Simulating the Impact of Cooperation and Management Strategies on Stress
and Economic Performance
Josef Daˇna
Masaryk University,
Faculty of Informatics
jdana@mail.muni.cz
Ivan Kopeˇcek
Masaryk University,
Faculty of Informatics
kopecek@fi.muni.cz
Radek Oˇslejˇsek
Masaryk University,
Faculty of Informatics
oslejsek@fi.muni.cz
Jarom´ır Plh´ak
Masaryk University,
Faculty of Informatics
xplhak@fi.muni.cz
Abstract
In this paper, we study the impact of the
management evaluation strategies that are aimed at
achieving a balance between rewarding the cooperative
behavior of employees and their economic performance.
We developed a model in the NetLogo simulation
environment that incorporates many socioeconomic
aspects such as the stress, effort, and productivity
of employees as well as insights into managing
cooperativeness and the performance of individual
workers. We conducted a series of simulations, each
representing a 10-year lifespan of an organization,
and the results reveal that organizations achieve the
highest performance when management prefers to
reward the cooperative behavior of employees instead
of performance. The detailed results are provided and
discussed in the paper, as are the future directions that
the research could take as well as possible extensions of
the model presented.
Keywords: agent-based modeling, cooperation,
organizational performance, Prisoner’s dilemma, stress.
1. Introduction
Levels of stress and the quality of relationships
among co-workers are known to have a direct influence
on job satisfaction and physical health, both resulting in
a negative economic impact on organizations [1,2].
The role of the management is to establish
an optimal working environment that will obviate
such problems while aiming to achieve the highest
possible organizational performance. As Livio & De
Chiara [3] point out, it is a priori unclear whether
the management should either support cooperative
or competitive environment between co-workers to
promote performance. Some researchers argue that
humans are reciprocal by nature [4], and that a friendly
environment fosters innovative thinking [5–7], whereas
others conclude that competition between co-workers
stimulates performance through a higher motivation of
individuals [8, 9]. While the existing studies focus on
the interactions within/among the team, and in some
exceptional cases on the managerial decisions, our
focus is on extending this research by implementing a
multi-variable agent-based model. This model allows
us to study complex interactions between employees
and how the system is influenced by the management
strategies that strike a balance between rewarding the
cooperative behavior of employees and their direct
economic performance for the sake of the profit of
the company. The model uses a variety of tunable
parameters which define attributes and behavioral rules
of agents, whose interaction unfolds in time and create
spatial and temporal patterns [10]. The evaluation
experiments demonstrated that the model behaves
correctly in predictable situations.
The rest of the paper is organized as follows: (1) In
Section 2, we locate our approach in the broader context
of socioeconomics and game theory. (2) In Section 3,
we describe our simulation model, its key features, and
principles. (3) In Section 4, we discuss the simulation
experiments and their results in detail, and (4) we draw
our conclusions and look to the future in Section 5.
2. Related Work
According to the American Institute of Stress [11],
about three quarters of the U.S. population regularly
experience physical and psychological symptoms
caused by work related stress and consequent costs to
employers are estimated to be $300 billion annually.
It is now widely accepted that stress has a significant
impact on organizational performance as it influences
employees’ motivation and their sense of wellbeing [2,
12]. The relationship between stress and performance
is most commonly explained by the Yerkes-Dodson
law [13] where the best performance is achieved at
a medium level of stress — the curve describing
the relationship is ∩-shaped. However, existing field
studies on samples of medical nurses [14], software
engineers [15], elite football players [16], industrial
workers [17], surgeons [18], and aviation pilots [19]
conclude that there may also be a positive or negative
linear relationship between stress and performance.
In our model, this relationship is mediated through
complex interactions between agents that are based on
the prisoner’s dilemma game, and further influenced
by the management’s decision making, as described in
Section 3 of this paper.
The prisoner’s dilemma game [20], henceforth
PDG, is commonly used as a paradigm in studying
cooperative behavior. In the original PDG, two
players simultaneously decide whether to cooperate or
to defect. They receive the reward R or punishment
P if both cooperate or defect, respectively. If one
player cooperates and the other defects, the former gets
a sucker’s payoff S while the latter receives a temptation
to defect T [21, 22]. In our model, players of PDG
correspond to employees that collaborate with their
co-workers.
Work by Nowak and May [21] showed that a
simple spatial PDG setting can produce remarkably
complex and indefinitely changing fractal-like patterns
of behavior. Later on, much effort has been devoted
to the evolutionary games on different topologies of
regular or complex networks [23–29]. Our model is
based on a regular lattice where each agent is surrounded
by eight neighboring agents (i.e. Moore neighborhood).
