Introduction
Sociophysics [
1, 2
] is a modern research eld focused on investigations of
socioeconomic systems by means of computational and analytical models. Just to
cite few, sociophysics deals with opinion dynamics [
1, 2
], language dynamics [
3,
4
], crowd dynamics [
2
], economy [
5
].Notably, simple models like the voter
models [
6
] are able to represent simpli ed scenarios of opinion spreading, and to
identify exact solutions. Although these analytical approaches often require a high
level of abstraction compared to the real scenarios (e.g., electoral campaigns),
they allow to introduce a mathematical formalism to study social issues.
Moreover, agent-based models constitute a powerful framework |see [
7
] for modeling
social dynamics, that can be combined with the modern network theory [
8
]. It
is worth to recall that a list of qualitative models, developed in sociology and
in social psychology, has been analyzed under the lens of statistical physics. In
the last years, the WWW has deeply shaped our society and, in general, the
life of several people.Therefore, both sociology and social psychology have to
consider this modern world when studying social phenomena and behaviors. In
the light of these considerations, in this work we report a brief summary of some
socio-psychological behaviors analyzed in the context of complex networks [
8
].
In particular, we consider relevant to identify computational models able to
describe human behaviors because, although a lot of data (currently de ned `Big
Data'), a general mathematical framework to deal with them still lacks.
Models
We brie y present two di erent study-cases to show how human behaviors
strongly a ects dynamics in social systems, as social networks in the WWW.
Competitiveness. In the proposed model [
9
], we study a population whose
agents play the Prisoner's Dilemma (hereinafter PD) in a continuous space (see
also [
10
]). In so doing, agents play the PD with their neighbors computed
according to an interaction radius. In principle, the PD is a very simple game where
agents behave as cooperators or as defectors and, according to a payo matrix,
they compute their payo after each challenge. Notably, the payo matrix of the
PD can be de ned as follows
(1)
C
D
C
1
T
D
S
0
The two strategies, i.e., cooperation (C) and defection (D), are grouped in the
set = fC; Dg. Moreover, the parameter T represents the Temptation, i.e.,
the payo gained by defectors when face cooperators, while parameter S the
Sucker's payo , i.e., the payo obtained by cooperators when face defectors.
Values of T and S are in the following range (in the PD): 1 T 2 and
1 S 0. Results of numerical simulations can be studied by analyzing
the T S-plane, computed on varying the value of S and T . In this scenario, it
is interesting to analyze if a cooperative behavior emerges on varying S and T ,
when considering `competitive' agents. Notably, agents have an interaction radius
whose length depends on their payo : as it increases/decreases their interaction
radius increases/decreases. Thus, agents with high payo become more
competitive.Here, we consider the same geometrical framework of [
11
]) but with two
main di erences: i) agents cannot move and ii) agents may vary their interaction
radius. Eventually, in all simulations we consider an equal initial distribution of
strategies. Results, shown in panel a of Figure 1, suggest that `competitiveness'
strongly increases the level of cooperation in a population playing a game (i.e.,
the PD), characterized by an opposite Nash equilibrium (i.e., defection)
Group Polarization. Now we focus on the emergence of extreme opinions [
12
],
by considering the theory of group polarization [
13
]. The latter is a collective
phenomenon that occurs when groups of individuals are taking a decision. In
order to model this phenomenon, in the context of social networks (and then
of the WWW), we propose an agent-based model considering a system with 3
opinions: two opposite opinions and one representing the extreme form of one of
them. For instance, opposite opinions may represent feelings pro-western (pw)
and anti-western (aw), respectively, while the third opinion may represent the
terrorist/passive supporter [
14
] ideal. Agents are arranged on a small-world
network, so that they can interact with their neighbors; although we impose that
they cannot change opinion from +1 (i.e., pw) to 1 (i.e., aw), and vice versa,
over time. We suppose that one agent of the network is a terrorist (hereinafter
TL), with an opinion s = 2 representing an extreme form of the anti-western
feeling. Then, at each time step, TL tries to convince other agents, among those
with the aw feeling, in order to organize meetings. Each aw agent accepts the
invitation with probability pr 2 [0; 1] (equal for all aw agents). As aw agents
accept to attend secret meetings, new connections emerge among them, giving
rise to the emergence of a sub-community (having a structure similar to a
fullyconnected network). According to the theory of `group polarization', a small
set of people with the same idea can be lead to take the idea to the extreme
level; hence, a small set of aw agents risks to become terrorist due to the
intrainteractions. The recruiting of aw agents is the underlying mechanism responsible
for the variation of the social network. Considering the i-th recruited agent (i.e.,
one of the meetings' participants), its pt (i.e., probability to become terrorist)
and pout (i.e., probability to quit to attend secret meetings) are computed as
follows: pit = f ( i ; i ) and piout = i+, with i and i densities of aw and
terrorist agents in the social circle of the ith agent, respectively; and i+ density
of pw agents in the social circle of the ith agent. The function f ( i ; i ) has
been devised in order to consider the presence of both aw and terrorist agents
among neighbors of the ith agent. Results (see panel b of Figure 1) show that a
high fraction of agents which takes part to meetings undergoes the phenomenon
of group polarization.
3
Conclusions
In the era of WWW, the studying of social behaviors recovers a particular
importance. Notably, our lives are strongly a ected by social networks and all
devices that are connected on Internet. Friendships and other human relations
now are developed and supported by virtual connections that allow individuals
to be connected with a wide list of people. As results, several socio-psychological
behaviors must be analyzed in this new technological context. Moreover the
increasing number of digital traces, currently de ned as `Big Data', still requires
the de nition of a formal mathematical theory. Thus, analytical and
computational approaches for studying the evolution of social systems, considering human
behaviors, may represent viable methods to investigate social network dynamics.
With this idea in mind, we present a brief report about social behaviors modeled
in the context of the WWW, showing their central role in the dynamics and in
the evolution of a population.