Some Models of Reproducing Graphs: III Game Based Reproduction

Abstract

Many real world networks change over time. This may arise due to individuals joining or leaving the network or due to links forming or being broken. These events may arise because of interactions between the vertices which occasion payoffs which subsequently determine the fate of the vertices, due to ageing or crowding, or perhaps due to isolation. Such phenomena result in a dynamical system which may lead to complex behaviours, to selfreplication, to chaotic or regular patterns, or to emergent phenomena from local interactions. They hopefully give insight to the nature of the real-world phenomena which the network, and its dynamics, may approximate. To a large extent the models considered here are motivated by biological and social phenomena, where the vertices may be genes, proteins, genomes or organisms, and the links interactions of various kinds. In this, the third paper of a series, we consider the vertices to be players of some game. Offspring inherit their parent’s strategies and vertices which behave poorly in games with their neighbours get destroyed. The process is analogous to the way different kinds of animals reproduce whilst unfit animals die. Some game based systems are analytically tractable, others are highly complex-causing small initial structures to grow and break into large collections of self replicating structures.