This basic setting allows us to investigate the dynamics
of the cooperation that our model is designed to
test, while excluding possible topological effects of
interaction. Note that within the context of modeling
and simulation, the basic interaction unit in a model is
called an agent. In our model, the agent represents an
employee, therefore we use words agent and employee
interchangeably throughout the text, depending on the
context.
Voluntary participation is considered as an effective
approach to promote cooperation in PDGs [30–32].
Under this setup, a third strategy called ’loner’ is
involved. A loner does not temporarily participate in
PDG and both, the loner and the other player, take
a fixed small payoff. Chen et al. [33] propose an
aspiration-induced dormant mechanism, in which loners
temporarily quit the game if their payoffs are less than
the aspiration level. Our model also permits an agent
to temporarily stop participating in the PDG, under the
following conditions: agent reaching a given degree
of stress become sick, which excludes them from the
collaboration for a given number of simulation steps. To
mimic real-world situations, the agent returns to work
after the ”sick leave” ends. However, agents whose
recurrent sickness overcomes a given tolerance may quit
the job and be subsequently replaced with newcomers.
3. Model
Our model represents an organization, such as a
company, a university, a factory, etc., where employees
are provided with a salary to deliver added value (see
section 3.2.1) back to the organization.
The model provides a certain degree of cooperation
between individuals — part of the work is done by the
employee alone and part of the work can be mutually
exchanged with a colleague. This concept is based
on the idea that employees exchange the specific work
that the other colleague can process more efficiently.
This exchange consequently benefits both parties. The
willingness to deliver the exchanged part of the work
between employees is simulated by PDG. This is a
standard approach to studying aspects of cooperation
since it is known that spatialized PDG is an undecidable
problem [34]. The management of the organization
evaluates each employee, where performance and
cooperativeness are considered for salary adjustments.
The individual workload, the outcome of cooperation,
and the salary increase or decrease have an impact on
the employees’ stress level and consequently on their
motivation and related performance.
The core of the model is based on the primary
features of cooperation, stress and economic
performance. Throughout its development, we
have been implementing additional components of
the model so that it will be of use to more specific
situations. All of the extending components are
adjustable by parameters and may be turned off —
this was mainly used during the testing of the model.
While the values of some parameters have to meet
certain criteria, e.g. PDG payoff function (see Table 2),
the value of other parameters were set arbitrarily, as
a result of series of tests. Testing simulations proved
that, under given settings, the system is relatively robust
and produces reasonable results. Some parameters
had to be controlled carefully, as they were highly
sensitive to each other (e.g. stress production and
stress regeneration) which could significantly influence
overall behavior of the system.
3.1. Terms and Concepts
In our model, employees are described using the
following key features that account for their individual
properties.
Strategy is a predefined behavior of the employee
when PDG is played. For use in our model, we have
selected seven simple strategies commonly used in the
PDG context, as listed in Table 1. The strategies that the
employees use are assigned randomly and never change
during their lifespan.
Productivity θ represents employee’s ability to create
profit for the company. For the sake of simplicity, we
assume each employee having fixed productivity during
their lifetime. This number is used in Equation 2 and set
as described in Table 3.
Effort κ represents an employee’s inner motivation
to work. While productivity describes the employee’s
abilities, effort describes how much the employee uses
these abilities at a particular moment — 0% can be
understood as ”an employee does not work at all” while
100% as ”an employee does their best”.
Existing research addressing the influence of
external rewards on employees’ performance and
motivation comes to contradictory conclusions — some
state that pay increases the employee performance
[35], while others found payment harmful to intrinsic
motivation [36]. Cameron et al. [37] pointed out
that the influence is also affected by the attractiveness
of tasks. In our simplified model, the only factor
affecting the effort are changes in salary. Decreasing the
salary demotivates employees and decreases their effort
and vice versa. However, the influence is not linear.
Employees with a high current effort are more sensitive
to a salary decrease which leads to a noticeable decrease
in their effort. Conversely, employees with a low current
effort react more significantly to a salary increase.
Resistance to stress is modeled as a capacity of a
virtual stress container. If the stress level is below
the given threshold, the employee is healthy and
working. When the stress level exceeds the limit, the
employee becomes sick and unable to work. When a
sick employee returns to work, the stress container is
emptied. See Subsection 3.2.2 for closer details.
Sickness is a metaphor used to simulate the impact
of high stress on working activities of employees. Sick
employees do not produce any profit, but the company
still supports them financially. Employees that are sick
too often are fired and replaced. The tolerance for
repeated sick leave is adjustable in the model, common
to all employees, and fixed during the simulation.
