# Team Resilience in Complex and Turbulent Environments: The Effect of Size and Density of Social Interactions Page: 6

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Complexity

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)

k -

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 [33].

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(8)

( y05

(V) 1(V 1+(2The 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

conditions [18].

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 [25], 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

iteration steps.6

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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.