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0RGHOLQJRI&RPSOH[(FRQRPLF6\VWHPVZLWK$JHQW1HWV
$OH[HL$*DLYRURQVNL
Department of Industrial Economics and Technology
ManagementNTNU-Norwegian University of Science and Technology
Alfred Getz vei 1, N-7034 TrondheimNorway
email:[email protected]
$EVWUDFW
We consider a methodology for modeling,simulation and design of
complex economicsystems which we call $JHQW 1HWV. It isspecifically
designed to represent complexsystems composed from independent
entitiescalled DJHQWV which transform and exchangeinformation and
other resources takingindependent and coordinated decisions on
thebasis of incomplete information about state ofthe whole system
and actions of other agents.
Specifying particular cases of agents we candescribe as Agent
Nets distributed systems,which include mobile software agents as
well asmany different economic systems. In this paperwe present
mathematical description of AgentNets, describe an Agent Net
simulatorMODAGENT created for simulation ofmultiagent systems and
present a case studydealing with agent modeling of
industrialrelations in information industry which haveimplications
for electronic commerce.
,1752'8&7,21Variety of distributed systems can be described
as acollection of relatively independent units called hereDJHQWV
which process and exchange information,products, services, money
and other resources, formulateand pursue strategies and make
decentralized decisionsdirected towards achievement of aims. Taking
as areference telecommunications, we can see that in the caseof the
global area network such agents are the networknodes which exchange
traffic flows and signaling andmake routing and congestion control
decisions. In thecase of local ATM networks such agents are
localexchanges with admission control units which
negotiateresources with users and supervise the user behavior,
while the users themselves can be considered another typeof
agents.
Another important example of multiagent system ispresented by
information industry understood asprogressive intertwining of
telecommunication industry,computer industry and content provision.
As a result ofderegulation and technological innovation this
industry iscomposed from rich variety of enterprises which
cancombine different industry roles and engage in complexrelations
of competition and cooperation. In this caseagents are enterprises
and users of information products.More detailed analysis of
information industry asmultiagent system can be found in (Bonatti,
Ermolievand Gaivoronski 1998, Bonatti and Gaivoronski 1996,Bonatti
HWDO1996).
Historically the word DJHQW was used extensively ineconomic
modeling to describe economic subjects whichmake independent
decisions. More recently the notion of"intelligent agents" was
introduced to describe computerprograms operating in distributed
and networked realitylike Internet and acting on behalf of a human
takingintelligent decisions (Boman 97, Jennings HWDO98). In
ourmodeling of systems composed of agents we draw uponboth of these
notions.
In all of these cases there exist a number of
successfulapproaches for modeling of individual agents. Themodeling
of systems of agents is, however, much moredifficult task and
became only recently a subject of active
research. In this paper we consider an approach formodeling of
multiagent systems which we call $JHQW1HWV
Let us start by observing that although multiagent
systemsmentioned above are very different by nature, theypossess
the following common features, which suggest adevelopment of common
methodological approach fortheir modeling.
1HWZRUNVWUXFWXUH. All these systems can be representedas graphs
with agents being the vertices of the graph. Theedges of the graph
represent exchanges and interactionsbetween agents. In the case of
telecommunicationnetwork these edges correspond to the links
betweennodes, while in the case of information economy theedges are
supplier-consumer relationships.
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7UDQVIRUPDWLRQDQGH[FKDQJHRIUHVRXUFHVDQGIORZV. Inall cases agents
possess internal resources, transforminput resources and flows in
output resources and flows,and exchange traffic flows and
resources. In case of the
network nodes such internal resources are represented
byprocessing capacities and buffers, the input flows arereceived
packets and inbound connections, the outputflows are outgoing
packets and connections. In case ofenterprizes internal resources
are production capacitieswhich transform input resources into
products andservices. In case of end users internal resources
areterminals while input resources are connections, productsand
services. Agents exchange flows and resources.Examples of such
exchanges include exchange ofproducts for money, exchange of
signaling betweennetwork nodes while establishing a connection,
exchangeof information for information. In what follows weconsider
as UHVRXUFHV all passive commoditiestransformed and exchanged by
agents, includingresources in common sense, but also all kinds of
products,services, information and traffic flows.
