Some Models of Reproducing Graphs: III Game Based Reproduction

Richard Southwell; Chris Cannings

doi:10.4236/am.2010.15044

Home > Journals > Physics & Mathematics > AM

Applied Mathematics > Vol.1 No.5, November 2010

Some Models of Reproducing Graphs: III Game Based Reproduction ()

Richard Southwell, Chris Cannings

DOI: 10.4236/am.2010.15044 PDF HTML 5,423 Downloads 9,802 Views Citations

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.

Keywords

Reproduction, Graph, Network, Game, Replication

Share and Cite:

R. Southwell and C. Cannings, "Some Models of Reproducing Graphs: III Game Based Reproduction," Applied Mathematics, Vol. 1 No. 5, 2010, pp. 335-343. doi: 10.4236/am.2010.15044.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	M. Nowak and R. May, “Evolutionary Games and Spatial Chaos,” Nature, Vol. 359, No. 6398, 1992, pp. 826-829.
[2]	R. Southwell and C. Cannings, “Best Response Games on Regular Graphs,” Under Review, 2010.
[3]	F. Santos, J. Pacheco and T. Lenaerts, “Evolutionary Dynamics of Social Dilemmas in Structured Heterogeneous Populations,” Proceedings of the National Academy of Sciences of the United States of America, Iowa, Vol. 103, 2006, pp. 3490-3494.
[4]	R. Southwell and C. Cannings, “Some Models of Reproducing Graphs: I Pure Reproduction,” Applied Mathematics, Vol. 1, No. 3, 2010, pp. 137-145.
[5]	R. Southwell and C. Cannings, “Some Models of Reproducing Graphs: II Age Capped Vertices,” Applied Mathematics, Vol. 1, No. 4, 2010, pp. 251-259.
[6]	R. Southwell and C. Cannings, “Games on Graphs that Grow Deterministically,” Proceedings of the 1st International Conference on Game Theory for Networks (GameNets), Istanbul, 13-15 May 2009.
[7]	H. Tomita, H. Kurokawa and S. Murata, “Automatic Generation of Self-Replicating Patterns in Graph Automata,” International Journal of Bifurcation and Chaos, Vol. 16, No. 4, 2006, pp. 1011-1018.
[8]	J. Jordan and R. Southwell, “Further Properties of Reproducing Graphs,” Under Review, 2010.