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Mathematical Problems in Engineering
Volume 2014, Article ID 730652, 8 pages
http://dx.doi.org/10.1155/2014/730652
Research Article

Matthew Effect of the Random Drift on the Evolution of Cooperation

1Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, China
2Department of Applied Mathematics, Shanghai Finance University, Shanghai 201209, China

Received 22 November 2013; Accepted 7 January 2014; Published 16 February 2014

Academic Editor: Wenwu Yu

Copyright © 2014 Chao Liu and Rong Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The effect of the random drift on the evolutionary prisoner’s dilemma game is studied on regular lattices. A new evolutionary rule is proposed, which stochastically combines the deterministic rule with the random drift rule. It is found that the random drift has an effect on the evolutionary dynamics depending on the values of the temptation-to-defect and the probability of the random drift. When the random drift occurs with low probabilities, which interests us more, a phenomenon of the Matthew effect on the evolution of cooperation is found. Explanations of this phenomenon are deduced through the analysis on the dynamics and pattern formations of the PDG system.