Modeling of Emotional Influence in Multiagent System

Jiří Jelínek

Institute of Applied Informatics, Faculty of Science, University of South Bohemia,

Branišovská 1760, České Budějovice, Czech Republic

Keywords: Emotion Simulation, Emotional Appraisal, Social Systems, Multi-agent Systems.

Abstract: Emotions are an integral part of human personality. That is why it is necessary to take them into account

when modeling human behavior and to implement them appropriately with respect to the given objective.

For simulation models, a so-called computational approach based on the emotional appraisal of the stimuli

the individual is exposed to is usually used. The selection of criteria for this appraisal is not strictly given,

just as the transformation of their values into the emotional space. It depends primarily on the purpose of the

model and the environment in which the model exists. This paper describes a specific emotional appraisal

setting for the modeling of social structures based on communication between individuals in a multi-agent

environment. The experiments present simulations of several scenarios showing the development of selected

model parameters over time, as well as the effect of the possible involvement of the emotional appraisal in

the simulation of the authentic behavior of individuals in the network.

1 INTRODUCTION

Emotions are an integral part of human personality.

It is, therefore, necessary to take them into account

when modeling the human behavior (concerning

given goal).

There are several approaches to describe

emotions, more or less emphasizing the

psychological or computational point of view. For

modeling of emotions using IT, the so-called

computational models of emotions are suitable. They

are based on the emotional evaluation of the

stimulus the individual is exposed to.

Many of these models with different

methodologies of emotion appraisal are presented in

the literature, but the critical parts of the model are

rarely described, especially the transformation of the

evaluation variables into their emotional impact. The

paper focuses on this topic and presents one of the

possible settings of the emotional appraisal process

for use in multiagent social models and also on

examples of agent’s coping with appraisal results.

The stress is also placed on the dynamics of the

process of emotional appraisal.

This contribution is part of a larger research

project aiming at simulation of the global behavior

of humans in an environment based on events and

communication.

The next sections of the paper are organized as

follows. Section 2 focuses on a brief description of

state of the art in the field of emotional appraisal.

Section 3 then concentrates on the description of the

proposed appraisal model, and Section 4 presents

experiments with the model aimed primarily at

testing the overall approach.

2 STATE OF THE ART

Study of emotions from multiagent systems view is

a constant topic in which we can find different

approaches. Current survey on this field can be

found in (Bourgais et al., 2018). Our model can be

assigned to a group of computational appraisal

models of emotions, which are based on an

emotional appraisal of all the influences or

perceptions the individual can capture.

The example is a model based on valence and

arousal of emotion (Russell, 1980). The emotion

invoked here is represented by a point in 2D space,

so it is possible to examine the whole range of

emotions specified by different combinations of

valence and arousal. However, it is clear that the use

of only two variables is a little bit restrictive and

minor differences in emotions can be hidden in other

dimensions and cannot be captured. On the other

154

Jelínek, J.

Modeling of Emotional Inﬂuence in Multiagent System.

DOI: 10.5220/0007363701540161

In Proceedings of the 11th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2019), pages 154-161

ISBN: 978-989-758-350-6

hand, the significant question is if it is necessary

from the point of coping with the emotions to work

with more emotional dimensions. Sometimes we just

want to know the overall mood of the individual to

determine the emotional influence on agent’s

actions.

A cognitive theory of emotions usually works in

the process of emotional appraisal of a given event

with several input dimensions (e.g., Ellsworth and

Scherer, 2003; Lazarus, 1991; Roseman et al., 1990;

Scherer, 1999). The list of these dimensions

typically includes (Siemer et al., 2007) the self-

importance of the event for the agent, event

expectancy, possibility to control the event

(controllability) and responsibility for the event. The

appraisal value is usually normalized, the discrete

value scale (0; 10) is frequently used from 0

(strongly disagree) to 10 (strongly agree). All of

these are factors capable of generating emotional

excitation. The proposed model is based on this

dimensional approach.

A description by (Bylsma et al., 2011) can also

be used to describe the event which then has also

other metadata as a type, global type, location and

type of interaction.