'LVWULEXWHGDV\QFKURQRXVGHFLVLRQPDNLQJDQGFRQWURO.All agents take
decisions, which involve assignment ofinput resources, treatment of
input and output resources,selection of partners for exchange.
These decisions aretaken in independent and asynchronous way,
althoughthey can be coordinated. Examples of such decisions
arerouting, admission control and congestion controlalgorithms of
telecommunication network nodes,production, development and
marketing policies ofenterprises, selection of service providers by
end users. In
selection of decision strategies agents seek to follow
theirindividual criterions and aims which may or may not
becoordinated with each other. Therefore the design ofmultiagent
systems can not be reduced to simple globaloptimization criterions,
like minimization of total costs ormaximization of properly defined
"public good".
'\QDPLFV. Multiagent systems can exhibit widelydifferent dynamic
behavior due to richness of positive andnegative feedbacks usually
present in such systems. Theycan have many equilibriums and switch
in catastrophicmanner between them. They can exhibit totally
chaoticbehavior even in the absence of random disturbances.Design
based on the study of steady state behavior is not
adequate because in many cases such systems changeconstantly.
Examples of such nonstationary changesinclude rapid development of
mobile networks andexplosion of Internet.
,QFRPSOHWHLQIRUPDWLRQDQGERXQGHGUDWLRQDOLW\ . Thereare two main
sources of uncertainty in multiagentsystems: external and internal.
External uncertainty is dueto the fact that multiagent systems
operate in uncertainand changing environment. Changing demand
patternsand technological change are two examples of
suchuncertainty. Internal uncertainty appears because theagents
have limited knowledge of strategies and states ofother agents.
Agents should employ decision principles,
which take into account such uncertainty. However, evenif the
complete information would be available it is often
impossible to use due to constraints on processing
times.Therefore it is not realistic to consider agents as
beingcompletely rational maximizing some utility function.Instead
decisions are made by ERXQGHGO\UDWLRQDO agents
on the basis of changing set of heuristics based onprevious
experience (Arthur, 1994).
In order to represent these features we consider a class
ofmodels called $JHQW1HWV. It is a network like structurewith
agents being the vertices of oriented graph whichedges define the
exchanges between agents. This structureis associated with
appropriate resource space with agentstransforming and exchanging
resources from this space.Each vertice of the graph is equipped
with the set oftransformation functions and strategies. The state
of thevertice (agent) is defined by the vector of internal,
inputand output resources. There are dynamic relations whichguide
the evolution of the state of the agents similar to
those considered in the theory of Discrete Event DynamicSystems
(Ho and Cao 1991, Gaivoronski HWDO1992, Pflug1992, Cassandras 1993,
Rubinstein and Schapiro 1993).
We utilize the experience accumulated recently in othernetwork
models, in particular Petri Nets (Peterson 1981,Archetti,
Gaivoronski and Sciomachen 1993), NeuralNets (Hertz et al 1991,
Gaivoronski 1994) and BayesianNets (Neapolitan 1990, Archetti,
Gaivoronski and Stella1997). Petri Nets are very good in
representingasynchronous distributed processes, however it is
difficultto use them to represent nontrivial agents with
resourcetransformation, exchange and control strategies. NeuralNets
are useful models for recognition of complex
patterns which can be present in multiagent systems,however they
are lacking tools for representingdistributed decision making.
Bayesian Nets are good inprocessing incomplete information, but
again lackingstructure for agent representation. Therefore a
newnetwork model is needed for representing multiagentsystems.
