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Game theoretical modelling of a dynamically evolving network Ⅱ: Target sequences of score 1

Cannings, C. and Broom, M. ORCID: 0000-0002-1698-5495 (2019). Game theoretical modelling of a dynamically evolving network Ⅱ: Target sequences of score 1. Journal of Dynamics & Games, doi: 10.3934/jdg.2020003

Abstract

In previous work we considered a model of a population where individuals have an optimum level of social interaction, governed by a graph representing social connections between the individuals, who formed or broke those links to achieve their target number of contacts. In the original work an improvement in the number of links was carried out by breaking or joining to a randomly selected individual. In the most recent work, however, these actions were often not random, but chosen strategically, and this led to significant complications. One of these was that in any state, multiple individuals might wish to change their number of links. In this paper we consider a systematic analysis of the structure of the simplest class of non-trivial cases, where in general only a single individual has reason to make a change, and prove some general results. We then consider in detail an example game, and introduce a method of analysis for our chosen class based upon cycles on a graph. We see that whilst we can gain significant insight into the general structure of the state space, the analysis for specific games remains difficult.

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 Cannings, C. and Broom, M. (2019). Game theoretical modelling of a dynamically evolving network Ⅱ: Target sequences of score 1. Journal of Dynamics & Games, is available online at: http://dx.doi.org/10.3934/jdg.2020003
Publisher Keywords: Degree preferences, graphic sequences, Nash equilibrium, Markov process, stationary distribution
Subjects: H Social Sciences > HB Economic Theory
Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
Date Deposited: 23 Jan 2020 08:43
URI: https://openaccess.city.ac.uk/id/eprint/23536
[img] Text - Accepted Version
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