Two Modes of Scheduling in a Simple Economic Agent-Based Model

Sarah Wolf

1,2

, Steffen F

urst

1,2

, Sophie Knell

, Wiebke Lass

, Daniel Lincke

1,2

, Antoine Mandel

Jonas Teitge

and Carlo Jaeger

Global Climate Forum, Berlin, Germany

Potsdam Institute for Climate Impact Research, Potsdam, Germany

Centre d’

Economie de la Sorbonne, Universit

e 1 Panth

eon-Sorbonne, Paris, France

Keywords:

Economic Agent-based Models, Scheduling, Climate Policy, Win-win Strategies.

Abstract:

Agent-based models (ABMs), and with them simulation, are gaining importance in economics. As they allow

to study coordination problems in a dynamic setting, they can be helpful tools for identifying win-win strate-

gies for climate policy. This paper argues that strongly simpliﬁed models can support a better understanding

of economic ABMs. We present work in progress on an example case: while in economic systems in the real

world many actions and interactions by various agents take place in parallel, often ABMs use sequential com-

putation. With a simple economic agent-based model of ﬁrms that trade and produce goods, we explore and

discuss two alternative modes of scheduling: the timetable model, where all agents complete one step after the

other, and the heliotropic model, where one agent after the other completes steps. We ﬁnd that the timetable

model is better suited for working with data from national statistics, while the heliotropic model dispenses

with random shufﬂing that is often introduced to guarantee symmetric expectations for agents. The latter can

be used in a completely deterministic fashion, providing a baseline case for studying the system’s dynamics.

1 INTRODUCTION

Simulation plays an ever more important role in eco-

nomics as agent-based models (ABMs) are used more

frequently. These represent the economy as a com-

plex system in which macro-features emerge from

the interaction of many heterogeneous agents. Imple-

menting a system of agents on a computer and observ-

ing simulation runs to study the system’s behaviour

poses the question whether some of the observations

owe to computational features of the implementation

rather than being characteristic of the system under

study. For example, in real-world economic systems,

many actions take place in parallel, while on the com-

puter, parallel actions are often represented by se-

quential steps. Some observations might occur due

to the sequencing chosen by the modeller

Various platforms for agent-based modelling

(such as Swarm, Repast, MASON, Netlogo, etc.) pro-

vide tools for representing time and scheduling ac-

Parallel computation may provide ways to avoid this

problem, but parallelisation is beyond the scope of this

short paper: interdependence between the agents makes the

model used difﬁcult to parallelise. Also, we aim at a simple

model, while parallel computation raises complexity.

tions by different agents. ABMs may implement a

simple sequence of agents all conducting the same ac-

tion one after the other, or complex message passing

systems between agents that trigger actions in event-

driven simulation. In some cases, randomness needs

to be introduced to to guarantee symmetric expecta-

tions for agents. For example, in a representation of

trade, the ﬁrst ﬁrms buying goods might ﬁnd full in-

ventories of all others, while the last ones may ﬁnd

inventories rather empty. To avoid such a bias, which

would be an artefact of computing sequentially, the

order in which agents act is often determined by ran-

dom shufﬂing. This means that randomness is intro-

duced for computational reasons

Most works related to ABMs provide little detail

on how simulations are executed and rather focus on

describing agents and their environment, as stated by

Mathieu and Secq (2012), who ﬁnd that the represen-

tation of time and scheduling in the simulator used, as

well as sequential or parallel execution of actions can

have crucial impacts on simulation results.

The present paper focuses on the case of sequen-

Other sources of randomness, such as random muta-

tions to represent innovation, may be essential to the model,

but are not of interest here.

303

Wolf S., Fürst S., Knell S., Lass W., Lincke D., Mandel A., Teitge J. and Jaeger C..

Two Modes of Scheduling in a Simple Economic Agent-Based Model.

DOI: 10.5220/0004032203030308

In Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH-2012),

pages 303-308

ISBN: 978-989-8565-20-4

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

tial computations with a ﬁxed schedule

. We use a

simplistic economic ABM of ﬁrms that trade and pro-

duce goods in order to explore and discuss two al-

ternative modes of scheduling: the timetable model,

where all agents complete one step after the other, and

the heliotropic model, where one agent after the other

completes steps. In particular, our work in progress

focuses on the questions how much randomness is

necessary, whether and how the model behaviour be-

comes mathematically tractable, and how model in-

put and output relates to economic data from national

statistics. We argue that a better understanding of

these questions, and of economic ABMs in general, is

relevant to climate policy making. Therefore, the cli-

mate policy background is sketched in Section 2 be-

fore Section 3 brieﬂy describes the simplistic model.

