Reproducing Symmetry Breaking in Exit Choice under Emergency

Evacuation Situation using Response Threshold Model

Akira Tsurushima

SECOM CO., LTD., Intelligent Systems Laboratory,

8-10-16 Shimorenjaku, Mitaka, Tokyo, Japan

Keywords:

Response Threshold Model, Exit Choice, Evacuation, Herd Behavior.

Abstract:

When people evacuate from a room with two identical exits, it is known that these exits are often unequally

used, with evacuees gathering at one of them. This inappropriate and irrational behavior sometimes results

in serious loss of life. In this paper, this symmetry breaking in exit choice is discussed from the viewpoint

of herding, a cognitive bias in humans during disaster evacuations. The aim of this paper is to show that

the origin of symmetry breaking in exit choice is simple herd behavior, whereas many models in the literature

consider the exit choice decisions either as panic or rational behavior. The evacuation decision model, based on

the response threshold model in biology, is presented to reproduce human herd behavior. Simulation with the

evacuation decision model shows that almost all agents gather at one exit at some frequency, despite individual

agents choosing the exit randomly.

1 INTRODUCTION

The choice of exits is a crucial factor in emergency

evacuations. The wrong choice will cause inefﬁcient

evacuations which are possible to result in serious loss

of life. Much work have been done investigating hu-

man exit choice in evacuations. Some of these works

point to symmetry breaking in exit choice (Elliott and

Smith, 1993; Helbing et al., 2002).

Symmetry breaking in exit choice is a phe-

nomenon observed when people evacuate from a

room with two identical exits, in which the exits are

often unequally used and evacuees gather at one of

them. These behaviors result in the inefﬁcient use of

exits, increasing the total evacuation time. This inef-

ﬁcient use of exits is not necessarily limited to panic

situations. It was observed that, even in an evacuation

drill conducted at the New National Theater in Tokyo

(Onishi et al., 2015), with incorrect routing of the peo-

ple at the front, all subsequent people followed, re-

sulted in inappropriate evacuation.

Many researchers consider herd behavior, one of

the most representative and important cognitive biases

in disaster evacuations, to be an underlying mech-

anism of symmetry breaking in exit choice (Hel-

bing et al., 2000; Altshuler et al., 2005; Pan, 2006;

Lovreglio et al., 2014b). Herd behavior, which is

caused by the mental tendency to decide one’s behav-

ior based on the behavior of others, has been observed

in many evacuations including the Three Mile Is-

land nuclear power plan accident (Cutter and Barnes,

1982) and football stadium disasters in the United

Kingdom (Elliott and Smith, 1993). It has been stud-

ied extensively in numerous ﬁelds and is also known

as crowd behavior, conformity bias, peer effect, band-

wagon effect and majority syncing bias (Henrich and

Boyd, 1998; Dyer et al., 2008; Raafat et al., 2009).

Numerous models have been proposed to repre-

sent exit choice in evacuations. However, many of

these models consider the major cause of symme-

try breaking in exit choice to be either panic (Hel-

bing et al., 2000) or rational behaviors (Lovreglio

et al., 2016b). The aim of this paper is to show

that symmetry breaking in exit choice can be repro-

duced by simple herd behaviors. A method is pro-

posed to reproduce symmetry breaking in evacuation

through two exits with the use of the evacuation de-

cision model which represents herd behavior in hu-

mans (Tsurushima, 2018a). The evacuation decision

model is based on the response threshold model in bi-

ology. Furthermore, the model does not incorporate

predeﬁned rules or scenarios nor assumes the ratio of

individualistic and herd behaviors in advance.

The remainder of this paper is organized as fol-

lows. Section 2 shows the models of exit choice in

the literature. Section 3 discusses herd behavior from

Tsurushima, A.

Reproducing Symmetry Breaking in Exit Choice under Emergency Evacuation Situation using Response Threshold Model.