3.2. Simulation Step of One Employee
Each simulation round can be considered as one
working day during which an employee produces a
certain amount of added value. In what follows,
we explain how this amount is calculated and how it
is influenced by certain features of employees, their
willingness to cooperate, and stress factors.
3.2.1. Fulfilling the Work Tasks: The primary
input for this step is a salary β,which represents the
amount of money that the employee is given by the
management.
The management expects that the employee will
produce the work at least commensurate with the value
of the salary. The primary output is an added value
V , which corresponds to the input salary increased (or
decreased) as a result of the work produced. The added
value is affected by three weighted components Ve, Vc,
and Vrc:
V = β(Ve + Vc + Vrc). (1)
Efficiency contribution Ve reflects the employee’s
current working effort κ relative to their productivity
θ. Cooperation weight, wv, 0 ≤ wv ≤ 1 denotes
the portion of the work which is mutually exchanged
between two employees, while the rest is done directly
by one employee:
Ve = (1 − wv)θκ. (2)
Cooperation contribution Vc reflects the cooperation
initiated by the employee:
Vc = wvϕ. (3)
This contribution can be interpreted as exchanging the
same portion of the work with a co-worker because they
are able to do it more effectively and vice versa.
ϕ is the results of the iterated PDG played with a
co-worker. The game is driven by the payoff matrix
defined in Table 2. The values satisfy condition T >
R > P > S and can be interpreted as follows:
• Sucker’s payoff S: I did the partner’s work as
was agreed, but my partner did not do my work.
I cannot earn anything from my work because it
was not done.
• Cheater’s payoff T: I did not do the partner’s
work, but the partner did my work as we agreed.
Because they did the work more efficiently than
me, I get the payoff 1.25. Moreover, I had time to
do my own work, and so the final payoff is 2.25.
• Punishment P: We did not agree on cooperation
and did the work as usual, with normal efficiency.
• Reward R: Both of us met the agreement, and
because we did the work more efficiently, we get
a payoff 1.25.
Strategy Label Description of behavior.
Defect D Always defects.
Cooperate C Always cooperates.
Tit for Tat T Repeats partner’s last move.
Tit for two Tats T2 Defects only if defected in the last two rounds, otherwise cooperates.
Tit for Tat — Na¨ıve Peacemaker nT Repeats partner’s last move. When defected in the last round, there is a
probability of cooperative response.
Pavlov P Starts with cooperation. Repeats action when won last round and switches
action when lost last round.
Unforgiving U Once defected by a partner, it will always respond with a defection.
Otherwise cooperates.
Table 1. The description of employees’ collaboration strategies.
In each simulation round, an employee can cooperate
with a different co-worker. The collaboration history
of the particular partner is always taken into account,
which is important for strategies that decide their move
based on previous ones, e.g., the ”Tit for Tat” strategies,
see Table 1.
Cooperate Defect
Cooperate R = 1.25 S = 0
Defect T = 2.25 P = 1
Table 2. The payoff matrix of the PD game.
Requested cooperations contribution Vrc: Apart
from the cooperation initiated by the employee, any
of the neighbors can also ask them for cooperation.
Because the cooperation is interpreted as an exchange
of part of the work, the requested cooperations Vrc have
a similar effect to the added value as before, but seen
now from the opposite direction:
Vrc =
∑
j
wjϕj, (4)
where j corresponds to the j-th requested cooperation,
wj is the cooperation weight assigned to the co-worker
(co-worker’s wv), and ϕj is the employee’s results of the
iterated PDG played with the j-th co-worker.
3.2.2. Stress Factors: Fulfilling the tasks is
stressful. We deal with two types of stress factors,
namely, inter-individual and intra-individual stress.
The impact of both types of stress on employees is
adjustable.
Inter-individual stress is associated with the
collaboration ϕ and its extent depends on the result of
the PDG for every simulation step.
Intra-individual stress results from the subjective
perception of the employee. The stress level of every
employee is updated relative to their current effort κ.
The more effort an employee exerts, the more stress is
produced (regardless of productivity).
Stress regeneration is a mechanism incorporated
into every simulation step to counterbalance stress
production. The value of regeneration is adjustable by
the model.
Resistance to stress is conceived as a capacity to
withstand a certain amount of stress. If the total
increased stress is greater than the value of regeneration,
the stress level rises further. Once it exceeds the capacity
of the ”stress container”, the employee becomes sick.
For the stress container, we assume a normal statistical
distribution among the population, similar to other
personality traits that are determined by numerous
independent factors.
