Agent-based Approaches for
A Social Dilemma of Travel Mode Choice(交通手段選択の社会的ジレンマに対するエージェントベース・アプローチ)
インフラ計画研究室 ＹＯＳ ＳＵＮＩＴＩＹＯＳＯ
指導教官 松本 昌二
Abstract – The research focused on modelling a social dilemmaof travel mode choice for commuters. In order to understandbehavioral process of individuals, two types of simulation model ofmulti-agent learning was built and applied to examining behavior
of commuters. The first behavioral model is based on
inductive-learning’s capability of human beings and the second
model is based on their beliefs and expectations. Evolutionary
approach is introduced in order to simulate travelers’ learning
process.
The first model showed that the same user equilibrium point
as predicted by conventional equilibrium analysis could bereached and stabilized. At the equilibrium point, most of travelers
specialize in a car-only user or a bus-only user, leaving a small
number of mixed users. The stable situation is produced byinteraction process among travelers and by behavioural change
process of each traveler.
Furthermore, when travelers are very sensitive to payoff
differences between car and bus, there is a situation that may
produce other equilibrium points in addition to the user
equilibrium point. In these new kinds of equilibrium, which are
known as ‘deluded’ equilibrium and ‘frozen’ equilibrium, higher
level of cooperation could be achieved and stabilized.
The second model revealed that some insightful results could
be obtained, such as the conditions that make cooperation as apossible outcome. They are group-based interactions, limited
information,
andconformist
transmission.
Emergent
phenomenon of the system may favor cooperation and resolve thedilemma of travel mode choice, if there exists a strong conformist
transmission. This gives insight to the possibility of solving thesocial dilemma by incorporating an employer-based Travel
Demand Management (TDM) measure.
Keywords: travel mode choice, social dilemma, agent-based
approach, microsimulation.

1. INTRODUCTION
Most of models in transportation planning and analysis
rely on the equation-based modeling. Agent-based approaches
are still not as widely used as equation-based approaches. An
agent-based model has the advantage of being validated at anindividual level, since the behaviors encoded for each agent canbe compared with local observations on the actual behavior of
domain individuals. Understanding individual’s behavior isimportant especially in studying effects of transportation
policies.
Several works on route choice behavior by Nakayama et al[11][12] are the examples of agent-based approaches intransportation modeling. Travelers are modeled to havebounded rationality, limited information and also capability to
do cognitive learning. Klugl and Bazzan [9] also studied route
choice behavior by using a simple heuristic model. In travel
mode choice, there are not so many works done by researchers.
One of the inspiring works by Kitamura et al [8] is on travel
mode choice by using a simple bi-modal transportation systemand cellular automata.
Our study focuses on commuters’ mode choice behavior.

On the highway, all people have right of commuting by private
car or public transport. As a common good, which is shared bypeople, a social dilemma [2] situation may happen on the
highway. Selfish behavior of people, who use cars based on
their personal interest to minimize travel cost, creates traffic
congestion, and furthermore increases travel cost for users bothof car and public transit.
By using a simple bi-modal transportation system, thesocial dilemma situation of travel mode choice is modeled.
Travelers who use public transit, for example bus, are called ascooperative travelers, since they behave cooperatively for thesake of all people’s benefit. Car users are defective travelers
since they consider only their personal interests.
This study aims to provide an agent-based simulation modelof travel mode choice in order to understand behavioral processof commuters on choosing travel mode. A user equilibrium
point may also be reached, but more important is the process toreach the point and the behavioral change of travelers during
the process. We attempt to observe complex dynamical
processes of commuters’ behavior by considering interactions
and learning processes influential. New findings are expected
in order to gain an insight into the way of solving the social
dilemma.
2. SIMULATION MODEL:MODELLING BY FINITE-STATE MACHINES
Two types of simulation model of multi-agent learning wasbuilt and applied to examining behavior of commuters. The
first behavioral model is based on inductive-learning’s
capability of human beings and the second model is based on
their beliefs and expectations. Evolutionary approach is
introduced in order to simulate travelers’ learning process. In
this section, we will focus on the first model.
Behavior of autonomous agents may represent behavior of
travelers who choose mode of commuting. A multiagent
simulation is utilized to model and to show a complex
decision-making process of travelers. An agent behaves basedon a behavioral rule embedded in a kind of inductive learning
machine named as a finite-state machine (FSM).
Our simulation model consists of two submodels,transportation model and traveler model (see Figure 1). In thetraveler model, travelers decide the choice of mode guided bydecision making rules. After all travelers decide the mode ofcommuting, then travel time is calculated in the transportation
model. Generalized travel cost for each mode can be calculated
and it returns to travelers as payoffs. Amount of payoff for eachtraveler depends on the mode he has chosen. Day-by-day, thegeneralized travel cost of car and bus may vary dynamically,
depend on the changes of travelers’ choice. These processes arerepeated for 10 iterations. After that, an evolutionary process to
update travelers’ FSM by using genetic algorithm is utilized inorder to acquire adaptive behavior.