DOI: 10.5220/0007256000310041

In Proceedings of the 11th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2019), pages 31-41

ISBN: 978-989-758-350-6

the viewpoint of leaders and followers. Section 4 in-

troduces the response threshold model and Section 5

presents the evacuation decision model. The simula-

tion model of exit choice is stated in Section 6 and

the simulation results are analyzed in Section 7. The

discussion and the conclusion are given in Section 8

and Section 9, respectively.

2 RELATED WORKS

Numerous studies for exit choice in evacuations have

been conducted since Helbing et al. (2000). Evac-

uation experiments with human subjects were con-

ducted to investigate several features of human exit

choice behaviors (Kobes et al., 2010; Fridolf et al.,

2013) and a database containing evacuation data in-

cluding exit choice was developed (Shi et al., 2009).

It was also reported that symmetry breaking in emer-

gencies occurs not only in humans but also in ants

(Altshuler et al., 2005; Ji et al., 2017) and mice (Sa-

loma et al., 2003).

Multi-agent simulations and cell automaton mod-

els have been used to study efﬁcient evacuations in

disaster situations. Many models to reproduce human

exit choice in evacuations have been proposed by sev-

eral authors and these models can be categorized into

the following ﬁve classes.

Rule based Model

Agents in this class have predeﬁned rules, scenarios,

or sequences of actions, and their choice of exits is

made by these rules. One example of such a rule is “if

an agent detects two exits and its uncertainty level is

high, then the agent pursues the exit that has the most

crowds” (Pan et al., 2005) . These rules are built by

surveys conducted at target sites and some literature

(Augustijn-Beckers et al., 2010), or based on theo-

ries such as Cialdini’s social proof theory (Pan, 2006),

the OCC(Ortony, Clore and Collins) model (Sharpan-

skykh and Treur, 2010; Zia et al., 2011), etc. The

choice of rules are arbitrary made by designers though

there is no widely accepted general way of choosing

these rules.

Cell Automaton Model

The cell automaton (CA) model represents collective

behaviors of evacuees using a two dimensional matrix

with simple rules. This model can efﬁciently repro-

duce dynamics of self-organization phenomena such

as jamming, clogging, oscillation and so on. The re-

lation between evacuation time and exit width or door

separation was studied using the CA model (Perez

et al., 2002). The ﬂoor ﬁeld model was also used

to analyze herd behaviors by varying the length be-

tween two exits (Kirchner and Schadschneider, 2002)

and in environments with multiple exits and obsta-

cles (Huang and Guo, 2008). One of the strengths

of the CA model is its high computational efﬁciency

since the model itself is simple and abstract. How-

ever, none of the above was able to reproduce the

symmetry breaking in exit choice.

Social Force Model

Helbing et al. (2000) introduced the phenomenon

of inefﬁcient use of alternative exits in evacuations.

They conducted simulations of evacuation from a

room with multiple exits ﬁlled with smoke using the

social force model (Helbing et al., 2000; Helbing

et al., 2002). They showed that some mixture of indi-

vidualistic and herd behaviors is more efﬁcient than

purely individualistic or herd behaviors. However,

in their simulations, the relation between exit choice

and evacuation efﬁciency is unclear. What they have

shown is the efﬁciency of ﬁnding unknown exits in in-

visible environments, not the evacuation efﬁciency of

choosing alternative exits. The agents in their model

do not choose exits in any meaningful way since, in

the social force model, the desired direction of an

agent is predetermined via input to the model.

Game Theory based Model

Some models assume the existence of a utility func-

tion in an agent, with the agent behaving to maximize

its utility. In the game theory based model, agents in-

teract with each other and try to achieve Nash equilib-

rium for the game in order to maximize mutual utili-

ties. In (Lo et al., 2006) the choice of exits was formu-

lated as a non-cooperative game, and the mixed strat-

egy solution of the game was analyzed. In exit choice

experiments using ants, the number of ants escaping

from different exits was found to be equal to the ratio

between the widths of the exits; and this ﬁnding was

analyzed from the viewpoint of Nash equilibrium (Ji

et al., 2017).