We should mention here related work in other fields,which
partially addressed some of the issues treated here.Research in
computational economy and market orientedprogramming resulted in
creation of several tools fordistributed resource allocation in
financial and other fields(Even and Mishra 1996, Steiglitz et al
1995, Waldspurger
et al 1992, Wellman 1993). Dynamic interactionsbetween economic
agents were considered in evolutionaryeconomics (Dosi and Nelson
1993, Lane 1993).
In order to cope with uncertainties inherent in
multi-agentsystems we utilized approaches developed in
stochasticprogramming (Birge and Wets 1987, Ermoliev and Wets1988,
Gaivoronski 1982, Higle and Sen 1991, Kall andWallace 1994, Mulvey
and Ruszczynski 1992).
The rest of the paper is organized as follows. In Section 2we
describe the notion of Agent Net and discuss some itsproperties.
Simulation system MODAGENT developedfor simulation of Agent Nets
with application to modelingof information economy is presented in
Section 3. Section
4 is dedicated to the case study from modeling of relations
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between network providers and providers of informationservices
over telecommunication networks.
$*(171(76$JHQW 1HW is composed of two oriented coordinatedgraphs
)},(),,{( 351$ where
$1 - the DJHQWJUDSK defined by the set ofD
Q vertices$ called DJHQWV and the set of oriented arcs $$1
.Agents possess additional structure which will be
definedseparately. Arcs connect those agents which can beinvolved
potentially in WUDQVDFWLRQV.
53 - the UHVRXUFH JUDSK defined by the set ofU
Qvertices 5 called UHVRXUFHV and the set of oriented arcs
553 . Quantity and other attributes may beassociated with each
resource.
For each agent $DL
let us define two sets:
{ }1DDD$LMML
=+ ),(| - the set of agents from which
oriented arcs point to agentL
D ;
{ }1DDD$MLML
= ),(| - the set of agents to which
oriented arcs point from agentL
D ;
Similarly for each resource 5UL
we define:
3UUU5LMML
= ),(| - the set of resources from which
oriented arcs point to resourceL
U ;
{ }3UUU5M
L
M
L
= ),(| - the set of resources to which
oriented arcs point from resourceL
U ;
The purpose of the Agent Net is to model transformation
of resources from 5 by agents from $. Informally,L
5 is
the set of resources which participate in transformation
which result in resourceL
U . In order to transform
resources agents make transactions between each other.
The setL
$ is composed from all agents which possess
resources used in transformations performed by agentL
D .
6758&785(2)$*(176Agent Nets differ from other network like
structures,notably Petri Nets, Neural nets and Bayesian Nets bymore
involved node structure which permits to modeldifferent types of
agents found in real multiagent systems.
AgentL
D is a tuple ),,,,,,,(LLLLLLLL
'0)6(2,7 where
57L
- set of internal resources, these resources are
needed to model production capacities and technical
capabilities;
5,L
- set of input resources, these resources are
obtained from agents belonging toL
$ in the process of
transactions;
52L
- set of output resources, these resources areobtained by
transformation from input resources with the
help of internal resources and constitute the RIIHU of agent
L
D to agents from L
$ ;
5(L
- set of exchange resources, these resources are
exchanged by agentL
D with agents fromL
$ for inputresources.
These resource sets are connected with agent and resourcegraphs
by the set of constraints, in particular
C1. For eachLN
,U exists +L
$D such thatMN
2U .
C2. For each +LM
$D existsMN
2U such that.L
,U .
C3. For eachLN
2U we haveLLN
,75 + .
C4. For eachLLM
,7U existsLN
2U such that+
NM
5U .
)(W6L
- VWDWH of the agentL
D which is the vector of
quantities of resources from LLLL (2,7 . Thisvector is indexed
by members of resource sets of agent
L
D
and is varying with time W. In this way the state 6W of thewhole
multiagent system is composed of the states of
individual agents: ))(),...,(()( 1 W6W6W6 Q= .