a/1

U p d ating R ulesb/1

G enetic Alg o rithm

new chrom osom eAneighbors'
chrom osom es

FSM'schrom osom es

B
c/0

a/0
a/0 b/1

T ransp o rtatio n M o d el
trav el tim e, payoff

c/0

T raveler M o d el
M em o ry- prev ious payoff- expected payoff- total payoff

b/0

b/0

R ules(F inite State
M achine )T ravel T im e M o d elandPayo ff F unctio ns

Da/1

set of states {A,B,C,D}
set of input symbols {a,b,c}
set of output symbols {0,1}

C
c/0

c/1
O u tp u t

state

Figure 2: An illustration of a finite-state machinem odechosen m ode

Figure 1: Multiagent simulation model by FSMs

Table 1: A representation of a FSM in a table form
current state
input

A

B

C

D

2.1 Transportation Modela(A,1) (D,0) (A,0) (D,1)

A simple bi-modal transportation system, which comprises
private car and bus as choices of commuting, is used as atransportation model. The two modes are assumed to be
operated in the same lane so that there will be more interactions
than if they are operated in exclusive lanes. This simple modelis used in order to understand basic travel mode choice that
represents social dilemma situation.
All travelers own cars so that they can easily change modes
and they only know the cost of mode they choose. Private car
users are assumed to be solo drivers. For public transport, bus
operating frequencies and fare are adjusted so that bus
passengers can pay the full cost of operating buses. Equations
and their parameters of generalized travel costs for car and bus
are derived from the work of Kitamura et al [8].

bc(D,1) (A,1) (A,0) (B,0)

2.2 Traveler Model
A finite-state machine (FSM) or finite state automaton(FSA) is an abstract machine that has only a finite, constantamount of memory (the states). FSM looks like a mathematical
logic that represents a sequence of instructions to be executed,
depending on a current state of the machine and a current input.
Formally, a FSM is a 5-tuple: M=(Q,τ,ρ,s,o) [3]. Where Q isa set of states, τ is a set of input symbols, ρ is a set of output
symbols, s:QxτÆQ is the next state function, and o:QxτÆρ isthe output function. A 5-tuple is to be interpreted as a machine
that, if given an input symbol x while it is in the state q, will
give output o(q,x) and transition to state s(q,x). Only the
information contained in the current state describes the
behavior of the machine for a given stimulus, while the entire
set of states serves as the ‘memory’ of the machine.
Figure 2 illustrates a finite-state machine with 4 finite states,
3 input symbols and 2 output symbols. A FSM can also be
represented by a kind of table as Table 1. A pair of values ineach cell is a pair of next state function and output function(s,o). For example, (A,1) means that next state will be A andcurrent output is 1. The number of states, input symbols andoutput symbols can be varied according to modeling needs.
In our simulation, each agent has a FSM which functions as
a decision rule to choose mode of traveling. Each agent has a
FSM with 4 states, 5 input symbols and 2 output symbols.

(C,0) (C,0) (D,0) (D,1)

Past payoffs that are memorized as expected payoffs, areused to decide the input symbols for the next step. Expected
payoffs of a traveler are calculated and updated based on awork of McFadzean [10]. A traveler received payoff Ptj ofusing mode j at time t. This payoff is then recorded and used to
update its expected payoff. The expected payoff Utj is updated
according to Equation (1).