Discrete Choice Model

The discrete choice model assumes that agents make

exit choices decisions based on a ﬁnite set of attributes

associated with the exit alternatives. The utility func-

tion of an agent consists of two terms: the ﬁrst part

is the expected value of the perceived utility derived

from the attributes, and the second term is its random

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

residual from the real value. A mixed logit model

or multinomial logit model is often used to formu-

late the utility function, and data collected from hu-

man subjects are applied to estimate its coefﬁcients.

For example, Lovreglio et al. uses the following fac-

tors to formulate the utility function (Lovreglio et al.,

2016a).

• Number of evacuees close to the exits

• Flow of evacuees through the exits

• Number of evacuees close to the decision maker

towards one of the exits

• Smoke near the exits

• Evacuation lights above the exits

• Distance of the decision maker from the exit

The relation between evacuation time and exit choice

strategies (e.g, least distance, least travel time, hive,

vision ﬁeld) was studied using multinomial logit mod-

els and an internet survey (Duives and Mahmas-

sani, 2012). Paper-based surveys and face-to-face in-

terviews have been conducted using the SP-off-RP

method to formulate the exit choice behaviors us-

ing multinomial logit models and mixed logit mod-

els (Haghani et al., 2014). The difference between

behavioral features of emergency and non-emergency

egress was analyzed using a mixed logit model and

face-to-face interviews (Haghani and Sarvi, 2016).

Online surveys using video simulations were con-

ducted to formulate a mixed logit model (Lovreglio

et al., 2014a; Lovreglio et al., 2014b). In (Lovreglio

et al., 2016a) the effect of the presence of smoke and

emergency lighting was analyzed using online sur-

veys with virtual reality and a mixed logit model.

Utility-based models (e.g. game theory-based

models and discrete choice models) consider the exit

choice decisions as rational behaviors, whereas other

models consider them as the result of panic or irra-

tional behaviors (Lovreglio et al., 2016b). The major

limitation of utility based approaches is the assump-

tion that decisions in emergency evacuations can be

obtained through surveys and interviews. This is be-

cause it is difﬁcult to reproduce the imminent situ-

ation of real evacuations, and subjects are only able

to respond to questionnaires based on conscious deci-

sions.

In this paper, we propose a novel approach to re-

produce the symmetry breakage in exit choice. Our

approach, which is able to reproduce herd behaviors

in evacuations, is based on the response threshold

model in biology. It shows that symmetry breaking in

exit choice can be reproduced without assuming any

decision making process including rules, scenarios, or

utilities. In this approach, the symmetry breaking in

exit choice emerges as the result of herd behaviors,

even though agents choose the exit randomly.

3 LEADERS AND FOLLOWERS

IN HERDING

Raafat et al. (Raafat et al., 2009) deﬁned herding as

“the alignment of thoughts or behaviors of individu-

als in a group (herd) through local interactions rather

than centralized coordination.” According to this def-

inition, each individual is affected by other individu-

als in some way when determining its own behavior.

However, there must at least be one individual that be-

haves through its own intentions and affects the oth-

ers, otherwise no one would be able to act.

Thus it is reasonable to assume that a herd consists

of leaders and followers, where the leaders determine

their behaviors through their own intentions and the

followers determine their behaviors through the be-

havior of other leaders or followers. In addition, no

individual shall affect or be affected by all the mem-

bers of the group.

This leads to several questions. How is a leader or

follower determined? Is there an appropriate ratio of

leaders to followers? Are the roles of the leaders and

followers ﬁxed, or do they change dynamically? If

they change, what rules affect those changes? The an-

swers to these questions are not obvious, especially if

a privileged and centralized control mechanism does

not exist. This can be called the leader and follower

problem.

If the leader and follower problem is focused on

evacuation, where a room with a single exit is ﬁlled

with randomly distributed agents, the goal would be

to evacuate all the agents from the room. A leader will

be intent on leaving the room and be able to adjust its

behaviors accordingly, so clearly it is able to leave the

room. On the other hand, a follower determines its

own behavior through the behavior of others, regard-

less of its own intention. In this case, a follower will

move toward the exit if many agents move, but will

stay put if they do not. Thus it is unclear whether a

follower will be able to leave the room.