First results are presented in Section 4 and discussed

in Section 5, before Section 6 concludes.

2 CLIMATE POLICY AND ABMs

The motivation for our work on economic ABMs

stems from the climate change context. Climate

policy analysis and recommendations are generally

based on standard economic modelling; the most fre-

quently used models are computable general equilib-

rium models (Capros et al., 1999, for example) or op-

timal growth models (Nordhaus, 2008; Stern, 2007).

The general set-up is to concentrate on a a busi-

ness as usual (BAU) growth path as the single sta-

ble equilibrium path of the system, that is optimal

in the short run, and compare this with a situation

where measures for the mitigation of greenhouse gas

emissions are taken. Mitigation is framed as a wel-

fare trade-off between present and future generations:

greenhouse gas emissions are an external effect of the

present upon future generations, so that for these the

path is not optimal. The current generation uses the

atmosphere (as also a few previous generations did) as

a “waste dump” for emissions without considering the

future negative effects this will due to climate change

resulting from the emissions. Introducing a price on

emissions, this externality can be internalized, that is,

eliminated. However, on the BAU growth path this

implies costs in the short run, usually expressed in

terms of a reduction in GDP, because the current gen-

eration will have to pay for using the atmosphere, that

before it simply used “for free”.

This widely accepted welfare trade-off argument

has coined a narrative of mitigation as a problem of

Here ﬁxed is meant as in opposition to event-driven.

The schedule may still involve randomness in the order in

which agents act.

burden sharing (Jaeger et al., 2012). While the miti-

gation costs are legitimated by the beneﬁts of avoided

climate change and its impacts, these beneﬁts lie in

a rather far away future, so that on shorter planning

horizons, such as the election periods of politicians,

the costs seem much more relevant. In this setting, in-

ternational negotiations have made little progress to-

wards signiﬁcant world-wide reductions of emissions.

There is, however, in this argument a fundamen-

tal assumption that is problematic: the existence of a

unique stable equilibrium growth path of the system

is warranted neither by economic theory nor, much

more importantly, by real-world observations as sum-

marized in empirical data. For example, Ormerod

et al. (2009) ﬁnd that the US, the UK, and the Ger-

man economic system from time to time switch from

a steady to a weak pattern. Also, the comparison of

countries that at a certain point in time were in similar

situations but now differ in economic growth, such as

Poland and Hungary at the moment, deserves the con-

sideration of different growth paths.

Likewise for economic theory: the Arrow-Debreu

framework of general equilibrium shows the existence

of equilibria in an abstract setting – a growth path is

determined by prices that, for each time-step under

consideration, balance supply and demand. However,

equilibria need not be unique nor stable. Assump-

tions made to guarantee uniqueness and stability in-

clude that of a single representative agent, discussed

for example by Kirman (1992).

Hence, the narrative of climate change mitigation

as a problem of burden sharing is not the only story

to be told. Jaeger et al. (2012) suggest to “reframe

the problem of climate change, from zero-sum game

to win-win solutions”, i.e., mitigation measures which

are beneﬁcial for the economy. Win-win strategies for

climate policy can be identiﬁed when widening the

focus – from concentrating on a single equilibrium to

considering several possible equilibria (Jaeger et al.,

2010; Shi and Zhang, 2011). A low carbon econ-

omy needs a good deal of restructuring as compared

with the current economic situation, for example from

fossil to renewable energy. Such a structural change,

from the perspective of economic theory, involves a

shift to another equilibrium growth path. Win-win op-

portunities arise when the new path is in some sense

“better” than the current one. In this case, micro-costs

which occur due to mitigation measures, such as in-

creased energy prices due to emission trading, can be

more than compensated by macro-beneﬁts, such as

higher growth and less unemployment, that the new

growth path entails (Jaeger et al., 2010).