U t j ← wU t j−1 + (1 − wi ) Pt j ;j = A,B(1)

where A means automobile or car and B means bus. Only
expected payoff of the chosen mode is updated. When a traveler
choose car, his expected payoff of car is then updated. But
expected payoff of bus will not be updated until the traveler
chooses bus.
Weight factor w ranges from 0 to 1. It depends on a
traveler’s perception of the influence of his payoff Ptj on the
expected payoff Utj. A traveler with high weight factor isresilient to his current payoff. On the other side, a traveler withlow weight factor is easily affected by his current payoff.
There are 5 input symbols that are used in the agent’s FSM(see Table 2). They represent choices of strategy for a traveler
to decide which mode they will use for next trip. Each choice ofstrategy has a range of value to differentiate it to other choicesof strategy. How much is the difference can be categorized into
several levels, depending on the value of d. Parameter drepresents the sensitivity of a traveler the difference between
payoff of car and bus. A larger value of d implies that a traveler
does not consider so much about payoff differences whenchoosing mode. For example, for a traveler who has a low valueof d, if he observes that the expected payoff of car is muchhigher than bus, then the input symbol will be 1. But for a
traveler with high value of d, he might behave differently.
Initially, for input symbol 1, choices of mode in its set ofstrategy are only car, and for input symbol 5 are only bus. Input
symbol 2 has 75% choices of car and input symbol 4 has 75%
choices of bus. Input 3 has 50-50 proportions of car and bus. In
the beginning, all commuters received a random initial value ofexpected payoff of car and bus ranged from 1 to 2. The first
choice would determine all the following choices without any
variation, if an initial value were not assigned.
Decision making processes of a commuter starts with input
symbol 3 and state 1. For example, a commuter, say commuterC, has a FSM as in Table 2. Let us assume that initial values ofUA and UB are 1.1 and 1.2, and w=0.9. Initial pair of state andoutput is (3,0), which means that the decision is to choose car,coded as 0, and next state will be state 3. After all commuters
had chosen a mode based on their FSM, they received a payoffof their decision. PA is given to commuters who chose car and
PB is given to commuters who chose bus. Commuter C received
PA and then he updated his expected payoff of car using
Equation (1) ( U A = 0.9 ⋅1.1 + (1 − 0.9) P A = 0.99 + 0.1P A ). He
observed that d < (0.99 + 0.1P A ) − 1.2 ≤ 2d , so that for next
iteration, the input symbol is 2. Based on input symbol 2, andnext state 3, Commuter C got new pair of state and output fromhis FSM. The pair is (4,0), so that the decision is to choose car,coded as 0, and next state will be state 4. These processes
continue until the end of iterations (10 trips).

learning and acquire adaptive behaviors by learning fromothers. In this paper, we utilize social learning only.
Social learning requires interaction among agents, so that
we arrange agents in a kind of plane without border, known as a
torus plane, which were used in Yamashita et al [13], so thateach agent has 8 surrounding neighbors. It makes possible forthem to interact each other. Each agent updates his rules (FSM)
based on the fitness (sum of payoffs) of his own rules and also
his neighbors’ rules. Genetic algorithm is implemented to
evolve agents’ rules. Each agent only knows rules owned by hisneighbors only and also payoffs gained by those rules, so thatagents are assumed to operate with incomplete information
regarding with other agents’ behavior. The learning process ofusers is in the process of evolution of rules. Figure 4 illustrates
the rules-updating process of each agent.
bit no:1binary code 1

value

2
0

3
0

4
0

1

2

3

(3,0) (2,0) (3,0) (4,0)

d < U A − U B ≤ 2d(2,0) (3,1) (4,0) (1,0)

(2)
(3)
(4)

U

A

−U

B

< d

d < U B − U A ≤ 2d(5) U B − U A > 2 dcurrent state(3,0) (1,1) (4,0) (2,1)(4,1) (1,0) (2,1) (3,1)(2,1) (1,1) (3,1) (2,1)

...
...

1

input

4

input
A
B
(1) U − U > 2 d

6
0

56
1

57
0

58
0

0
1
0
2
state: 3 mode: 0 state: 2 mode: 0

Table 2: An example of agent’s FSM in table form
current state

5
1

U

A

−U

B

> 2d

...

U

−U

A

> 2d

60
1

1
1
state: 2 mode: 1234(3,0) (2,0) (4,0) (4,0)

...
B

59
1

...

...

...

(2,1) (1,1) (3,1) (2,1)

Figure 3: Decoding process of a chromosome into a FSM
Ne ighbor 8

Ne ighbor 1

Ne ighbor 2

Chrom . Traveler 1
1 1 1 0...
1

Ch rom . Trav eler 2
1 0 1 1.. .
1

Ch rom . Trav eler 3
1 0 1 0
.. .
0

...

...

...