3.3. Lattice of Employees
The employees are arranged in a square lattice,
as illustrated in Figure 1. At the beginning of each
simulation, the collaboration strategies of employees,
their productivity and stress limits are set up to meet the
desired parameters.
In the beginning, the company earmarks a budget
α ∈ N for all employees. This budget may remain
the same for the whole simulation or it can be slightly
adjusted at every step, depending on the economic
performance of the employees. Then the simulation
algorithm performs the Simulation step of an employee
as discussed in Section 3.2 to calculate their values
added Vi. The steps follow these rules:
• All employees have exactly eight neighbors. This
also applies to the employees at the edge of the
interaction plane, as the end of any row or any
Management
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Figure 1. The visualization of the model. Each square represents an employee and their strategy (see Label in
Table 1). The gray color scale indicates stress level where darker gray refers to a higher level of stress, and the
yellow color implies that the given employee is sick.
column continues from the beginning of the same
row or column. The interaction place appears to
be a square but is in fact a torus (see Figure 1).
• The employees interact with their neighbors only.
Therefore, the Vrc contribution in Equation 4 is
calculated from at most eight co-workers.
• A neighbor for the interaction is chosen randomly.
Sick co-workers are omitted, and their added
value Vi is set to zero. Also, if there is no healthy
neighbor available for the cooperation, then the
added value Vi of the employee is set to zero.
• The salary βi given to the i-th employee is
calculated from the distribution of the budget α
among all employees as follows:
βi =
αρi
n
, (5)
where n is the number of employees in the
lattice. The performance ρi represents a relative
efficiency of the employee compared to other
employees. Its value is set to 1 by default for
all employees, which ensures an even distribution
of the budget among them. However, the
management can influence this value based on the
results of an employee’s evaluation in a way that
prospective employees can be motivated by higher
salaries (see Equation 9 in Section 3.4).
The final profit generated by each employee is
calculated as a difference between their added value and
input salary: Vi − βi. The total of profits generated
by all employees during one simulation round, in a
chosen period, or continuously from the beginning of
a simulation, are observed during the simulation to
analyze the impact of the factors on the profit of the
company.
Apart from the inter-individual and intra-individual
stress factors discussed above, changes in salary βi
represent an additional factor that affects stress. The
increase of the salary decreases the employee’s stress
and vice versa. The amount of stress caused by salary
change is modified by the employee’s stress capacity
— the greater the capacity, the higher the stress level
is increased or decreased. Moreover, the current salary
is taken into consideration during the stress calculation.
The lower the salary, the more stressful any further
reduction is, and conversely, a lower stress regeneration
is associated with any salary increase.
3.4. Management Insight and Intervention
3.4.1. Evaluation of Employees Behavior: After
a certain number of simulation steps, given by the
parameter evaluation period, the management evaluates
employees’ behavior taking into account two aspects:
cooperativeness and effort. The evaluation Ei of i-th
employee is computed by the relation:
Ei = weCi + (1 − we)Fi, (6)
where Ci and Fi are a cooperation-based insight and
an effort-based insight respectively, and 0 ≤ we ≤ 1
is a weight, which enables us to prioritize Ci and Fi.
Later in the paper, this weight is denoted as management
strategy.
Cooperative employees are beneficial for
the company. To reflect this phenomenon, the
cooperation-based insight Ci is used by the management
to privilege cooperating employees:
Ci = wc
ci
ci + di
+ (1 − wc)ϵ, (7)
where ci is the number of cooperations that
the employee participated in during the management
evaluation period of one month, di is the number of
defections, and 0 ≤ ϵ ≤ 1 is a random number. The
weight 0 ≤ wc ≤ 1 reflects how much insight the
management has into the cooperativeness of employees:
0 means random decision (no insight at all) while 1
means that the management has precise information
about the cooperativeness of the employees. Employees
that are sick during the whole inspected period have no
cooperation so only a random number ϵ is used for them.
In a similar manner, the management can use
insights into the employees’ effort. The effort-based
insight Fi is adjustable by the weight parameter 0 ≤
wf ≤ 1, where 0 means ’random decision’ (no insight)
and 1 means that precise information about the effort
of employees is available. The effort-based insight is
defined as follows:
Fi = wf
∑
Wi
max1≤j≤n(
∑
Wj)
+ (1 − wf )ϵ, (8)
where
∑
Wi is the added value that the i-th employee
accumulated during the inspected period, n is the
number of employees, and 0 ≤ ϵ ≤ 1 is a random
number.
For healthy employees, Wi = Vi and Fi privileges
employees working harder than others, as expected.
However, sick employees produce Vi = 0 which would
result in a penalization in the same way as healthy
employees are penalized for their zero effort. To prevent
this, Wi of sick employees are set to their salary βi so
that they are not directly penalized for being sick.