If speaking about the selection of the appraisal

dimensions (variables) there is no standard set of

these variables; the specific choice depends on the

particular purpose (Moors et al., 2013). However,

a simple rule can be applied - the more degrees of

freedom we have (i.e., variables and their possible

values) the more types of emotions can be identified

and modeled.

Our model is focused on event processing, so it

necessary to use appraisal variables based on events

and their relation to the individual's goals (more

general interests):

 Agent's goal relevance

 Agent's goal congruence

 Event's certainty

 Event's causality

 Agent's potential for coping the event or control

or influence on control

 Event's novelty or usefulness

 Event's expectancy

 Event's urgency

 Event's intentionality

 Event's legitimacy or fairness

 Compatibility with the agent's norms

The list taken from (Moors et al., 2013) is very

diverse and unclosed and includes variables from

which emotional reaction can arise. When

determining the emotional impact of these variables,

the interests of an individual (his or her desires or

beliefs) should also be taken into account.

What is mentioned only marginally in the

literature is the transformation of these variables’

values into the emotional output or the specification

of a particular emotion. An exception may be the

approach used in the OCC model (Clore and Ortony,

2000) which partly describes used rule-based

mechanism. More detailed information we can also

find in (Courgeon et al., 2009), where the event

appraisal transformation is nonlinear and is focused

on selected emotions expressed on a human model.

Our approach is similar to this one, but our goal is to

obtain information about the actual emotional state

in the form of mood.

Machine learning methods (with or without

a teacher) are can also be used to generate emotional

appraisal (e.g., Nakatsu et al., 1999). These methods

need both computational power and (in case of

supervised learning) also the annotated training set.

That was the reason we tried to propose a more

straightforward way of computing the appraisal.

Just a part of the researchers focuses on the

dynamics of an individual’s emotional state. The

approach used in this paper is similar to that of

(Schweitzer and Garcia, 2010) where continuous 2D

space is used. Our model works with the continuous

mood 1D space with no value limits.

However, the above event-based approach is

currently considered by some scientists to be

limited. This consideration is evident, for example,

in the theory of (Gebhard et al., 2018), which

denotes the emotions generated by the events as only

a part of the emotional space (so-called situation

emotions). Apart from these emotions, there are also

defined the structural emotions (arising from the

internal stimuli of the individual) and emotions

expressed non-verbally (communication emotions).

However, with a suitable event definition also

covering both the latter categories, it is possible to

convert them into events appraised according to the

above dimensions.

From the multiagent point of view, we build on

the previous work of the author focused on modeling

of dynamics of multiagent social systems based on

communication between agents (Jelínek, 2011) and

aspects influencing this process (Jelínek, 2018).

3 PROPOSED MODEL

The presented approach aims to focus on

determining the emotional impact of the given event,

i.e., on the definition of R

-> R

, where R

is the

Modeling of Emotional Inﬂuence in Multiagent System

155

input space of appraisal variables, and R

the space

of emotional output. Unlike the approach, where

these variables are chosen to allow differentiation of

emotions, the presented model focuses primarily on

the variables that can cause any emotional

excitation.

In the emotional output space R

, specific types

of emotions can be used as dimensions or computed

from them. We use the set of six dimensions

mentioned later in this paper. However, we think

that the global level of emotional excitement is

crucial to investigate the influence of emotions on

the agent's behavior. Therefore the presented model

transforms these dimensions to just a single one

(n = 1), the mood of the agent. The possible output

values of this dimension are then in (-1; 1), with

negative values denoting negative emotions and vice

versa.

The underlying environment model builds on the

previous work of the author (Jelínek, 2018). The

model is implemented in Java, and the social

network is made up of agents communicating with

each other in the form of messages. The message is

here understood as an event and has to be

emotionally appraised. In a broader look, we can

say, that event is everything that the agent can

(generated directly by the environment or as a result

of communication between the agents) or a result of

the agent's cognitive processes. In every simulation

step, the incoming event is accepted by the agent

with a certain probability, which is the agent’s

parameter.