Fitness of chromosome
In order to acquire an adaptive strategy, a genetic algorithm
Fitness of chromosome
Fitness of chromosome(GA) is applied to the FSM of each agent. A chromosome in... ... ...
Ne ighbor 7
GA encodes the transition function and the output function of
Ne ighbor 3
Chrom. Traveler 6 5
C hrom. Trave ler 6 7
1
2
3
...
...
1 0 1 0...
0
FSM in each agent with bit strings. A chromosome with length0 0 1 0.. .
1...
60 bit strings encodes a FSM, which consists of 5x4 pairs of... 65 6 6 67 ...
...
state and output. Figure 3 illustrates the process.
Fitness of chromosome
Fitness of chromosome... 129 130 131 ...
For a state, it requires 2-bit strings. The value of 2-bit... ... ...
strings ranges from 0 (for binary code 00, the value is
Ne ighbor 6
Ne ighbor 5
Ne ighbor 4
0.21+0.20) to 3 (for binary code 11, the value is 1.21+1.20). A
Chr om. Travel er 12 9
Chr om . Traveler 13 0
Ch rom . Travel er 13 1
1 0 1 1...
1
1 0 0 0.. .
1
1 1 1 0.. .
1value of 0 represents State 1, a value of 1 represents State 2, a
...
...
...
value of 2 represents State 3, and a value of 3 represents State 4.
A choice of mode is represented by a single bit string, since theFitness of chromosome
Fitness of chromosome
Fitness of chromosome
choices of mode are only two, car and bus. A value of 0
represents car and a value of 1 represents bus.
someo f Trav eler 66
Chromosome
6
6 1 0 1C hromo
66
Tr av el er 66
Travel0 1 1 1 1 0 1
...
1 0 1
66
66
Genetic operators, such as selection and two-point
Own chromosome
Fitness
crossover, are used. Mutation is not implemented in order to
Neighbor 1 chromosome
Fitness
Rules (FSM)
Neighbor 2 chromosome
Fitness
avoid capricious changes of output value for input symbol 1
50-days
10-daystrips
trips
...
...
Neighbor 8 chromosome
Fitnessand 5. We still maintain variation of chromosomes by crossover
Trip 1
Trip
Car
Payoff Car at
at t=1t=1
Trip 2
Trip
Car
Payoff Car at
at t=2t=2among travelers, since travelers are interrelated with each other.
Trip 3Bus
Trip
Payoff Bus at t=3
G enetic Alg ori thm
Genetic
...
...
...
...
Agents must have adaptive process in order to evolve
Payoff10
Trip 50
Car
Payoff Car
Car at
att=10t=50
Total Payoff
New chromosome
decision rules they have. There are two kinds of learning
Fitness of chromosome
process that can be used by agents to acquire adaptive rules;
Figure 4: Rules-updating process of an agent
individual learning and social learning. In individual learning,
travelers learn based solely on their own experience. 2.3 Simulation Results and Discussions
Sometimes it requires longer time to acquire adaptive behaviors,
We run simulations with 4,096 travelers, who are arranged
and also it limits travelers’ knowledge about other kinds of ruleinstead of their own rules. Compared to individual learning, in a torus plane. Each traveler has a finite-state machine as asocial learning has advantages since it can short-cut individual decision making rule. Memory weights w of travelers areassumed to be 0.9. To study the influence of the sensitivity
parameter d, we vary the value from 0.05 to 0.15 withincrement 0.025. Simulation is run up to 500 generations with
10 iterations in a generation.
Four simulation runs were made for each value of d. Afterobserving the results, we decided to discuss the details for
d=0.1 and d=0.05, since the former case resulted in a morestable situation than the cases of d > 0.1 and the latter case gave
interesting results.
A. Dynamic Equilibrium Situation at d=0.1
We run four runs for this case. Statistics for last 100
generation is summarized in Table 3. Similar to conventional
analysis, a user equilibrium point is reached when the cost of
car equals to the cost of bus. For all these runs, the average costof car is almost equal to the cost of bus. But statistically with
95% confidence interval, only for Run 1 and Run 4, the cost of
car is significantly equal to cost of bus. The number of bus
users in Run 1 and Run 4 are significantly the same, as well as
the equality between Run 2 and Run3. We will discuss in moredetails for Run 1 in this section up to Section C.
Figure 5 shows the day-to-day dynamics of number of bus
users. The fluctuation reduced to a small value after Iteration
2,000’s (Generation 200’s) and maintained until the end of
simulation, with only a few fluctuations around Iteration
4,000’s (Generation 400’s). The system is stabilized at the user
equilibrium point.