Two simulation experiments

were conducted to

investigate the nature of the leader and follower prob-

lem. The aim of these experiments is to show that

simple rules of assigning the role of leaders and fol-

lowers are inadequate to reproduce evacuation behav-

iors. In these experiments, 200 agents are distributed

NetLogo 6.0.2 (Wilensky, 1999) is used to implement

the models presented in this paper.

Reproducing Symmetry Breaking in Exit Choice under Emergency Evacuation Situation using Response Threshold Model

Figure 1: The leader and follower simulations. a) Experiment 1 or 2 - Initial state, b) Experiment 1 - Terminal state, c)

Experiment 2 - State near the end of the experiment (Thin lines following agents indicate their trails).

in a room (33 × 33 units) with an exit (Figure 1a). A

leader agent (white) moves toward the exit but a fol-

lower agent (gray) randomly chooses an agent in its

vicinity and mimics its movement.

Experiment 1

In experiment 1, 10% of the agents are randomly se-

lected as the leaders and the remaining agents are fol-

lowers. The roles of the leader and follower are ﬁxed

during simulation.

Figure 1b shows the terminal state of experiment

1. All leaders and some followers have evacuated but

most of the followers are still in the room. Since they

are all followers, they cannot move through their own

intention, and thus all of them are unable to move.

This is because most followers choose to follow other

followers, but only some follow leaders. Chains of

followers who do not have a leader will not be able to

exit under these conditions. Only followers following

a leader will be able to exit.

It is obvious that the assumptions of experiment 1

are not suitable as a solution to the leader and follower

problem.

Experiment 2

In experiment 2, 10% of agents are chosen as lead-

ers as in experiment 1, but the roles of the leaders

and followers dynamically change during the simula-

tion. Therefore, an agent acts as a leader at certain

moments, but acts as a follower at other times. Only

the ratio of the leaders and followers is constant.

At the end of the simulation, all agents have left

the room. Thus experiment 2 may be a candidate so-

lution of the leader and follower problem. However,

as shown in Figure 1c, some unnatural and wasteful

movements (e.g. oscillating back and forth between

the two walls) of the followers are observed just be-

fore the end of the simulation. Such unnatural move-

ments can be avoided by increasing the ratio of lead-

ers, but it is not obvious what ratio is appropriate.

Also, the assumption that the ratio of the leaders and

followers is always constant is unrealistic.

Derek Sivers pointed out the importance of the

ﬁrst follower in his famous talk at TED2010 and said

“the ﬁrst follower is what transforms a lone nut into a

leader”

. This implies that there is no leader without

any follower, and vice versa. Therefore, leader and

follower is a mutual dependence relation since the ex-

istence of one can only be supported by the existence

of the other.

From the above, we conclude that

• the roles of leaders and followers should change

over time

• the assumption that the ratio of leaders to follow-

ers is constant is unrealistic.

• leaders and followers is a mutual dependence re-

lation

Hasegawa et al. (2016) showed a similar kind of

mutual relation between hardworking ants and lazy

ants using the response threshold model. There

was a negative correlation between hardworking and

lazy workers. Lazy workers automatically replaced

hardworking but resting workers in processing tasks

when the number of hardworking workers decreased

(Hasegawa et al., 2016). Therefore, the existence of

inactive workers is only supported by the existence of

https://www.ted.com/talks/derek sivers how to start

a movement

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

active workers, and vice versa. To take these points

into account, the response threshold model, which is

an ideal model to represent this kind of mutual rela-

tionship, is adopted as a model for human herd behav-

iors in evacuation situations.

4 THE RESPONSE THRESHOLD

MODEL

The response threshold model (Bonabeau et al., 1996)

is well known in biology and ecology as a model

for division of labor in eusocial organisms. It is

also known as an efﬁcient distributed algorithm to

solve task allocation problems (Bonabeau et al., 1997)

and has a variety of applications in engineering in-

cluding the coordination of multiple robots (Castello

et al., 2016; Krieger et al., 2000), efﬁcient coverage

of distributed mobile sensor networks (Low et al.,

2004), and distributed allocation of multi-agent sys-

tems (Agassounon and Martinoli, 2002).