Equilibrium selection is a coordination problem

(Jaeger, 2012): as for the case of conventions (such

SIMULTECH2012-2ndInternationalConferenceonSimulationandModelingMethodologies,Technologiesand

Applications

304

as driving on the left or driving on the right) there are

several viable alternatives – which one is in place de-

pends on interactions of many agents and on institu-

tions evolving between them. In order to shift an eco-

nomic system to a different equilibrium, agents need

to re-coordinate to another alternative. Agent-based

models are a promising tool for studying such prob-

lems as they allow to consider coordination problems

between many agents in a dynamic setting. However,

few ABMs have been applied in the climate change

context, and even less to study climate economics (see

Balbi and Giupponi, 2009, for a review).

Macro-economic ABMs, of particular interest in

the climate policy context, are often rather complex

models with a huge amount of state variables (Gintis,

2007; Dawid et al., 2011; Mandel et al., 2009). Study-

ing equilibrium selection as a coordination problem

between many agents requires much more complex

models than the standard representative agent models.

However, while the simulations of a complex ABM

allow to observe the modelled system’s dynamics, this

does not necessarily mean that one understands these

dynamics. In a simulation, iterations compute one

new state after the other from a given initial state of

all agents and their environment. Hence, an ABM

could be described as a dynamical system given by a

state space together with a transition function. How-

ever, models are too complex to write these down ex-

plicitly, and it is not even clear whether the dynami-

cal system should be deterministic (Epstein, 2006) or

a Markov process, that is, probabilistic (Tesfatsion,

2006; Gintis, 2007). For the model’s implementation,

randomness can be discussed away with the argument

that the computer generates pseudo random numbers.

Many ABMs have random elements that are essen-

tial to the modelled system, but others might be intro-

duced for implementational/computational reasons.

Macro-economic agent-based modelling for (cli-

mate) policy does not always start from simple mod-

els that are then further elaborated. Therefore, as a

second track besides complex economic ABMs, we

advocate strongly simpliﬁed economic ABMs to gain

a better understanding of their properties as dynam-

ical systems and related methodological issues. In

the following, we present a preliminary example in

this spirit. While this work is further away from real-

world applications such as climate policy analysis, it

aims at small improvements of our understanding of

economic ABMs – which in turn may be very help-

ful in that context. In particular, the interdependence

between agents, that makes scheduling an issue here,

is an essential aspect also in more closely climate

change related problems.

3 THE SIMPLE ABM

The model used here is based on the Lagom model

family of economic ABMs (Mandel et al., 2009; Wolf

et al., 2012) but it radically simpliﬁes the economic

system considered: 100 ﬁrms, grouped into 5 sectors,

“trade”

and produce the good of their sector. Pro-

duction requires intermediary inputs, the production

structure is based on an input output table.

Firms’ parameters are a desired production d ∈

≥0

, input coefﬁcients for circulating capital γ ∈

[0, 1]

, and an inventory depreciation rate

r ∈ [0, 1].

It sufﬁces to consider their inventory I ∈

≥0

as state

variables in this simplistic model. Economic input

data (total production, an input-output table, and the

inventory depreciation rate) is used to initialize the

model.

3.1 Activities: Trade and Production

For each sector s = 1, . . . , 5, ﬁrms try to “buy” the

inputs for their desired production d. Being my-

opic, they only see a few ﬁrms; the number of ﬁrms

observed, and whether these are ﬁxed or randomly

drawn ﬁrms, are model input parameters. In the case

of ﬁxed suppliers, a ﬁrm “sees” the ﬁrms listed just

before itself in the model’s ﬁrm list. The set of ob-

served ﬁrms from sector s is denoted O

. Firms ﬁrst

ﬁnd out the available supply of inputs among the ﬁrms

they observe for each sector. This is a

∑

i∈O

for

sector s. The quantity to be produced is determined

as q = min



d, min

s∈S



and the required amounts

of inputs are then given by q · γ

. The ﬁrm then buys

q · γ

for each sector s, and the sellers subtract the re-

spective amounts from their inventories.

Production corresponds to a simple change of

state variables for a ﬁrm: the produced quantity q

is added to the inventory. In particular, production

changes state variables for the active ﬁrm only, while

The model uses a caricature of trade, without any pay-

ments being made. Rather than of “buying goods”, one

might speak of “obtaining presents”.

This rate can be seen as a work-around for the miss-

ing consumption in the simplistic model: inventory is de-

creased, which it would also be if the good was sold to

consumers. As money does not play a role here, this ap-

proximation is good enough for our purposes.

