epl draft
Diverse strategy-learning styles promote cooperation in evolution-
ary spatial prisoner’s dilemma game
Run-Ran Liu
1
, Chun-Xiao Jia
1 (a)
and Zhihai Rong
2,3
1
Institute of Information Economy, Hangzhou Normal University, Hangzhou, 311121, People’s Republic of China
2
Complex Lab, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054,
People’s Republic of China
3
Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hung Hom,
Kowloon, Hong Kong
PACS 87.23.Kg – Dynamics of evolution
PACS 02.50.Le – Decision theory and game theory
PACS 89.65.-s – Social and economic systems
Abstract. - Observational learning and practice learning are two important learning styles and
play important roles in our information acquisition. In this paper, we study a spacial evolutionary
prisoner’s dilemma game, where players can choose observational learning rule or practice learning
rule when update their strategies. In the proposed model, we use a parameter p controlling the
preference of players choosing observational learning rule, and found that there exists an optimal
value of p leading to the highest cooperation level, which indicates that the cooperation can be
promoted by these two learning rule collaboratively and one single learning rule is not favor the
promotion of cooperation. By analysing the dynamical behavior of the system, we find that the
observational learning rule can make the players residing on cooperative clusters more easily realize
the bad sequence of mutual defection. However, a too high observational learning probability
suppresses the players to form compact cooperative clusters. Our results highlight the importance
of strategy-updating rule, more importantly, the observational learning rule in the evolutionary
co operation.
Introduction. – The prisoner’s dilemma
game(P DG) is considered as a powerful tool for s-
tudying the emergence of collective cooperation behaviors
among selfish individuals [1, 2]. The P DG model consider
that two players can choose either to cooperate (C) or
to defect (D). If they both choose C (or D), each will
get a payoff of R (or P ). If one of them chooses C while
the other chooses D, the defector will get a maximum
payoff of T , and the cooperator gets a minimum payoff
of S. The rank of the four payoff values is arranged
as T > R > P > S, with precondition 2R > T + S.
The model illustrates the conflict of interest between
individuals and group, and creates the social dilemma.
In a traditionally well-mixed population, cooperators
cannot defeat defectors and are doomed to extinction [3].
In order to understand the widespread cooperation in real
world, five prominent rules for the successful evolution of
cooperation have been found, such as kin selection [4], di-
(a)
E-mail: chunxiaojia@163.com
rect or indirect reciprocity [5], group selection [6], spatial
reciprocity [7], and so on. Further more, starting with the
work of Nowak and May [8], population structures with
local interactions have been brought to the focus of re-
search and network topology and hierarchies have been
identified as a crucial determinant for the success of co-
operative behavior [9]. The related researches have also
uncovered that the cooperation level is improved by the
heterogeneities of players induced by the heterogeneous
population structures, including the scale-free topology
[10–12], small-world effects [13–15], clustering [16,17], and
mixing patterns [18, 19]. Later on, the heterogeneity and
diversity have been introduced to the evolutionary coop-
eration, such as teaching activity [20], social diversity [21],
inertia [22], payoff noise [23] and fluctuation [24], mobility
[25–29], myopically selective interactions [30], and repro-
duction time scale [31, 32]. In addition, recent research
also studied the coevolutionary rules, which enrich the het-
erogeneities of players or population structures and hence
p-1
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