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.
Highlights
With the growth of the internet and digital economy, it is becoming increasingly important to understand how the way individuals interact relates to the structure of the network connecting them
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
In [4] we introduced eight reproducing graph models within which graphs grow because their vertices reproduce
Summary
With the growth of the internet and digital economy, it is becoming increasingly important to understand how the way individuals interact relates to the structure of the network connecting them. That many real world networks, such as the internet, ecosystems, economies and social networks, are highly dynamic and often change in response to strategic decisions of vertices To study this issue we propose a class of models where networks grow in a way that depends upon the strategic interactions of the vertices within. Looking at these systems we can ask a different question how does the behaviour of the players affect the topology of the network?. The difference between this work and ours is that our models were not explicitly designed to promote self replication This fascinating behaviour arose unexpectedly as a result of our biologically inspired rules
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