3.4.2. Impact on Salary: The result of an evaluation
(see Equation 5) is involved in the salary distribution
process. After every evaluation, the performance
parameter ρi is re-calculated, taking into account the
evaluation result Ei of the i-th employee compared with
the average evaluation value Eavg of all employees:
ρi = ρi + ρi(
Ei
Eavg
− 1)wρ, (9)
where 0 ≤ wρ ≤ 1 is a parameter that defines the
intensity of the impact of the evaluation process on
employees’ performance.
3.4.3. Impact of employees’ substitution:
Management interventions based on the evaluation
process influence the stress of individual employees
and, consequently, their sickness. Repeatedly sick
employees leave the organization and are substituted.
The model also incorporates the substitution of
employees that have a low performance over an
extended period. The tolerance for sickness and low
performance are adjustable and are common for all
employees. This mechanism of substituting employees
can be seen either as firing an employee due to their
long-term poor performance or that employees left
the company because of frequent sickness caused by
non-cooperating co-workers or bad decisions of the
management which do not reflect the employee’s effort
sufficiently.
Unlimited substitution of employees would
be unrealistic because the number of available
workers on the job market is limited, depending on
the unemployment rate. Furthermore, hiring new
employees usually brings additional costs to the
organization as newcomers require training and have
reduced performance during this period. To bring our
model closer to reality, we incorporated a penalization
for each employee being substituted by a newcomer.
This penalization reduces a company’s profit and
corresponds to additional costs related to the hiring
process and the training of new employees. The
amount of penalization is adjustable by a parameter
and also reflects the average salary of employees in the
organization.
4. Testing and Simulations
Our model has been implemented and evaluated
in the NetLogo [38] simulation environment. For
the repository with the source code, see [39]. Each
simulation included 3,600 simulation steps. Taking each
step as one day, the results of the simulations can be
seen as covering a period of ten years in the life of
an organization that is providing monthly evaluation
of employees with the consequent intervention of the
management. The values of the fixed parameters used
for the simulations are summarized in Table 3. For
any given simulation setting, 100 runs were executed to
obtain average values and eliminate possible bias caused
by any stochasticity of the simulation process.
The simulations covered the impact of management
Features of employees
wv cooperation weight 20% The portion of assigned work to be done with a co-worker
κ effort 75% Initial effort of all employees
θ productivity 2.8 ± 0.1 Mean value and standard deviation of the distribution
stress limit 70 ± 5 Mean value and standard deviation of the distribution
cooperativeness 4:1 Proportion of employees with cooperative vs. defective strategies
Features of the management
evaluation period 30 steps Frequency of the management intervention
patience 12 Tolerance for repeated sicknesses or low-performance of the employees
Table 3. Fixed settings of simulations.
strategies on the economic performance of an
organization. These results are presented in the
following section.
4.1. Impact of Management Strategies on
Profit
The two 3D scatter plots in Figure 2 provide an
overview of the impact of the management interventions
on the company’s profit. The horizontal axes represent
the insights that the management has into employees’
cooperation (insight into cooperation = wc in the
model) and performance (insight into performance =
wf in the model) respectively, where 0 = no insight,
1 = absolute insight. The vertical axes encode the
management evaluation strategy we from 0 (only the
performance of employees is taken into consideration)
to 1 (only the cooperativeness of employees is taken
into consideration), see section 3.4.1. The color of the
individual samples encodes the simulation results, as
depicted in the color bar on the right-hand side of the
figure. The darker hue of red indicates that a higher
profit has been generated by the organization at the given
settings.
A detailed analysis and visualization of the data lead
to the following observations:
• Focusing on cooperativeness and a sufficiently
deep insight into the cooperation result in the
highest value produced by an organization.
• The strategy based mostly on cooperativeness
(we > 0.8) can achieve an approximately 80-90%
performance level compared to the best result, as
long as the insight for cooperation is also high
enough (i.e. wc > 0.8). In such settings, the
impact of performance insights is weak, and its
particular value has no significant influence on the
total value of an organization.
• The lowest observed performance (below 10%
compared to the best result) is achieved by an
organization where the management has very
low or zero insight into both cooperation and
performance regardless of which aspect of the
work is preferred. Such a setting creates a
favorable environment for agents with defective
strategies whose population fluctuate around
30-40% of the total agent population, compared
to the initial 20%.
• Balanced strategies (we = 0.5) can achieve a fair
relative performance (i.e. 60–70%) only if the
insight for cooperation is relatively high (wc >
0.7). When wc drops below 0.5, an organizations
performance does not exceed 50% of the best
result.