The response threshold model consists of agents

with response thresholds θ and an environment with

task-related stimuli s. An agent responds to the stim-

uli and engages in a task if s exceeds its θ. The in-

tensity of s will increase if the task is not performed

sufﬁciently and will decrease if a sufﬁcient number

of agents are engaged in the task. An agent i has a

random variable X representing its mental state. The

agent is active if X = 1, and inactive if X = 0. The

probability P

that an agent will be active per unit time

is:

(X = 0 → X = 1) =

+ θ

, (1)

and inactive per unit time is:

(X = 1 → X = 0) = ε, (2)

where ε is a constant probability with which an active

agent gives up task performance. The intensity of s

per unit time is given by:

s(t + 1) = s(t) + δ − α

, (3)

where δ is the increase of the stimulus per unit time, α

is a scale factor of the efﬁciency of task performance,

c is the number of agents engaging in the task, and C

is the total number of agents.

5 THE EVACUATION DECISION

MODEL

In this paper, the evacuation decision model (Tsu-

rushima, 2018a), based on the response threshold

model, which reproduced the evacuation behaviors

observed at the Great East Japan Earthquake (Tsu-

rushima, 2018b), is adopted to study symmetry break-

ing in exit choice in evacuations.

By designating the task to be performed as remov-

ing all agents from the room, the evacuation decision

model can be applied for solving the leader and fol-

lower problem in order to represent human herd be-

haviors. The environment (the room) has a risk value

r which represents the level of objective risks in the

environment, and an agent has risk perception param-

eter µ which represents an individual’s risk sensitivity.

In contrast to the model (equation 3) discussed in

Section 4, each agent in this model has its own stimu-

lus s

which is the local estimate of the stimulus s in-

stead of the global stimulus of the environment. The

stimulus of the agent i is deﬁned as:

(t + 1) = max{s

(t) +

δ − α(1 − R)F, 0}, (4)

where

δ is the increase of the stimulus per unit of time

δ =



δ if r > 0

0 otherwise,

(5)

α is a scale factor of the stimulus. R is the risk per-

ception which is the function of r:

R(r) =

1 + e

−g(r−µ

)

, (6)

where g is the activation gain which determines the

slope of the sigmoid function. F is the task progress

function, the local estimate of task performance:

F(n) =



1 − n/N

max

n < N

max

0 otherwise,

(7)

where n is the number of agents in the vicinity, and

max

is the maximum number of agents in the vicinity.

Each agent has a visibility of 120 degrees and a sight

distance of ﬁve units toward the west direction. This

range is considered the vicinity of an agent.

6 THE EXIT CHOICE

SIMULATION

We assumed a rectangular room (40 × 128 units) with

four walls in the directions north, east, south, and west

clockwise from the top, with two exits at the west end

of the room, where the north and south exits are lo-

cated at the top left and bottom left, respectively (Fig-

ure 2). As shown in Figure 2, there are 600 agents

initially distributed in the middle of the room in a rect-

angular shape (14 × 96 units) and start moving to the

west according to the risk level r.

Reproducing Symmetry Breaking in Exit Choice under Emergency Evacuation Situation using Response Threshold Model

Figure 2: The initial screen of the simulation.

Algorithm 1: Follower’s action (X = 0).

V ← the set of agents in the vicinity

← the number of agents not moving in V

← the number of agents moving in V

if v

> v

then

M ← a set of the moving agents in the vicinity

← the number of agents with d = north in M

← the number of agents with d = south in M

← the number of agents with d = undecided

in M

if e

is the maximum then

d ← north

face to the north exit

else if e

is the maximum then

d ← south

face to the south exit

else if e

is the maximum then

d ← undecided

face to the west

end if

take one step forward

else

do nothing

end if

The northern and southern sections of the room

are initially left empty at the beginning of the simu-

lation because each agent will choose either north or

south direction later (the initial choice of the direction

is set to undecided). The gray vertical line at −48

(G-line) indicates the position where an agent must

decide to go to the northern or southern exit, if its di-

rection is not determined by herd behavior (X = 0).

