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Game theoretical modelling of a dynamically evolving network I: general target sequences

Broom, M. and Cannings, C. (2017). Game theoretical modelling of a dynamically evolving network I: general target sequences. Journal of Dynamics and Games, 4(4), pp. 285-318. doi: 10.3934/jdg.2017016

Abstract

Animal (and human) populations contain a finite number of individuals with social and geographical relationships which evolve over time, at least in part dependent upon the actions of members of the population. These actions are often not random, but chosen strategically. In this paper we introduce a game-theoretical model of a population where the individuals have an optimal level of social engagement, and form or break social relationships strategically to obtain the correct level. This builds on previous work where individuals tried to optimise their number of connections by forming or breaking random links; the difference being that here we introduce a truly game-theoretic version where they can choose which specific links to form/break. This is more realistic and makes a significant difference to the model, one consequence of which is that the analysis is much more complicated. We prove some general results and then consider a single example in depth.

Publication Type: Article
Additional Information: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Journal of Dynamics and Games following peer review. The definitive publisher-authenticated version Broom, M. & Cannings, C. (2017). Game theoretical modelling of a dynamically evolving network I: general target sequences. Journal of Dynamics and Games, 4(4), pp. 285-318. is available online at: http://dx.doi.org/10.3934/jdg.2017016
Publisher Keywords: degree preferences; graphic sequences; Markov process; stationary distribution; Nash equilibrium
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/17808
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