• Strategies that prefer to reward individual
performance (we < 0.2) are performing poorly.
The results show that it is still better to reflect
cooperativeness at least a bit, as the company
can achieve 25-40% of the best performance
as long as the insight for cooperation is high
(wc > 0.6). A management strategy that
completely disregards cooperativeness of agents
(we = 0) can never perform better than
23% of the best result for wf = 0.6 while
higher values of wf result in an even lower
performance. Having precise information about
individual performance (wf = 1) accounts for only
approximately 13% of the best performance. In
other words, even when the management rewards
agents completely on their performance, it is
reasonable to tolerate fluctuation in an agent’s
performance which is achieved by a submaximal
insight for performance.
4.2. Impact of Management Strategies on
Stress
The scatter plot in Figure 3 encodes the impact
of management insight and the evaluation strategy
0
0.2 0.4 0.6 0.8 1 0
0.5
1
0
0.5
1
insight into cooperation
insight into
performance
managementstrategy
00.20.40.60.8
1
0
0.5
1
0
0.5
1
insight into cooperation
insight into
performance
managementstrategy
0.5
1
1.5
2
·108
profit
Figure 2. The impact on profit of the management’s insight and strategy.
0
0.2 0.4 0.6 0.8 1 0
0.5
1
0
0.5
1
insight into cooperation
insight into
performance
managementstrategy
00.20.40.60.8
1
0
0.5
1
0
0.5
1
insight into cooperation
insight into
performance
managementstrategy
0
20
40
60
numberofsickemployees
Figure 3. The impact on sickness of the management insight and strategy.
on the total number of employees that have left the
organization due to frequent sickness. As sickness
correlates with stress, we can interpret these results also
as the impact on stress.
The rate of sickness is high when the management
strategy is focused on rewarding performance while the
insight for performance is low, or when the strategy aims
at rewarding cooperation and the insight for cooperation
is low. In other words, the two above-mentioned
rewarding strategies exhibit high levels of randomness,
resulting in a high level of stress among employees. See
Figure 3 for details.
4.3. Impact of Management Strategies on
Employment Fluctuation
Figure 4 depicts the impact of management
interventions on the fluctuation of employees. The
fluctuation is calculated as a total count of employees
that leave the organization, either due to repeated
sickness or to long-term underperformance.
As illustrated in Figure 4, a strategy of rewards that
aims to improve performance causes high fluctuation
when the insight for performance is also high.
5. Conclusions and Future Work
We have developed a multi-variable model based
on a prisoner’s dilemma game in the NetLogo
simulation environment. This model allows us
to study various aspects of cooperation among
employees in an organization. The key parameters
are organizational performance, employment fluctuation
resulting from stress level, sickness rates and the
individual performance of employees. We have
also implemented a concept of management strategy
which represents a decision how to reward employees’
cooperative behavior and individual performance. This
concept is extended by implementing a management
insight, i.e. a parameter describing the accuracy
of information that the management applies when
employees are rewarded. Less than maximal insight
can be perceived as a level of tolerance for rewarding
or punishing employees’ behavior.
0
0.2 0.4 0.6 0.8 1 0
0.5
1
0
0.5
1
insight into cooperation
insight into
performance
managementstrategy
00.20.40.60.8
1
0
0.5
1
0
0.5
1
insight into cooperation
insight into
performance
managementstrategy
100
150
200
250
numberofdismissedemployees
Figure 4. The impact of the fluctuation of employees on the management’s insight and strategy.
Our experiments have shown that management
strategies and the quality of insight into employees’
cooperativeness and performance has a significant
effect on both the organizational performance and the
employees’ wellbeing. The highest organizational
performance is achievable in settings when the
management focuses on rewarding the cooperativeness
of employees. In comparison, focusing solely on
individual performance accounts for an organizational
performance approximately four times lower. The
lowest observed performance (less than 10% of the
highest result) is related to the situation when employees
are rewarded randomly. This situation also reports the
highest levels of stress. The employment fluctuation
reaches its peak when management prefers to reward
individual performance and have precise information
about it, therefore there is no tolerance for a suboptimal
performance of employees.
The experiments demonstrate the possibilities of our
model at their current state of development and provide
results that are general in nature. To obtain specific
results on which conclusions and recommendations for
an organization can be formulated, the parameters of the
model need to mirror the real situation in a particular
company. This can be a starting point for a case study in
future research.
The model can be further extended by implementing
a social network model where the interaction of
employees would be more complex, influenced by
the topology of a network, and exploring the
potential impact of more central agents on the overall
performance of the organization.