This is a typical case of interaction in an economic

ABM that is easy to describe in words and rather easy to

implement, but not so easy to describe as a mathematical

dynamical system. State variables of “passive” seller ﬁrms

change, and the amount q that is bought may depend on the

inventory of some ﬁrm in O

that again may depend on how

much other ﬁrms have previously bought from this ﬁrm.

TwoModesofSchedulinginaSimpleEconomicAgent-BasedModel

305

trade makes changes to the state variables of other

ﬁrms as well.

3.2 Two Modes of Scheduling

Time evolves discretely. In each period, each ﬁrm car-

ries out each activity once. Within periods, we con-

sider two modes of scheduling.

In the timetable model, two steps constitute a pe-

riod: trade and production. In each step, all ﬁrms

carry out the corresponding activity. The real-world

time interval that a period represents may be chosen

by the model user by calibrating the input data accord-

ingly. In each period, goods are produced using only

goods from previous periods as inputs. This means

that the aggregate production of all ﬁrms in one period

corresponds to the production amount in the time span

represented by this period. Therefore, data from na-

tional statistics can easily be used in this model, both

to calibrate parameters in such a way as to represent a

given real-world economic system at a given moment

in time, and to validate the model output by compari-

son with national statistics data. The trade step, how-

ever, has a “ﬁrst come ﬁrst serve”-element, therefore,

the order in which ﬁrms trade is important.

In the heliotropic model, ﬁrms enter activity

phases one after the other. Within an activity phase,

a ﬁrm ﬁrst trades and then produces. Here, all agents

are “in the same situation”: each ﬁrm ﬁnds some other

ﬁrms that have just produced goods with a full inven-

tory, while others may have sold most of their inven-

tory since they last produced. That is, in this model

no bias arises from the order in which agents act, or in

other words, ﬁrms have symmetric expectations even

though they always act in the same order. However,

production is not simultaneous here. A period can-

not easily be mapped to a time interval in the real

world because the production from one period is not

clearly separated from that of another one: ﬁrms can

use goods that others have already produced in the

same period as inputs for production. This compli-

cates the link with national statistics data.

4 SIMULATIONS

Input parameters have been calibrated in order to

identify the range of parameter values where the

model is susceptible to changes in scheduling. This

means considering an economic system in which the

production inputs are scarce, so that trading ﬁrst or

last in the timetable has an effect. The inputs used are

toy data, for example, all entries in the input-output

table are equal to 1 for simplicity. With a production

value of 5.1 for all sectors, input coefﬁcients are high

compared with the desired production and initial in-

ventories. Also, the inventory depreciation rate is set

rather high, so that inventories stay low compared to

the demand of production inputs in later periods.

4.1 Shufﬂing in the Timetable Model

Figure 1 shows that shufﬂing of ﬁrms at the begin-

ning of the trade step is indeed necessary to avoid a

bias that favours ﬁrms who trade ﬁrst: reduced pro-

ductions occur only for the last ﬁrms in the list when

no shufﬂing takes place, while, when ﬁrms are shuf-

ﬂed at the beginning of each trade step, the reduced

production amounts are scattered over all ﬁrms.

Figure 1: Timetable model with (above) and without (be-

low) shufﬂing before trade. The model output shown is the

produced quantity of ﬁrms, columns are sectors, cells show

ﬁrms. All parameters (including random seed) are the same

in the two example runs. The desired production is at the

upper border of the ﬁrms’ cells, the downward spikes show

when a ﬁrm produces less than desired.

Without scarcity, the order in which ﬁrms trade

would not have mattered here. However, it might

not always be as obvious that shufﬂing is required to

provide symmetric expectations for agents. In more

complex models, higher prices or less skilled workers

might be examples of how agents acting last are disad-

vantaged. Such biases between agents are artiﬁcially

introduced by sequential operations on the computer

that represent parallel actions in the real world.

4.2 Scarcity in the Heliotropic Model

The heliotropic model can – without a need to shufﬂe

ﬁrms – produce output that resembles the one seen in

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Fig. 1 with shufﬂing. However, with the same input

data, one sees less scarcity effects, and the inventory

depreciation rate needs to be raised to obtain a similar

picture as above. This was to be expected because

ﬁrms trading late in a period may buy goods from

ﬁrms that have already produced in that period, but

it underlines the difﬁculty of mapping output to na-

tional statistics data. Produced goods may enter back

into the production scheme in the same period when

they were produced, meaning the separation between

production inputs and produced goods is lost.