{ }LLL
M N
LL
,7N2M)) = ,),( - the set of
transformation functions which define relations
)([)\ M NL
=
where \ is the amount of internal or input resourceN
Unecessary to obtain amount [ of output resource
M
U .Similar transformation functions are defined for
internalresources and they describe amount of input
resourcesnecessary for obtaining of specified amount of
internalresource. In this case such functions are used to
describeprocesses of investment and development.
)(W0 - the information available to agent D at time W.
Generally, it is some subset of the state 6W of agent
netobtained with some delay and contaminated by errors.
)(W'L
- the set of strategies of agentL
D at time W. These
strategies depend on the state )(W6L
and information
)(W0L
and can belong to several classes 3URGXFWLRQ
VWUDWHJLHV define amount of output resources to offer.
([SDQVLRQVWUDWHJLHV define amount of internal resourcesto add to
existing ones. 7UDQVDFWLRQVWUDWHJLHV involvingselection of partner
agents to make offer of output
resources to, fixing the amount of exchange resource
asked for the output resource, choice of partners for
obtaining input resources.
(92/87,212)$*(171(76Agent Net evolves in continuous or discrete
time. Itsevolution is driven by transactions between agents.
Eachagent selects its production, expansion and transactionprogram
according to the set of its strategies and available
information. Each transaction involves exchange of
inputresources for exchange resources which changes the
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volumes of these resources in possession of agents.Evolution of
Agent Net is described in more detail in(Bonatti, Ermoliev and
Gaivoronski, 1998).
Agent Nets can be studied using graph theoretical
methods and methods used in the study of Discrete EventSystems.
There are many open research issues which arediscussed together
with some properties of Agent Nets in(Bonatti, Ermoliev and
Gaivoronski,1998).
6
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discrete time.
Resources can belong to one of five top level classes:,QSXW,
2XWSXW, ,QWHUQDO, 'HPDQG and 1HHG.Besides, there are exchange
resources which are handled
by special class $FFRXQWDQW. ,QSXW resources areprocured in the
0DUNHW in exchange for exchangeresources, are transformed by an
agent in 2XWSXWresources using ,QWHUQDO resources and offered to
the0DUNHW in exchange to exchange resources. 1HHGresources are
satisfied by end user consuming 'HPDQGresources procured in the
0DUNHW in exchange toexchange resources. Thus, resources belonging
to ,QSXWclass of one agent may belong to 2XWSXW class ofanother
agent and to 'HPDQG class of end user. Therelations between
different resource classes and classes$JHQW and 0DUNHW are shown on
Figure 2, similar butsimpler relations connect 0DUNHW and
(QG8VHU
, Q W H U Q D O
$ J H Q W
0 D U N H W
, Q S X W ( [ F K D Q J H ( [ F K D Q J H 2 X W S X W
Figure 2: Relations Between Resource Classes andClasses 0DUNHW
and $JHQW
The complex relations which connect agents and endusers
necessitated to make further structuring of$JHQWclass into high
level subclasses. Besides resource classes,QSXW, 2XWSXW and
,QWHUQDO mentioned above theseclasses include:
,QIRUPDWLRQ handles information available to $JHQW;&RQVXPHU
procures and handles ,QSXW resources;3URGXFHU transforms ,QSXW
resources into 2XWSXWand handles expansion of,QWHUQDO
resources;6XSSOLHU handles and dispatches 2XWSXW resourcesproduced
by $JHQW;6HOOHU markets 2XWSXW resources;
$FFRXQWDQW handles the flow of exchange resources,keep balances
and generally keeps track of $JHQWperformance;0DQDJHU defines
policies executed by other members of$JHQW;
The top level structure of$JHQW is shown on Figure 3.Many agents
will not possess fully developed componentsof thisstructure, in
such cases some of components willbe empty. Detailed description of
MODAGENT structurecan be found in (Gaivoronski, 1998).