There are several other suggestions for future
versions of the model, such as the introduction of
organizational growth to reflect the economic prosperity
of the company, implementing a more realistic model of
employees’ productivity, involving personality types to
fit specific organizations, and to focus on the space and
distance between employees that may have an impact on
the quality of interactions.
Finally, the employment fluctuation algorithm can be
further developed. It should be possible to relocate the
employees or change their collaboration strategy before
they leave the organization. And a higher penalization of
a company for repeatedly dismissing employees could
be implemented to better simulate a situation where
there is low unemployment in the job market.
References
[1] S. E. Sullivan and R. S. Bhagat, “Organizational stress,
job satisfaction and job performance: Where do we go
from here?,” Journal of Management, vol. 18, no. 2,
pp. 357–374, 1992.
[2] K. Pugliesi, “The consequences of emotional labor:
Effects on work stress, job satisfaction, and well-being,”
Motivation and Emotion, vol. 23, no. 2, pp. 125–154,
1999.
[3] L. Livio and A. D. Chiara, “Friends or foes? optimal
incentives for reciprocal agents.,” Journal of Economic
Behavior & Organization, 2018.
[4] D. H. Thomas Dohmen, Armin Falk and U. Sunde,
“Homo reciprocans: Survey evidence on behavioural
outcomes.,” The Economic Journal, vol. 119, p. 592 612,
2009.
[5] J. Chen, W. S. Leung, and K. P. Evans, “Are
employee-friendly workplaces conducive to
innovation?,” Journal of Corporate Finance, vol. 40,
pp. 61 – 79, 2016.
[6] X. Tian and T. Y. Wang, “Tolerance for failure and
corporate innovation.,” The Review of Financial Studies,
vol. 27, p. 211 255, 2011.
[7] Y. W. Seo and S. W. Chae, “Market dynamics
and innovation management on performance in smes:
Multi-agent simulation approach,” Procedia Computer
Science, vol. 91, pp. 707 – 714, 2016.
[8] B. Beersma, J. R. Hollenbeck, S. E. Humphrey,
H. Moon, D. E. Conlon, and D. R. Ilgen, “Cooperation,
competition, and team performance: Toward a
contingency approach.,” Academy of Management
Journal, vol. 46, p. 572 590, 2003.
[9] J. Luft, “Cooperation and competition among
employees: Experimental evidence on the role of
management control systems.,” Management Accounting
Research, vol. 31, pp. 75 – 85, 2016.
[10] N. Nan, “Capturing bottom-up information technology
use processes: A complex adaptive systems model,” MIS
Quarterly, vol. 35, pp. 505 – 532, 2011.
[11] “The American Institute of Stress: stress statistics.”
https://www.stress.org/stress-research/. Accessed:
2018-05-28.
[12] J. W. Ness, V. Tepe, and D. R. Ritzer, The science
and simulation of human performance. The address:
Emerald Group Publishing Limited, 2004.
[13] R. M. Yerkes and J. D. Dodson, “The relation of strength
of stimulus to rapidity of habit-formation.,” Journal of
Comparative Neurology and Psychology, vol. 18, p. 459
482, 1908.
[14] S. J. Motowidlo, J. S. Packard, and M. R. Manning,
“Occupational stress: its causes and consequences
for job performance.,” Journal of applied psychology,
vol. 71, p. 618 629, 1986.
[15] M. Laanti, “Agile and wellbeing–stress, empowerment,
and performance in scrum and kanban teams.,” IEEE
46th Hawaii International Conference on System
Sciences (HICSS), p. 4761 4770, 2013.
[16] D. A. Savage and B. Torgler, “Nerves of steel?
stress, work performance and elite athletes.,” Applied
economics, vol. 44, p. 2423 2435, 2012.
[17] F. Zhong, E. Yano, Y. Lan, M. Wang, Z. Wang,
and X. Wang, “Mental ability and psychological work
performance in chinese workers.,” Industrial Health,
vol. 44, p. 598 603, 2006.
[18] C. M. Wetzel, R. L. Kneebone, M. Woloshynowych,
D. Nestel, K. Moorthy, J. Kidd, and A. Darzi, “The
effects of stress on surgical performance.,” The American
Journal of Surgery, vol. 191, p. 5 10, 2006.
[19] S. J. Vine, L. Uiga, A. Lavric, L. J. Moore,
K. Tsaneva-Atanasova, and M. R. Wilson, “Individual
reactions to stress predict performance during a critical
aviation incident.,” Anxiety, Stress & Coping, vol. 28,
p. 467 477, 2015.
[20] R. Axelrod and W. D. Hamilton, “The evolution
of cooperation,” science, vol. 211, no. 4489,
pp. 1390–1396, 1981.