The content of the event is some fact comparable

with agent’s knowledge base. Content can be further

structured depending on the used form of data

representation. The modeling of the agent's

knowledge base can be simplified, and it may not

have much to do with real problems. The essential

thing is that the knowledge base allows the setting of

the emotional appraisal for a given event.

In addition to content, each event is

complemented by related metadata that can also be

used to determine emotional variables:

 Event origin - who caused or triggered an event.

 Time and location of the event - when and where

the event happened.

 The event type - determines the appearance of

the event message (e.g., information, command

or question).

Also, it is necessary to take into account the

attributes of the message itself and also the agent

attributes:

 Message sender - from whom we received the

information.

 Priority - how urgent is the message marked.

 Form - determines the shape of the event

message. Here we can choose for instance the

transmission channel (audio, video, text, data or

their combinations).

 The time and location of the agent at the time of

receiving the event message - when and where

the agent learned about it.

We accept the premise that emotions can arise

only as a result of receiving an event message,

which means only by a cognitive stimulus that the

agent processes. However, emotion can occur even

when we expect the event, but it does not occur or

vice versa. Nevertheless, this situation can also be

included under the concept of expectations and its

comparison to reality (model uses for this situation

a particular type of event).

The appraisal process is based on the fact that

the rate of the emotional state change depends on the

difference between the expectations or desires of an

individual, and the reality. Expectations of an

individual are based on an internal model of his / her

knowledge about the world and the communication

history and are constructed with the help of the

metadata mentioned above (both message and event

ones).

For example, for a specific agent location, the

agent recalls events previously received at this

location, and on their base, he/she defines the

expectations for a new event. The same can be done

for the specific sender and other metadata. The

difference between the expectations and the given

event is the basis for the emergence of the emotion

— the bigger the difference, the stronger emotional

excitation.

There are two possible ways to model and study

emotions in the communication environment. The

first way leads to a model in which the emotional

appraise of the event is directly assigned to the event

by the model controlling mechanism. The advantage

of this approach is the simplification of the model

and the possibility to focus on the influence of

emotion on the individual's mood and behavior and

not on the factors that cause it. The disadvantage is

the absence of an appraisal process which cannot be

studied. The second way is to create a more

comprehensive model that will include emotional

calculations from the values of input variables and

appropriate expectations. Thus, the event must be

described in the manner mentioned above (content

and metadata).

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The presented model is designed in a second

way to enable the broader study of emotional

influence on the agent’s behavior.

3.1 Model Details

The presented model was created on the base of the

text description of the event’s content and message

metadata (except for the time that is defined in

simulation steps, and priorities which are also

numeric). The randomly generated text was used to

identify specific content. We use Levenshtein

distance for comparing data and setting its

similarity. The text is not the only way of data

representation, an approach based on a numerical

data can also be used. However, text representation

was chosen for compatibility with other research

projects.

The first step in the appraisal process is to

determine emotional variables on message content

and metadata and also on historical data. The values

of all variables were normalized to the range of

(0; 1). The following variables were selected, based

on the nature and availability of the input data and

the information about the computational models of

emotions:

 Benefit for goal (b)

 Controllability, the possibility to control the

event (c)

 The urgency (u)

 The popularity of the form of the message (f)

 The type popularity of the event (t)

 The popularity of the sender (s)

This way the message is transformed into

a universal space that can be used for any content

and type of message. The list does not intentionally

mention the event expectancy. Its effect is reflected

in its use in the setting of agent x expectations.

Next step is the emotional appraise of variable

values to determine their emotional impact e in the

emotional space R

, in the model represented by

a value in the range of (-1; 1). The value e = 1

corresponds to the maximum positive emotion and

vice versa. The model uses a simple linear

transformation to speed up the appraisal process,

specific formulas for given variables are nearly the

same and are presented at the end of the next

paragraphs. However, it is also possible to select

another type of function.

For determining benefit for goal b, it is necessary

to define an agent’s goal. In the considered model it

is implicitly expressed as a widening the knowledge

base. The key here is the relation between message

content and the content of the agent's knowledge

base that arises from all the hitherto taken and

processed events. The degree of benefit is calculated

from the minimal Levenshtein distance between

event content and all contents from the agent’s

knowledge base. If the given event does not yet

occur, its benefit is maximal (b = 1). Positive

emotions arise when a beneficial message is

received (e

= 2b - 1).