This decision is only made if the mental state of the

agent is a leader (X = 1); and the choice of north or

south is made at random (choose north with probabil-

ity 0.5). Assuming d = undecided and X = 0 as initial

settings, an agent will perform Algorithm 1 if it is a

Figure 3: The exit choice simulation.

Algorithm 2: Leader’s action (X = 1).

cx ← the X-coordinate of the current position

gx ← the X-coordinate of G-line

if cx ≤ gx and d = undecided then

randValue ← randomly select a value ∈ [0,1]

if randValue < 0.5 then

d ← north

face to the north exit

else

d ← south

face to the south exit

end if

else

face to the west

end if

take one step forward

follower (X = 0) or Algorithm 2 if it is a leader (X =

1). An agent executes Algorithm 1 or Algorithm 2

every unit of time.

Thus the follower may determine its direction

even though it has not yet crossed G-line. The param-

eters of the evacuation decision model are assumed to

be ε = 0.8, δ = 0.5, α = 1.2, N

max

= 10, and g = 1.0.

7 RESULTS AND ANALYSIS

As shown in Figure 3, in many cases, the agents are

equally divided between north and south exits. De-

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

Figure 4: Symmetry breaking in the exit choice simulation. Notice the arc when agents choose the same exit.

Figure 5: The frequency of H.

spite the fact that each agent randomly chooses north

or south, most agents will automatically head toward

the closer exit.

Sometimes almost all agents happen to choose the

same direction and gather at one exit (Figure 4). In

this ﬁgure, the decisions of the white agents, which

move to the south direction, propagate far to the east

from G-line (the arc in the ﬁgure). This kind of behav-

ior is commonly observed when many agents choose

the same direction.

The entropy of the agents that select north or south

can be expressed by the following equation:

H = −r

log(r

) − r

log(r

), (8)

where r

is the ratio of the agents heading north and

is the ratio of the agents heading south at the end

of the simulation. The range of H is H ∈ [0.0,1.0].

The ratios of the agents moving north and south are

Figure 6: The distribution of D with different probabilities.

equal if H = 1.0, and all the agents moving toward

the same direction if H = 0.0. The frequency of H

over 180 simulations is shown in Figure 5. Although

the frequency is small, the phenomenon where most

of the agents gathered at a single exit was observed.

Figure 6 shows how the difference between the

number of agents choosing north and south (D) varies

with the probability to choose the north exit. For

example, D = 600 means all agents evacuated from

the north and D = −600 means all agents evacuated

from the south. The ﬁgure shows that most agents

may happen to gather at the opposite (south) exit even

though leaders chose the north exit with a probability

greater than 0.5. For instance, there was a case where

the leaders chose north with probability 0.6, but 586

agents (97.7%) gathered at the south exit.

The value of ε and the position of G-line are major

factors that affect the value of H. Figure 7 shows the

Reproducing Symmetry Breaking in Exit Choice under Emergency Evacuation Situation using Response Threshold Model

Figure 7: Relationship between ε and H over 50 simula-

tions.

Figure 8: Relationship between position of G-line and H

over 50 simulations.

results of simulations varying the value of ε from 0.1

to 0.9. The values of H in each simulation are shown

in Figure 7 (small circles on dotted lines). The means

of 50 simulations with different ε are shown by the

broken line and the standard deviations are shown by

the dotted line. In Figure 7, the symmetry breakings

are only observed when ε is greater than 0.5 and the

means of H tends to decrease as the values of ε in-

crease. This implies that the greater chances of herd

behavior results in the symmetry breakings.

Figure 8 shows the results of simulations where

the position of G-line was moved from -48 to +48.

