DOI
doi.org/10.1371/journal.pone.0126234

Summary
We present a study of the social dynamics among cooperative and competitive actors interacting on a complex network that has a small-world topology. In this model, the state of each actor depends on its previous state in time, its inertia to change, and the influence of its neighboring actors. Using numerical simulations, we determine how the distribution of final states of the actors and measures of the distances between the values of the actors at local and global levels, depend on the number of cooperative to competitive actors and the connectivity of the actors in the network. We find that similar numbers of cooperative and competitive actors yield the lowest values for the local and global measures of the distances between the values of the actors. On the other hand, when the number of either cooperative or competitive actors dominate the system, then the divergence is largest between the values of the actors. Our findings make new testable predictions on how the dynamics of a conflict depends on the strategies chosen by groups of actors and also have implications for the evolution of behaviors.

Relevance for Complex Systems Knowledge
To understand the complexity of social dynamics one approach is to look at the roles played by cooperation and competition, two basic forms of interaction that can be identified when people are involved in a given situation. The purpose of this paper is to present the dynamic consequences of the cooperative and
competitive behavior of actors interacting in a network..

A number of authors have studied cooperation. Nowak suggests that there are five mechanisms involved: kin selection, direct reciprocity, indirect reciprocity, network reciprocity and group selection. Cooperative behavior between groups of individuals is beneficial for improving group productivity, favorable interpersonal relations, and better psychological health. Studying the effects of cooperation and competition on intrinsic
motivation and performance, reveals that both attitudes have positive aspects.

Previous models of the dynamics of conflicts have been mainly based on qualitatively defined
reaction functions between the actors. Recently, attempts to model cooperative and
competitive behaviors in conflicts have considered non-linear differential equations. Some highlights:

considered time delays in the interactions between the actors
the structured topology, which defines who interacts with whom, plays an important role, specially in the context of evolutionary game models
scale-free topology together with a high clustering coefficient (which characterizes the local structure) seems to be beneficial for the evolution of cooperative structures
generalize the two-actor model of Liebovitch et al. to N-actors located in a small-world network
local interactions between nearest-neighbors but there are also extra connections which form interactions between much more distant actors in the network
use numerical simulations to compute the social dynamics, namely how the values of the actors
change in time
final states of the actors and different local and global measures of the distances between the values of the actors depend on the number of cooperative and competitive actors and the connectivity of those actors in the network

The article present the mathematical handling of the problem and the results of simulations. These are

the maximum divergence in the values of the actors is reached when the number of either cooperative or competitive actors dominates the system.
the actors have the most similar values and the fewest extremely different values when:
1) there is a roughly equal mix of actors with cooperative
and competitive behaviors and
2) the actors interact mostly with their nearest neighbors and sometimes, but not too often, with distant actors
a mixture of different behaviors actually leads to more coherence in the overall functioning of a system
both cooperation and competition acting together play a positive role in the overall effective
global functioning of a human social system
if systems with such mixtures of behaviors and small-world properties function
more coherently and therefore more effectively, does this mean that evolutionary processes will
drive the evolution of behaviors to produce an approximate balance between cooperators and
competitors as well as select their interactions with each other to form a network with smallworld
properties?

Point of Strength
The article provides an accesible explanation of mathematical modelling of social dynamics, though it would take some further clarification to use in social science classes where the mathematical understanding is lower. Replicating the model in a simulation software may be one way of increasing the understanding. It would require some work to make that sufficiently visual and accessible.