C. Emergence of Choice Stability
Traveler’s specialization of mode changes usually from a
car user to a mixed user and then to a bus user, or reversely froma bus user to a mixed user and then to a car user. Even though a
traveler has a tendency to become a car user or a bus user inevery generation, sometimes an interaction with other travelers
make him change into a mixed user, following the change of his
FSM due to crossover of chromosomes with neighbors. Figure
7 illustrates the change of a traveler’s choices of mode fromgeneration to generation, which have finally resulted in an
all-times bus user or car user.
D. Effect of Travelers’ Sensitivity at d=0.05
We found an interesting phenomenon when the value ofparameter d is at 0.05, which means travelers are 2 times moresensitive to payoff difference than d=0.1. In all four runs, thesystem converged to other equilibrium points (see Figure 8),
where the number of bus users in all runs is higher than the user
equilibrium point (dashed line in the figure).
Further discussions will be focused on Run 2. An
emergent process started from an outbreak of number of bus
users at iteration 8 in generation 31 (see Figure 9). The outbreakstarted with decreasing bus users to a lower level than the user
equilibrium point, so that travel time increased and payoff for
all users decreased, but payoff of bus was slightly higher thancar. Some travelers observed this situation and at the same timethey chose bus, resulting in a sudden increase of bus users.

Table 3: Averages and std. deviations (Gen.401-500)
Run
1
2
3
4

Bus users
Avg
Std. Dev.
1161.8555.17
1168.7153.33
1169.9052.81
1163.92
55.94

Car cost
Avg Std. Dev.
2.1667
0.09762.15430.09402.1523
0.09312.16300.0994Bus cost
Avg Std. Dev.
2.1652
0.0536
2.15840.0516
2.15720.05112.16320.0545Figure 6: Number of travelers in each level of chosen mode

Figure 5: Dynamics of number of bus users(a)B. Travelers’ Specialization
Figure 6 shows the specialization of travelers based on
their choices of mode in every 10-iterations. All-times car users
always chose car in 10 iterations and all-times bus users always
chose bus. There are also many mixed users who chose both car
and bus during 10 iterations. At the equilibrium point, thenumber of bus users is around 1,200, with 1,000 all-times bus
users. The number of car users is about 2,900, with 2,750
all-times car users. It can be inferred that travelers are mostly
specialized in either a car user or a bus user, leaving a small
number of mixed users.

(b)
Figure 7: A traveler’s changes of choice: (a) finally became abus user and (b) finally became a car user

Figure 8: Dynamic of number of bus users at d=0.05

Figure 11: Expected payoffs (UA,UB) of a traveler at gen. 29-33

Figure 9: Dynamics of number of bus users at gen. 29-33(a)(b)
Figure 10: (a) Car payoff PA and (b) bus payoff PB at gen. 29-33
The huge increase of bus users increased the payoff of car
and bus (see Figure 10), with higher level of increase for car
payoff than bus payoff, since car cost has stiffer curve than bus
cost. At that time, travelers who had car as their choice received
high increase of expected payoff as well as travelers with bus astheir choice. They observed that the payoff of the chosen mode
was much higher than the other one, so that they used input
symbol 1 or 5 in their FSMs and continued to use car or bus. If
majority of travelers experienced those processes, then thesystem converged to another equilibrium point.
Figure 11 shows changes of expected payoffs of a traveler
before and after the outbreak of cooperation. From the
beginning of generation 29 until beginning of generation 31,
the traveler mostly chose car, so that the changes of expected
payoffs are mostly on car. But during three iterations before theoutbreak, he chose bus and the outbreak pushed his choice into
bus only.
The changes of expected payoffs of all travelers can beseen in Figure 12. Fundamental changes happened during
generation 30-40’s as a result of the cooperation outbreak.
Starting from generation 31, travelers split off into two groups,
a group of car users and a group of bus users.