In Figure 8, the X-axis shows the position of G-

line. The G-lines in Figure 3 and Figure 4 are located

at -48, and the center of the room is at 0. The val-

ues of H in each simulation are shown in Figure 8

(small circles on dotted lines). The means of 50 sim-

ulations with different G-line positions are shown by

the broken line and the standard deviations are shown

by the dotted line. This clearly shows that the mean of

H tends to decrease as the position of G-line shifts to

east, meaning that an earlier decision results in the un-

even use of two exits. An earlier decision implies that

Figure 9: Correlation of arc length of agents and H.

the agents have more chances to be affected by others

because all agents move in the same direction and the

traveling time of an agent moving along with others

who have already chosen their direction increases.

The long arc of white agents in Figure 4 shows

that when symmetry breaking happens, many agents

have already made decisions well before G-line. The

results of 180 simulations in which the position of G-

line is set to -48 are given in Figure 9. This shows the

correlation of the values of H and the maximum dis-

tances between G-line and the positions of decisions

made by the agents (X-axis). The correlation coefﬁ-

cient of −0.6715 suggests that a longer arc will result

in a smaller H.

In Figure 9, a few samples with long arcs and large

H values are observed, whereas no samples with short

arcs and small H value is observed. This suggest that

the long arc of agents may be an important factor in

symmetry breaking in the exit choice problem.

8 DISCUSSION

Lovreglio et al. (2016b) stated that the evacuation de-

cision of choosing the most crowded exit can be the

result of a rational decision making process instead

of an “irrational-panic” decision (Lovreglio et al.,

2016b). In our exit choice simulation, the evacua-

tion decision model shows that even though an agent

selects exits randomly, with some frequency we can

observe almost all agents gathering at one exit. This

shows that symmetry breaking in exit choice during

evacuation can be the result of simple herd behavior,

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

disregarding any rational decision making processes.

The fact that the same phenomenon can be observed

in experiments using organisms without intelligence

such as ants and mice (Altshuler et al., 2005; Ji et al.,

2017; Saloma et al., 2003) also supports our result.

Furthermore, our results also show that herd behavior

is a major factor of this phenomenon and that the arc

length of agents, indicating early decision making, es-

pecially affects the occurrence of symmetry breaking

in the exit choice.

The evacuation decision model only deals with

cognitive or psychological factors such as decision,

perception, and bias; physical factors such as colli-

sion, clogging, and disturbance are not considered at

all. An agent can simply pass through other agents,

even though they are positioned in front of it. It is

worth noting that the symmetry breaking in evacua-

tion occurs despite disregarding physical factors.

The evacuation decision model is a bio-inspired

distributed task allocation algorithm based on the re-

sponse threshold model. The model itself is simple,

simply switching between two mental states, X = 0

and X = 1, in some probabilistic manner. What to do

in these states is not stated and is open to the user,

giving broad generality to the model. In the case of

the exit choice simulation, we chose Algorithm 1 and

Algorithm 2 for X = 0 and X = 1, respectively. The

evacuation decision model only represents the cogni-

tive bias in evacuation, but for actual evacuation sce-

narios, the consideration of physical factors is neces-

sary; and, especially in the case of human evacuation,

higher cognitive functions such as choosing the short-

est route are also very important to consider.

The generality of the evacuation decision model

allows these factors to be easily incorporated. The

higher cognitive model can be incorporated in the

state X = 1, which shows intentional decision mak-

ing. By assuming the output as a movement vector,

the evacuation decision model can be employed eas-

ily in conjunction with a physical pedestrian dynam-

ics model such as Helbing’s social force model. The

evacuation decision model can be viewed as a plat-

form that separates a higher cognitive function and a

physical model, and then naturally connects these two

by introducing the layer of cognitive bias.

9 CONCLUSION

The evacuation decision model, based on the response

threshold model in biology, represents human herd

behavior in evacuation situations. The exit choice

simulation with the evacuation decision model shows

that almost all evacuees gather at one exit at a non-

negligible frequency even though they choose exits

randomly. The results show that exit choice decision

can be the result of simple herd behaviors disregard-

ing any rational decision. The simulation also showed

the relation between these inappropriate uses of exits

and earlier decision making.

ACKNOWLEDGEMENTS

The author is grateful to Robert Ramirez, Yoshikazu

Shinoda, and Kei Marukawa for their helpful com-

ments and suggestions.

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