Effects of benefit-inspired network coevolution on spatial
reciprocity in the prisoner’s dilemma game
Lei Wang
a,b
, Juan Wang
c,
⇑
, Baohong Guo
a,b,
*
, Shuai Ding
d,e
, Yukun Li
a,b
, Chengyi Xia
a,b
a
Tianjin Key Laboratory of Intelligence Computing and Novel Software Technology, Tianjin University of Technology, Tianjin 300384, PR China
b
Key Laboratory of Computer Vision and System, Ministry of Education, Tianjin University of Technology, Tianjin 300384, PR China
c
School of Electrical Engineering, Tianjin University of Technology, Tianjin 300384, PR China
d
Key Laboratory of Process Optimization and Intelligent Decision-Making, Ministry of Education, Hefei University of Technology, Anhui Hefei 230009, PR China
e
School of Management, Hefei University of Technology, Anhui Hefei 230009, PR China
article info
Article history:
Received 17 January 2014
Accepted 26 April 2014
abstract
How to interpret the emergence and ubiquity of cooperation between selfish agents has
become a long-standing puzzle among the scientific communities. In this paper, we pro-
pose a co-evolutionary prisoner’s dilemma model to illustrate the evolution of cooperation,
in which the model evolution can be divided into two basic steps: (i) strategy update: all
agents play the game and perform the strategy update according to the Fermi rule; (ii)
topology adjustment: each agent can have a chance to prune the connection with a defect-
ing neighbor so as to decrease the potential benefit loss via an adjustment parameter (
a).
Large quantities of numerical simulation s indicate that the cooperation level in the station-
ary state will be highly elevated, w hen compared to the traditional prisoner’s dilemma
game on regular lattices. Meanwhile, we have also observed that the degree distribution
of network will be broadened or more skewed and structural heterogeneities will also
become higher when the dynamical adjustment of interaction topology is allowed during
the system evolution. In addition, it is also proven that the tunable parameter
a controls
the link reconnection process, and even the node elimination and reproduction so
that the whole cooperation level can be greatly influenced. Thus, the study points out a
suitable way for the sustainability of cooperation in structured populations, and current
findings are conducive to further understand the collective cooperation phenomenon
within many biological, social, economic and even man-made systems.
Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction
According to the principles of Darwinian natural elec-
tion, any behavior that brings benefits to others but not
directly to oneself will soon disappear [1]. However, this
theoretical prediction seems inconsistent with essential
observation that cooperative behavior is ubiquitous rang-
ing from the communities of microorganisms to animal
and human societies [2,3]. In this sense, elucidating the
evolution of cooperation among unrelated agents becomes
one of the major challenges in evolutionary biology and
behavioral sciences [4]. To date, evolutionary game theory
is a powerful mathematical tool for the analysis of this
long-standing puzzle in biological and social systems [5].
As a simple metaphor, the prisoner’s dilemma game has
attracted great attention, in both theoretical and experi-
mental literatures [6]. In its basic version, two players
simultaneously have the choice between cooperator and
defector. They both receive R under mutual cooperation
http://dx.doi.org/10.1016/j.chaos.2014.04.011
0960-0779/Ó 2014 Elsevier Ltd. All rights reserved.
⇑
Corresponding authors. Address: Tianjin Key Laboratory of Intelli-
gence Computing and Novel Software Technology, Tianjin University of
Technology, Tianjin 300384, PR China (B. Guo). Tel.: +86 18002042280 (J.
Wang).
E-mail addresses: juanwang75@163.com (J. Wang), bhguo@tjut.edu.cn
(B. Guo).
Chaos, Solitons & Fractals 66 (2014) 9–16
Contents lists available at ScienceDirect
Chaos, Solitons & Fractals
Nonlinear Science, and Nonequilibrium and Complex Phenomena
journal homepage: www.elsevier.com/locate/chaos