Another example of multi-agent modeling system isSwarm from
Santa Fe Institute (Minar et al, 1996).Compared to Swarm we place
much more emphasis on a
general way to model agent structure and agent strategies.
&$6(678'
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independent from infrastructural services of networkoperators,
like, for example, radio and TV service.
These services are partially substitutable between eachother.
End users chooses between different services
according to the following demand generation model.Attitude of
each end user towards any particular service 6
L
is characterized by service utility function IL
[ which isnondecreasing function varying from 0 to 1 which
definesthe fraction of need 1 satisfied by amount [ of service6
L
This function is characterized by two parameters:
(QGXVHUV
N1
$JHQWV
A1
A3
A2
S1
S2 I1
S3
S2
Figure 4: Information Service Provision
DL
- the maximal possible fraction of need which can besatisfied by
a given service when its amount [ tends toinfinity, we assume that
all D
L
sum up to 1.
EL
- the incremental fraction of the need satisfaction byservice
6
L
for small values of[. End user chooses betweenservices by
maximizing his need satisfaction within givenbudget (perhaps with
some error). This permits us tomodel nonhomogeneous user population
with thefollowing service adoption cycle. Suppose that there issome
established service and some emerging service. Onthe early stages
of service introduction there will be somefraction of "early bird"
users which will adopt a newservice even if it costs substantially
more than traditionalservice, it is enough that the new service has
some newappealing features. On the later stages the main body
ofusers will adopt the new service, but only if it willbecome price
competitive with the old service. Andfinally, there will remain
some fraction of users whichwill switch to the new service only if
it will become
substantially cheaper than the old service.Normally, there is
more than one provider of the sameservice on the market, which
offer service with differentprices. We assume, however, that there
are moreattributes to a service than the price and services
fromdifferent providers may differ in many other respects,
likequality, etc. Thus, not all end users select provider withthe
cheapest service. However, the price remainsimportant attribute of
a service and market quotas ofdifferent producers increase and
decrease depending onprice. This permits us to differentiate
between basicservice with standard quality and more expensive
servicewith enhanced quality.
Finally, we assume that end users follow with some delaythe
relative price dynamics of different producers.
3URGXFHUV. There are three groups of producers:
2a. 3URYLGHURIVWUXFWXUDODQGLQIUDVWUXFWXUDOVHUYLFHV$
.He provides structural information services 6
and 6
andinfrastructural service ,
necessary for provision of6
and
6
. We refer to this agent as 1HWZRUN2SHUDWRU.
2b. 3URYLGHU RI VWUXFWXUDO VHUYLFHV $
. He providesinformation service 6
for which he needs to buyinfrastructural service ,
from $
. Alternatively, we referto this provider as
,QIRUPDWLRQ6HUYLFH3URYLGHU. Thus, heis a competitor of$
, although in order to compete heneeds the service ,
provided by $
. Take, for example, as$
an Internet provider which leases lines from networkoperator to
provide information services and take as $
network operator which is also engaged in provision
ofinformation services.
2c. 3URYLGHU RI VWUXFWXUDO VHUYLFHV $
. He provides
information service 6
and is independent from both $
and $
. Think, for example, about newspaper publisher orowner of TV
channels. His economic function is toprovide a service which can
substitute to some extent both6
and 6
in case if they become too expensive orinadequate in some other
respect
7KHREMHFWLYHVRI HFRQRPLF DJHQWV. We assume thatend users
maximize satisfaction of their needs forinformation services as
described above. Providersmaximize their profit by choosing among
differentstrategies. These strategies belong to three classes:
- increase market offer, decrease price and expandprovision
capacities if necessary;
- decrease market offer and increase price, maybemoving to more
specialized market niche;
- keep constant the price and market offer.
Strategies from the same class differ by amount of changeof
price and market offer. Providers choose between thesethree
strategy classes according to information about themarket behavior.