Figure 12: Scatter plots of travelers’ expected payoffs at d=0.05
The kind of equilibrium found at d=0.05 is called as‘deluded equilibrium’ [11][12]. If travelers expect that thepayoff of a mode is much higher than another one, then they
will continue to choose the mode again. A deluded traveler

cannot acquire information about the choice of another mode
anymore, so that the delusion cannot be dissolved. Even though
the actual payoff of car is higher than payoff of bus, travelers
continue to use car, because in their perception the expected
payoff of bus is much higher than car.
If delusion continues, travelers form a habitual behavior
and they totally exclude other choice of mode fromconsideration. When all of them are frozen to their choices, theequilibrium becomes a ‘frozen equilibrium’ [11].
3. SIMULATION MODEL:MODELLING BY BELIEFS AND EXPECTATIONSThe second model also consists of traveler and transportation
model (see Figure 13).. The transportation model is the same as
the first model, but in the traveler model, travelers decide amode based on the rules of expectations, which shows
traveler’s belief about the influence of his action on othermembers of the groupthey chose, travelers receive payoffs and accumulate them.
After 10 iterations, the accumulation of payoffs is used as thefitness of agents’ type of curve.

Figure 14: Types of bandwagon expectations curve(from left to right; pessimistic, normal and optimistic. x axis:
fraction of cooperation, y axis: probability of cooperation)
InitialCalculate fraction ofcooperation

Social Learning
M echanisms

travel time,
payoffN

Traveler M odel
M emory- payoffs- fraction of cooperation

Rules(Expectations)Prob. ofcooperating>
criteria

Neighbors'
expectations curves
Social learning
mechanisms

Check expectations curve

Updating Rules

Transportation M odel

UPDATING RULES
RULES

New expectations
curve
N

Y

Use Bus

Use CarEnd ?

Travel Time M odel
andPayoff Functions

Y

O utputmode
chosen mode

Figure 13: Multi-agent simulation model by beliefs andexpectations
3.1 Transportation model
Please see Section 2.1.
3.2 Traveler model
A. Decision making rules: expectations’ curve
Behavior of a traveler is represented by an expectations
curve, which shows traveler’s belief about the influence of his
action on others [4]. Two classes of beliefs were considered in
the model: bandwagon expectations and opportunistic
expectations [7]. For each type, there are three types of curvethat represent agents’ level of expectations: pessimistic, normal
and optimistic. In this paper, we deal with only the bandwagon
expectations (see Figure 14). A probability of cooperating
represents a degree of an individual’s beliefs about the
influences of his action on others; and a criteria, which lies on
45 degree of straight line and the value is equal to the fractionof cooperation, represents a base of beliefs.
Figure 15 shows decision making processes of a traveler.
Initially, travelers are given a type of curve and a randomly
chosen mode. Travelers make decision at an asynchronous timeso that only 10% of them observe current level of cooperationand make a choice at the same time. Another 90% continue to
use their current mode of commuting. Based on travel mode

End

Figure 15: Decision making of a traveler
B. Interaction among agents: group-based interaction
A possibility of incorporating employer-based TDM
measures to solve a social dilemma of travel mode choice isstudied by introducing a group-based interaction, where agroup represents employees of a company. We also need thisgrouping to make travelers interact each other in order toacquire adaptive behavior by local interactions. A traveler
interacts with travelers of the same company he works in a
torus plane so that eight neighbors around him influence his
choice of behavior. Each group is independent from others sothat there is no interaction among members of different
companies. Assuming limited information, a traveler knows
only his own payoff information and types of expectations
curve of eight surrounding neighbors.
C. Evolution of expectations by imitation
We apply an imitation game based on social learning
mechanism in order to evolve expectations’ curve of eachtraveler. Two kinds of mechanism are used: payoff-biased
transmission and conformist transmission [5]. The relative
strength of each transmission depends on the strength ofconformist (α) in a traveler’s psychology [6]. For each traveler,
there are α probability to use conformist transmission and(1–α) probability to use payoff-biased transmission.
3.3 Simulation Results and Discussions
A number of agents, exactly 4096, are assigned into 16
homogeneous groups with size 256. Each agent has a type of

bandwagon expectations curve (pessimistic, normal or
optimistic), which is assigned randomly giving the same
proportion of agents for every type of expectations’ curve. We
run a simulation with various initial levels of cooperation,
ranging from 0.2 to 0.8 with increment 0.1. The strength ofconformist transmission (α) ranges from 0.0 to 0.4. Simulations
are run up to 100 generations with 10 iterations per generation.

cooperation to the equilibrium point. It can be seen that low
initial level of cooperation 0.2 gave higher convergence value
than initial level 0.3, 0.4, 0.5, and 0.6.