[21] M. A. Nowak and R. M. May, “Evolutionary games and
spatial chaos,” Nature, vol. 359, no. 6398, p. 826, 1992.
[22] M. Perc and P. Grigolini, “Collective behavior and
evolutionary games - an introduction,” Chaos, Solitons
& Fractals, vol. 56, pp. 1 – 5, 2013. Collective Behavior
and Evolutionary Games.
[23] Z.-X. Wu and Y.-H. Wang, “Cooperation enhanced
by the difference between interaction and learning
neighborhoods for evolutionary spatial prisoner’s
dilemma games,” Phys. Rev. E, vol. 75, p. 041114, Apr
2007.
[24] G. Szab´o and A. Szolnoki, “Cooperation in spatial
prisoner’s dilemma with two types of players for
increasing number of neighbors,” Phys. Rev. E, vol. 79,
p. 016106, Jan 2009.
[25] M. c. v. Perc, A. Szolnoki, and G. Szab´o, “Restricted
connections among distinguished players support
cooperation,” Phys. Rev. E, vol. 78, p. 066101, Dec
2008.
[26] Z. Rong and Z.-X. Wu, “Effect of the degree correlation
in public goods game on scale-free networks,” EPL
(Europhysics Letters), vol. 87, no. 3, p. 30001, 2009.
[27] A. Szolnoki, M. Perc, and G. Szab´o, “Diversity of
reproduction rate supports cooperation in the prisoner’s
dilemma game on complex networks,” The European
Physical Journal B, vol. 61, pp. 505–509, Feb 2008.
[28] H.-X. Yang, W.-X. Wang, Z.-X. Wu, Y.-C. Lai, and B.-H.
Wang, “Diversity-optimized cooperation on complex
networks,” Phys. Rev. E, vol. 79, p. 056107, May 2009.
[29] S. Ding, J. Wang, S. Ruan, and C. Xia, “Inferring
to individual diversity promotes the cooperation in the
spatial prisoner’s dilemma game,” Chaos, Solitons &
Fractals, vol. 71, pp. 91 – 99, 2015.
[30] G. Szab´o and C. Hauert, “Evolutionary prisoner’s
dilemma games with voluntary participation,” Physical
Review E, vol. 66, no. 6, p. 062903, 2002.
[31] C.-L. Chen, X.-B. Cao, W.-B. Du, and Z.-H. Rong,
“Evolutionary prisoners dilemma game with voluntary
participation on regular lattices and scale-free networks,”
Physics Procedia, vol. 3, no. 5, pp. 1845 – 1852,
2010. The International Conference on Complexity
and Interdisciplinary Sciences. The 3rd China-Europe
Summer School on Complexity Sciences.
[32] D. Jia, C. Shen, H. Guo, C. Chu, J. Lu, and L. Shi,
“The impact of loners’ participation willingness on
cooperation in voluntary prisoner’s dilemma,” Chaos,
Solitons & Fractals, vol. 108, pp. 218 – 223, 2018.
[33] Y.-S. Chen, H.-X. Yang, and W.-Z. Guo,
“Aspiration-induced dormancy promotes cooperation
in the spatial prisoner’s dilemma games,” Physica A:
Statistical Mechanics and its Applications, vol. 469,
pp. 625 – 630, 2017.
[34] P. Grim, “The undecidability of the spatialized prisoner’s
dilemma.,” Theory and Decision, vol. 42, pp. 53 – 80,
1997.
[35] D. G. Gardner, L. Van Dyne, and J. L. Pierce,
“The effects of pay level on organization-based
self-esteem and performance: A field study,” Journal of
Occupational and Organizational Psychology, vol. 77,
no. 3, pp. 307–322, 2004.
[36] E. L. Deci, R. Koestner, and R. M. Ryan, “A
meta-analytic review of experiments examining the
effects of extrinsic rewards on intrinsic motivation.,”
Psychological bulletin, vol. 125, no. 6, p. 627, 1999.
[37] J. Cameron, K. M. Banko, and W. D. Pierce, “Pervasive
negative effects of rewards on intrinsic motivation: The
myth continues,” The Behavior Analyst, vol. 24, no. 1,
pp. 1–44, 2001.
[38] U. Wilensky, “Netlogo,” tech. rep., Northwestern
University, Evanston, IL, 1999.
[39] J. Daˇna, I. Kopeˇcek, R. Oˇslejˇsek, and
J. Plh´ak, “Git repository with the model.”
https://gitlab.fi.muni.cz/lsd/PDG-cooperation-simulator.git,
2018.