If profit increased during current periodthen the current strategy
is maintained or enforced,otherwise the strategy is likely to
change. This is doneaccording to OHDUQLQJ SURFHVV which uses
informationabout market behavior and is organized similarly to
thelearning process in the theory of learning automata. That
is, each strategy is characterized by probability accordingto
which this strategy is chosen on the next step. Theseprobabilities
are updated each period: the probability ofstrategy which improves
some specified performancecriterion is increased while
probabilities of otherstrategies are decreased. However,
probabilities of allstrategies remain positive, which reflects the
fact that theprofit maximization is the most important, but not
uniquedriving force of agent behavior. Therefore we permit alsothe
keeping of the strategy which leaded to profitdecrease, but with
smaller probability compared to thecase when this strategy
increases the profit.
Our objective was to model dynamics of competition and
cooperation between providers $ and $ , penetration ofservice
6
and dynamics of total market for information
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services 6
and 6
. This was studied under differentscenarios about market and
expansion strategies of bothproviders, different provision costs
for service 6
,different policies of market regulation.
-10
-5
0
5
10
15
20
25
30
35
40
1 21 41 61 81 101 121 141 161 181
v r r v q
S
U
R
I
L
W
Information Service Provider Netw ork Operator
Figure 5: Strong Wins
620(5(68/76Due to the space constraints we can present results
onlybriefly. We observed many interesting phenomena, whichhave
convincing economic interpretations, in particular
- "Strong wins": importance of pursuing aggressivemarket and
expansion policies (for those who can affordthem), the provider
with strong policies assures himselfthe largest profit share even
with somewhat inferiorprovision costs; see Figure 5 where the
weaker agent isdriven into bankruptcy.
- benefits of market regulation which may be performedeither by
appropriate regulation body or by agreementbetween providers. Such
regulated competition permits tosurvive providers which offer
superior service but can notexpand the offer rapidly, in many cases
safeguards thetotal market value and in many cases is beneficial to
allplayers since it stabilizes the market. This case isillustrated
by Figure 6 where compared to Figure 5 anupper limit on price for
service ,
was introduced.
- tendency of Network Operator to concentrate on his
corebusiness when his information service provision costs arehigh
and his tendency to compete in information serviceswhen his costs
are comparable with Information Service
Provider. Figure 7 gives breakdown of Network Operatorrevenue
for one such case.
- high instability of nonregulated market when everybodypursues
strong policies, price wars (Figure 8);
- emergence of qualitatively different dynamical patternsof the
system evolution which may include in some casesoscillations in
vicinities of different equilibriums and inother cases markedly
chaotic behavior.
In this example MODAGENT can be used to identifyregions of agent
parameters which guarantee desirablebehavior of economic
system.
&21&/86,216We presented here the concept of Agent Nets
formodeling of complex distributed multiagent systems,
described the system MODAGENT for simulation ofAgent Nets and
provided an example of Agent Netapplication to study of competition
and collaborationbetween different types of service providers
ininformation industry.
-10
-5
0
5
10
15
20
25
30
35
40
1 21 41 61 81 101 121 141 161 181
v r r v q
s v
Information Service Provider Network Operator
Figure 6: Regulated Price for Leased Lines
0
10
20
30
40
50
60
70
80
1 21 41 61 81 101 121 141 161 181
v r r v q
r
r
r
Serv ice S1 Serv ice S2 Serv ice I1
Figure 7: Network Provider Focuses on Core Business
0
10
20
30
40
50
60
70
80
90
100
1 21 41 61 81 101 121 141 161 181
v r r v q
H
h
x
r
s
v
s
h
v
r
v
p
r
Market value Information Service Provider Network Operator
Figure 8: Price War When Both Are Strong
$FNQRZOHGJPHQWV
The author is grateful to Dr. Mario Bonatti from Italtel for
useful discussions on the early stages of this project.
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