A. Social learning mechanism by payoff-biased transmission(α = 0.0)
The simulation resulted in an equilibrium point for initiallevel of cooperation from 0.2 to 0.7 (see Figure 16). According
to the cost functions defined before, the number of bus users at
the equilibrium point should be around 1200 or equal to 30% of
travelers. High initial level of cooperation (0.8) resulted in fulllevel of cooperation (all travelers chose bus) because for all
types of curve, the probability of cooperating at a fraction of 0.8
was higher than the criteria (see Figure 14), so that all travelers
suddenly cooperated.
Observing which kinds of type exist at the end of simulation,
all three types of curve still exist as seen in Figure 17.
Pessimistic type was chosen by the highest number of members,around 2500 travelers. Followed by normal type with around1000 members and the rest is optimistic type.

Figure 16: Dynamics of cooperation level (α=0.0)

B. Dynamics within a group at α = 0.0
Dynamics of behavioral change within a group can be seenin Figure 18, which is taken from a simulation run with initiallevel of cooperation 0.5. The number of bus users is taken fromthe average value of 10 iterations in one generation. WithinGroup 1, all members finally chose car. Pessimistic behavior
dominates the group with around 200 agents. Small numbers ofnormal and optimistic agents could not increase the level ofcooperation and furthermore they chose defection.
The situation in Group 7 is quite different. Group 7 shows
the role of optimistic agents to elicit cooperation, since they
acted alone as altruist agents following the fall of normal agents.
They could maintain the level of cooperation and increased tothe maximum level, after some pessimistic agents changed typeto optimistic one.

Figure 17: Type of curves at end of simulation (α=0.0)
Group 1

Group 7

Figure 18: Dynamics of behaviors within a group (α=0.0)

C. Combining payoff-biased transmission and conformist
transmission (α=0.1 - 0.4)
The strength of conformist is represented by a value of α.
High value means high probability of using conformist
transmission for an agent. For α=0.1 and 0.2, the dynamics are
only slightly different from α=0.0, so that we will focus on
α=0.4 (see Figure 19). The dashed line is the user-equilibriumline. At α=0.4, a higher level of cooperation than the user
equilibrium point could be reached for all initial levels ofcooperation.
Low initial level of cooperation (0.2) gave a quite different
behavior, because in the beginning the cost of bus was lower
than car, so that most of users preferred bus to car. The level ofcooperation suddenly increased and the conformist
transmission spread cooperative behavior to other travelers. If
the strength of conformist were strong enough then cooperative
behaviors could spread fast to make all group members
cooperate and stabilize cooperation within the group, without
giving payoff-biased transmission a chance to push the global

Figure 19: Dynamics of behaviors within a group (α=0.4)
Middle to high initial value of cooperation (0.4-0.7) had
different processes. In that range, the higher the initial level, thehigher is the convergence point. Let us focus on the case of
α=0.4. In the beginning, cooperation increased suddenly
because of the existence of optimistic agents who chose
cooperation, since the initial fraction of cooperation was higher
than the criteria of cooperation. They were followed by somenormal agents who later also cooperated, after observing acertain level of cooperation which was higher than their criteria.
Finally, payoff-biased transmission that has probability 0.6(1-α), had pushed the cooperation level to lower state before
the system converged. High initial level of cooperation (0.8)
favored cooperation for all types of expectations so that fulllevel of bus users was achieved.
D. Dynamics within a group at α = 0.4
Early dynamical processes within a group are complex andimportant to determine the succeeding processes and ending
results of simulation (see Figure 20). Conformist transmission
helped the spread of a type of expectations’ curve and later thegroup would become homogeneous with an only type of curve.
In some groups, optimistic expectations may dominate (eq.
Group1). But in some other groups, pessimistic or normal
expectations may also dominate (eq. Group 2).
Group 1

Group 2possible outcome. They are group-based interactions, limited
information, and conformist transmission. If there exists only
payoff-biased transmission (α=0.0), then a user equilibrium
point is reached. But, if there are a strong conformist
transmission (α=0.4) and an emergent phenomenon in thesystem, they may favor cooperation and resolve the dilemma of
travel mode choice. This gives insight to the possibility ofsolving the social dilemma by incorporating an employer-based
Travel Demand Management (TDM) measure.
In general, this research demonstrated the capability ofagent-based approaches to simulate dynamics of travel mode
choice under a social dilemma situation and to reveal some
findings, which are undisclosed by conventional analyses.
The results of both models showed that travel behaviour hasa dynamic nature as the results of learning process of eachindividual commuter. They also gave a new perspective onchanging the paradigm of modelling travel behaviour ofcommuters, from a conventional and static analysis into a more
dynamic analysis by using agent-based approaches
REFERENCES

