{"title":"Game theoretical modelling of a dynamically evolving network Ⅱ: Target sequences of score 1","authors":"C. Cannings, M. Broom","doi":"10.3934/jdg.2020003","DOIUrl":null,"url":null,"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.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"1 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Dynamics and Games","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/jdg.2020003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 5
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.
期刊介绍:
The Journal of Dynamics and Games (JDG) is a pure and applied mathematical journal that publishes high quality peer-review and expository papers in all research areas of expertise of its editors. The main focus of JDG is in the interface of Dynamical Systems and Game Theory.