Team Resilience in Complex and Turbulent Environments: The Effect of Size and Density of Social Interactions Page: 6
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necessarily imply that they will make the same decisions and
at the end, they will totally agree on a given configuration.
Therefore, since individuals in the team make their personal
combination of decisions, we use a realistic rule, that is, the
majority rule, on each single decision, to identify the team
configuration at each iteration step. Moreover, the majority
rule is proven to perform better than best and random mem-
ber rules in different situations [74, 75].
Given the set of opinions (oa, oa, ... , o) that the agents
have about the decision j at time step t, we set the team's
choice on the decision j as follows:
d(t) = sgn [M-1a(t)1, j= 1, 2, ... , N. (6)
If M is even and in the case of a parity condition, d is
uniformly chosen at random between the two possible
values +1, -1.
At each time step, the team fitness performance is then
calculated as V(t)= V[d(t)]. This quantity measures the
efficacy of the solution found by the team at the time step t.
For additional details about the model, the reader is referred
to [24, 25].
3.3. Turbulent Environment. Recalling that the time interval
between two consecutive steps of the Gillespie algorithm
(see the Appendix) is large or short depending on whether
the speed of opinion diffusion within the network is corre-
spondingly slow or fast, we use the simulation step, instead
of time, to represent the results of our simulations. This is
equivalent to scaled time accordingly to the speed of diffu-
sion. This specific choice comes from the fact that the depen-
dence of resilience on the speed of diffusion is too evident; a
low speed of diffusion hampers the ability of the system to
change its configuration and adapt to a new environment.
Therefore, considering that larger teams are necessarily char-
acterized by a lower speed of opinion diffusion, we preferred
to represent the results in terms of number of steps with the
aim of isolating the effect of structural properties on resil-
ience, besides their influence on the diffusion time. If no dis-
turbance or event occurs during the simulation period, the
environment is static. To model turbulence in the environ-
ment, we introduce disturbance during the simulation
period. In particular, the disturbance corresponds to a critical
event that modifies the NK fitness landscape .
Two dimensions are used to characterize the turbulence
of the environment: (1) the magnitude and (2) the frequency
of the disturbance. The magnitude corresponds to the extent
to which the critical event modifies the payoffs associated
with actions. We model this by means of the level of correla-
tion between the landscapes. A high correlation means that
the configurations will tend to maintain the same payoffs
before and after the disturbance and vice versa. To this end,
at each critical event, we define the new quantities C as
- 1 -
C= V + 3/1 +(2[ Cod - V) + E, (7)
where Cod is the undisturbed contribution to the fitness
landscape and e is a normal distributed random noise, with
zero average. The quantity ( = o6/CO is the ratio between
the standard deviations ofe and Cod, respectively. This choice
guarantees that the standard deviation o6c of the new sto-
chastic quantity C, satisfies the relation o c = co. Moreover,
the correlation coefficient r between the newly generated
landscape V and the old one Vo is given by
(V) 1(V 1+(2
The frequency of disturbance considers how fast the
environment is changing. A high frequency corresponds to
environments fast moving, irrespective of the magnitude of
change. We model this by means of the parameter (A), that
is, the number of times the critical event (i.e., the change of
the landscape) occurs over the given simulation period. Note
that the frequency of disturbance is defined with respect to
the total number of iteration steps, that is, referring to the
scaled time. Therefore, each disturbance, that is, each change
of the landscape, occurs after a given number of iteration
steps, depending on the frequency chosen.
3.4. Team Resilience Measurements. We measure team resil-
ience by capturing the ability of the team to adapt to distur-
bance and identify a new desirable condition characterized
by high fitness. This is consistent with the definition of resil-
ience as the ability of the team to provide positive outcome
and desirable performance, under challenging and critical
In particular, we compute the resilience performance of
the team by averaging the team fitness performance V(d)
at each simulation step (in percentage of the maximum pay-
off achievable on the landscape) across all the simulation
steps. The higher this value, the higher team resilience is.
This measure of resilience is consistent with other works
on the topic [33, 38].
4. Simulation Analysis
We consider a team of size M engaged in solving a combina-
torial decision-making problem characterized by N=12. We
set 3=10, I3J=0.5, and p=1. Following the analysis pre-
sented in , the values of the strength of social interaction
I#J and the self-confidence /3' have been chosen such that, in
the case of no disturbances (baseline model), the size of the
team does not affect its performance. Twelve environmental
scenarios are simulated resulting from the combination of
three values of complexity (K=1, 3, 11), two values of mag-
nitude of disturbance ((=0.75, 4.89) corresponding to cor-
relation coefficient values T =0.2, 0.8, respectively, and two
values of frequency of disturbance (A =10, 20). To analyze
the effect of team size and density, we perform simulations
changing the value of M (5 and 11) and the density (-0.33,
-0.67, 1). In the case of density < 1, a random pattern is set
for the social network of the interactions. Each scenario is
replicated 300 times for a simulation period of 100.000
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Giannoccaro, Ilaria; Massari, Giovanni F. & Carbone, Giuseppe. Team Resilience in Complex and Turbulent Environments: The Effect of Size and Density of Social Interactions, article, July 24, 2018; Cairo, Egypt. (https://digital.library.unt.edu/ark:/67531/metadc1234365/m1/6/: accessed April 18, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT College of Arts and Sciences.