Figure 20: Dynamics of behaviors within a group (α=0.4)
These results prove that the conformist transmission might
be able to stabilize cooperation when it is strong enoughcompared with payoff-biased transmission. By using a complex
process of interactions among agents, a combination of
payoff-biased and conformist transmissions, and also otheremergent components, a high level of cooperation can beachieved.
4. CONCLUSION
Simulation models of commuters’ learning on choosing
mode were built and applied to examining behavior ofcommuters. Both models showed that a user equilibrium point
as predicted by conventional analysis can be reached andstabilized, by interaction process among travelers and by
behavioral change process of each traveler, without any central
or external rule that organizes the objective function of thesystem. The equilibrium is a result of self-organization andcomplex process among travelers.
At the equilibrium point, there exist car users, bus users andmixed users. Most of travelers are specialized in either a car
user or bus user, leaving a small number of mixed users.
The first model revealed that an outbreak situation might
produce other equilibrium points, in addition to the user
equilibrium point, when travelers were very sensitive to payoff
differences. In these new kinds of equilibrium, which are
known as ‘deluded’ equilibrium and ‘frozen’ equilibrium,
higher level of cooperation could be achieved and stabilized.
The outbreak itself, as an emergent process of the system, madetravelers perceive an excessive increase of payoffs and form a
habit of choosing only either car or bus until the end of thesimulation.
The second model shows that cooperation level within agroup is highly related to the existence of type of expectations.
Domination of pessimistic agents would make a groupconverges to all defection and the appearance of optimistic
agents is very important to pioneer cooperation within a group.
The model revealed that some insightful results could beobtained, such as the conditions that make cooperation as a

[1]

R.Axelrod. Advancing the Art of Simulation in the Social Sciences,
Simulating Social Phenomena, Springer, Berlin, 1997.
[2] R.Dawes. Social Dilemmas, Annual Review of Psychology, Vol.31,
pp.169-193, 1980.
[3] D.B.Fogel. Handbook of Evolutionary Computation, IOP Publishing Ltd
and Oxford Univ. Press, 1997.
[4] N.Glance, B.Huberman. The outbreak of cooperation, Journal of
Mathematical Sociology, Vol.17(4), pp.281-302, 1993.
[5] J.Henrich. Cultural group selection, coevolutionary processes andlarge-scale cooperation, Journal of Economic Behavior and Organization,
Vol. 53, pp.3-35, 2004.
[6] J.Henrich, R.Boyd. Why people punish defectors: weak conformist
transmission can stabilize costly enforcement of norms in cooperative
dilemmas, Journal of Theoretical Biology, Vol.208, pp.79-89, 2001.
[7] B.Huberman, N.Glance. Beliefs and cooperation, Paper at Chaos andSociety’s International Conference, 1994.
[8] R.Kitamura, S.Nakayama, T.Yamamoto. Self-reinforcing Motorization:
Can Travel Demand Management Take Us Out of the Social Trap?,
Transport Policy, Vol.6, pp.135-145, 1999.
[9] F.Klugl, A.Bazzan. Route Decision Behaviour in a Commuting Scenario:
Simple Heuristics Adaptation and Effect of Traffic Forecast, Journal of
Artificial Societies and Social Simulation, Vol.7, No.1, 2004 (online at
http://jass.soc.surrey.ac.uk).
[10] D.McFadzean, L.Tesfatsion. A C++ Platform for the Evolution of Trade
Networks. Computational Economics 14, 109-134, 1999.
[11] S.Nakayama, R.Kitamura, S.Fujii. Drivers’ Learning and Network
Behavior: Dynamic Analysis of the Driver-Network System as aComplex System, Transportation Research Record 1676, pp.30-36, 1999.
[12] S.Nakayama, R.Kitamura. Route Choice Model with Inductive Learning.
Transportation Research Record 1725, pp.63-70, 2000.
[13] T.Yamashita, K.Suzuki, A.Ohuchi. Agent based Iterated Multiple Lake
Game with Local Governments. Complexity International, Vol 8, 1998
(online at www.complexity.org.au/ci/vol06/yamashita/yamashita.html).