Controllability c specifies the level to which an

event can be influenced or controlled by an agent.

The maximum value c = 1 is assigned if the agent is

the origin of the event. In addition, if the event is

caused by a known agent (our agent has already

received a message from him) the value c = 0.66, if

the origin is an unknown agent, the value c = 0.33

and if the source is an unknown circumstance given

directly by the environment, the value is c = 0. The

maximum positive emotion arises when our agent is

the origin of the event and has the best conditions to

control it (e

= 2c - 1).

The urgency u of a message has a direct link to

message priority, which is defined in the range of

(0; 1) and therefore u = priority. Positive emotions

here arise if the message is not urgent (e

= 1 - 2u).

The popularity of the message form f depends on

the form of the message and personal characteristics

of the agent. Typical forms were selected (oral

communication, letter, mail, SMS and telephone

call) and for testing were assigned particular values

of popularity f. The emotional appraisal is derived

directly from this value (e

= 2f - 1).

The popularity of the event type t is constructed

similarly to the popularity values of a message form,

the list of possible types is given, each of them

evaluated. The emotional appraisal is derived

directly from the value t (e

= 2t -1).

The popularity of the sender s is calculated as the

average of the emotional appraisal of all messages

received from this sender in the past. The emotional

impact is then defined as e

= 2s - 1.

For expectation calculation are collected the

average values of emotional variables according to

the following breakdown:

 Agent location in the simulation step in which

the message is received (x

)

 Message sender (x

)

The resulting expectation values for each

emotional variable  







are then

calculated as the average of the above values (Eq. 1).













 







(1)

Simulation time and possible periodicity of

events also could be taken into consideration.

Modeling of Emotional Inﬂuence in Multiagent System

157

However, this was not implemented in the model

yet.

Now we proceed to the calculation of the

emotional appraisal of the event concerning given

expectation. For each variable y we can determine

the difference between its expected x

value and the

value y for the given message (Eq. 2):





   



 

(2)

The difference of a

in the range (0; 1) is the

basis for calculating the emotional appraisal of the

given variable. It is set according to the formulas

presented for each emotional variable (e.g., for

urgency e

= 1 – 2a

). The reality better than

expectations generates positive emotions and vice

versa. The impact of the event in the emotional

space according to above-presented variables is in

Figure 1.

Figure 1: Event representation in the emotional space.

As we can see, the appraisal is determined

according to exact algorithms, but using individual

knowledge and individual history. Each dimension

also can be of particular importance to the agent

according to personal preferences. Therefore,

specific individual weights are assigned to the

variables and the resulting emotional excitation is

given by the Eq. 3.

   











(3)

In the Eq. 3, e

is the value of the emotional

appraisal for a given variable, w

weight assigned by

the individual to the given dimension, and N the

number of variables we work with (in our case

N = 6). These weights are set in range (-1; 1), the

negative allows to model agents with a reversed

emotional perception. This approach makes it

possible to work with the diversity of behaviors and

preferences in the population.

The weighted appraisals of the emotional

variables are in the model summed up, but other

methods, such as the calculation of the Euclidean

distance in the dimension space, are also applicable.

Emotional excitation e caused by the appraisal of

one event (message) is not isolated during the

simulation. Total excitation of the agent is given by

the superposition of all excitations of events whose

impact persists. The sum of these impacts can be

described as the current mood of an agent in the

range (-∞; ∞).

However, the event's influence on the mood

during the time decreases. Forgetting parameter d

from the interval (0; 1) models the speed of decay; it

defines the decrease of event’s impact on the agent

in one simulation step. Thus the real mood arises

from the superposition of emotions from all the

events the agent has observed, concerning the

forgetting (Eq. 4).

  



  













(4)

In Eq. 4 the m

is the mood at the beginning of

the simulation, K is the number of all recorded

events to current simulation step V, e

the emotional

appraisal of the given event and the v

simulation

step in which the agent observed the event k.

4 EXPERIMENTS

Several preliminary experiments were conducted

aimed at testing the overall approach. In all

experiment were parameters of all agents set on

values from Table 1.

