Game-theoretical modelling of a dynamically evolving network

Mark  Broom, City, University of London, UK

 

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 talk 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 or 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 discuss some general results and then focus on a particular example.