The game-theoretical modelling of a dynamically evolving network: Revisiting the target sequence 111

Abstract

In previous work we considered a model of a dynamically evolving network of interactions between a group of individuals, where each individual has an optimum level of social engagement with other group members. A randomly selected individual will form or break a link to obtain the required number of contacts. These interactions were formulated as a graph realisation problem. This short paper considers a game-theoretical version of the model, where individuals strategically choose the specific link to form or break. This game is known from previous work to be very complex for all but almost trivial cases, with the exception of an example with three players considered by Broom and Cannings. We revisit this example and show that even this is more complex than previously thought. In this paper, we find a general expression for the payoff functions for all possible strategy combinations. In addition to the three Nash equilibria previously found, we find a set of six more. The considerations of all possibilities proves to be infeasible, leaving the possibility of more solutions open.