Table 1: Agent's parameters in experiments.

Parameter

Value

Forgetting parameter d

0.9

Event acceptance probability in one

step

0.5

Initial mood m

0.0

Weights of emotional variables w

(for

all variables randomly chosen from

most likely range)

0.0 - 1.0

4.1 Standard Agent and Network

In the first experiment, we focus on a single agent

standard behavior (all the weights of emotional

ICAART 2019 - 11th International Conference on Agents and Artiﬁcial Intelligence

158

variables set to 1.0 ) and the behavior of the whole

network. Figure 2 shows the mood of the agent with

repeated receiving of the same message from the

same agent. The figure shows the initial positive

mood value due to the receiving messages about

unknown events. The mood of the agent worsened as

the communication continued and did not bring him

new information. However, during the time, the

incoming messages modify the agent expectation for

the sender, so further acceptance of the same message

generates the only minimal emotional response.

Figure 2: Single-agent mood change in time.

Receiving the same message frequently affects the

speed of process dynamics only marginally, the main

factor here is the factor of forgetting d.

The dynamics of a global mood in the network of

100 agents, 20 locations, and 15000 different

randomly generated message contents copies the

behavior of single agent (Figure 2).

4.2 Preferred Message Senders

Information about the emotional appraisal of

messages from each sender can be stored and used for

the selection of preferred communication partners

(senders of positively appraised messages).

This mechanism is demonstrated in the following

experiment where after the step s = 2000 starts the

preference of positively appraised message senders

(Figure 3).

The significant change of global mood to

positive values is caused by the better emotional

rating of message senders, which is a part of the

appraisal process. After some time the agents adapt

their expectations and the global mood decreases to

neutral zero value.

Figure 3: Global average mood change in time –

a selection of best-rated partners from step 2000.

4.3 Modified Event Probability

The last experiment was based on a previous one

and took into account the mood of an individual

when setting his willingness to communicate. This

influence was implemented by modifying the

probability of message reception (event probability)

of the agent in the given simulation step (Figure 4).

Figure 4: Global average mood change in time – modified

agent’s event probability, selection of best-rated partners

from step 2000.

The global mood had similar progression as in

the previous experiment, but the influence of

reception probability modification (Figure 5) caused

slower and not so high change.

With worsening agent's mood, the event

probability has fallen. However, from step 2000 the

mood started to increase and the willingness to

communicate increased too, also due to the selective

choice of message senders. The value on the y-axis

approaches 1, so about step 4000 the agents wanted

to communicate with the maximum probability.

Modeling of Emotional Inﬂuence in Multiagent System

159

Figure 5: Global average of an event rate change in time –

modified agent’s event probability, selection of best-rated

partners from step 2000.

5 CONCLUSIONS

The paper presented a detailed model of emotional

appraisal of events in a multiagent environment

simulating the dynamics of a social network built on

communication links. The output of the appraisal

process was the single value of the agent’s mood,

which can be further used in the process of coping to

modify the agent’s actual parameter’s values. To

simply implement the appraisal process was together

with the study of its dynamics also the goal of the

model. The proposed model can be the basis for

further discussion about the modeling of emotions in

computational models (procedures used allow

various implementations).

Three experiments were conducted with the

model to study its behavior and the overall approach

and to investigate agents' behavior in different

situations. Especially the experiments focused on the

practical use of emotional appraisal of messages (for

the selection of message senders or for modifying

the message acceptance probability) have brought

results usable for further investigation and

utilization.

This paper aimed to show a specific

implementation of emotional appraisal of events and

to open discussion of the proposed procedures.

Future work on the model will focus on the

methodology of its validating which is crucial for

every simulation model. The problem here is the

used format of messages and events and the

availability of necessary metadata. Attention will

also be layed on refining the appraisal process. The

open topics here are the transformation functions for

getting an emotional appraisal from content and

metadata and correct setting of the weights for

calculating the mood in Eq. 3. Further testing is also

needed on using the mood to modify the behavior of

the agent in accordance with the influence of

emotions on the human being in the real world.

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