.
  4. Filippo Bonchi, Pawel Sobocinski, and Fabio Zanasi. The calculus of signal flow diagrams I: linear relations on streams. Inf. Comput., 252:2-29, 2017. URL: https://doi.org/10.1016/j.ic.2016.03.002.
  5. Yann Bramoullé, Andrea Galeotti, and Brian Rogers. The Oxford handbook of the economics of networks. Oxford University Press, 2016. Google Scholar
  6. Roberto Bruni, Hernán C. Melgratti, and Ugo Montanari. A connector algebra for P/T nets interactions. In Concurrency Theory (CONCUR `11), volume 6901 of LNCS, pages 312-326. Springer, 2011. URL: https://doi.org/10.1007/978-3-642-23217-6_21.
  7. Apiwat Chantawibul and Paweł Sobociński. Towards compositional graph theory. In Proceedings of MFPS'15, volume 319 of ENTCS, pages 121-136, 2015. URL: https://doi.org/10.1016/j.entcs.2015.12.009.
  8. J. R. B. Cockett and R. A. G. Seely. Linearly distributive functors. Journal of Pure and Applied Algebra, 143(1-3):155-203, 1999. Google Scholar
  9. Brendan Fong. Decorated cospans. Theory and Applications of Categories, 30(33):1096-1120, 2015. Google Scholar
  10. James H Fowler and Nicholas A Christakis. Dynamic spread of happiness in a large social network: longitudinal analysis over 20 years in the framingham heart study. BMJ, 337, 2008. URL: https://doi.org/10.1136/bmj.a2338.
  11. Andrea Galeotti. Talking, searching and pricing. International Economic Review, 51(4):1159-1174, 2010. URL: https://doi.org/10.1111/j.1468-2354.2010.00614.x.
  12. Andrea Galeotti, Benjamin Golub, and Sanjeev Goyal. Targeting interventions in networks. Forthcoming in Econometrica, 2019. Google Scholar
  13. Neil Ghani, Jules Hedges, Viktor Winschel, and Philipp Zahn. Compositional game theory. In Proceedings of Logic in Computer Science (LiCS) 2018. ACM, 2018. URL: https://doi.org/10.1145/3209108.3209165.
  14. Matthew Jackson and Yves Zenou. Games on networks. In Handbook of game theory with economic applications, volume 4, chapter 3, pages 95-163. Elsevier, 2015. URL: https://doi.org/10.1016/B978-0-444-53766-9.00003-3.
  15. Stephen Lack. Composing PROPs. Theor. App. Categories, 13(9):147-163, 2004. Google Scholar
  16. Qiu Li, MingChu Li, Lin Lv, Cheng Guo, and Kun Lu. A new prediction model of infectious diseases with vaccination strategies based on evolutionary game theory. Chaos, Solitons & Fractals, 104:51-60, 2017. URL: https://doi.org/10.1016/j.chaos.2017.07.022.
  17. Saunders Mac Lane. Categorical algebra. Bull. Amer. Math. Soc., 71:40-106, 1965. Google Scholar
  18. Saunders Mac Lane. Categories for the Working Mathematician. Springer-Verlag New York, 1978. Google Scholar
  19. Frank Joseph Oles. A Category-theoretic Approach to the Semantics of Programming Languages. PhD thesis, Syracuse University, Syracuse, NY, USA, 1982. AAI8301650. Google Scholar
  20. Alfred Tarski. The concept of truth in the languages of the deductive sciences. Prace Towarzystwa Naukowego Warszawskiego, Wydzial III Nauk Matematyczno-Fizycznych, 34(13-172):198, 1933. Google Scholar
  21. Alfred Tarski and Robert L Vaught. Arithmetical extensions of relational systems. Compositio mathematica, 13:81-102, 1957. Google Scholar
  22. Giorgio Topa. Social Interactions, Local Spillovers and Unemployment. The Review of Economic Studies, 68(2):261-295, April 2001. URL: https://doi.org/10.1111/1467-937X.00169.
  23. Glynn Winskel. The formal semantics of programming languages: an introduction. MIT press, 1993. Google Scholar
  24. Fabio Zanasi. Interacting Hopf Algebras: the theory of linear systems. PhD thesis, École Normale Supérieure, 2015. Google Scholar
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