With ﬁxed suppliers, the heliotropic model can be

used to construct a completely deterministic baseline

case in which randomness is eliminated. Consider-

ing this model as a dynamical system, it is a truly

deterministic system. Writing down state space and

transition function is still a lengthy undertaking, and

therefore not done in this short paper. However, it be-

comes clearer how the system functions: depending

on the choice of data for the initialisation one can cre-

ate an economy in equilibrium, where stocks remain

the same or grow, or an economy in decline that will

in the end have to crash. For simplicity, the inventory

depreciation rate can be “switched off”, that is, set to

0. With an input of 1 unit from each sector, the econ-

omy stagnates when the production is set to 5. For

production values below this, the economy declines,

and production goes down to 0 (except for round-off

errors), and this the more quickly, the lower the ini-

tial production value is set, of course. In fact, it suf-

ﬁces to have one sector with a production that is not

sustainable to create an economy in decline when all

goods are needed as inputs. With an initial production

value greater than 5, ﬁrms always succeed in produc-

ing their desired production, and inventories simply

increase. The heliotropic model can thus be a starting

point for adding bits and pieces of complexity (e.g.,

an evolving, instead of a ﬁxed desired production), for

observing, and hopefully understanding, its effects.

5 DISCUSSION

The results presented are of course no deep modelling

results. Nevertheless, this simple model highlights

some interesting points concerning economic ABMs

that use sequential computation. In particular, both

modes of scheduling come with advantages and dis-

advantages.

In the timetable model, shufﬂing introduces ran-

domness that is not actually essential to the mod-

elled system, but required in order to provide sym-

metric expectations for agents, owing to the sequen-

tial implementation of the model. Randomness in

ABMs implies that the interpretation of model out-

put necessitates many model runs and statistical eval-

uations of these to learn about the distributions of

states. Looking at single trajectories, one might see

some effects of improbable events having taken place

in just this run. While in ergodic systems the proba-

bility distributions over states converge regardless of

the initial state chosen, one does not necessarily know

when the system arrives “close enough” to the limit

and while distributions converge, this does not mean

one only sees “average” trajectories. The heliotropic

model eliminates this randomness, allowing for a sim-

pler starting point for analysing the ABM. In the ef-

forts that are being made to create economic ABMs

which are mathematically tractable, this is a step for-

ward. In fact, the deterministic dynamical system that

arises when using ﬁxed matching rules for trade in

this model shows behaviour that depends on the input

data used in a clearly understandable way.

At the same time, efforts are being made to create

economic ABMs which are empirically satisfactory

(Fagiolo et al., 2006; Boero and Squazzoni, 2005, for

example). Here, the timetable model shows an advan-

tage. The “separation” of periods, meaning that all

goods produced in a given period can be used as pro-

duction inputs at the earliest in the next period, allows

to consider the aggregate production of all ﬁrms in a

period as corresponding to the real-world production

of the time span that this period represents. Greater

ease of mapping data from national statistics to input

data, and vice versa mapping model output to data

from national statistics facilitates the empirical vali-

dation of the model. This is an important advantage

also in the climate policy context, where empirically

relevant models are badly needed to “compete” with

single equilibrium models. As most data are in a for-

mat ﬁt for standard modeling approaches, ABMs that

can be fed and validated with these data formats have

the edge over those that cannot.

6 CONCLUSIONS AND

OUTLOOK

This paper presented work in progress on the compar-

ison of two scheduling modes for a simple economic

ABM. We ﬁnd that the output is similar. However, the

timetable model, where all ﬁrms complete one step af-

ter the other, is closer to data from national statistics,

facilitating their use as input and the interpretation

of aggregates in the model output. The heliotropic

model, where one ﬁrm after the other completes all

steps, can do without shufﬂing that in the other model

is necessary to avoid favouring agents who act ﬁrst.

TwoModesofSchedulinginaSimpleEconomicAgent-BasedModel

307

Thus, the heliotropic model eliminates randomness –

artiﬁcial, because required due to sequential compu-

tations – producing a simpler model.

For the task of helping to generate theoretical in-

sights, it can be helpful to start from simple economic

ABMs and add complexity in a step-by-step manner.

In fact, this is the aim of the models used here: too

simple to study real-world economic systems, they

may allow a better understanding of issues that can

be studied already at this simple stage. Indirectly, a

better understanding of economic ABMs as dynami-

cal systems then may contribute to policy analysis of

real-world problems – as for example the questions of

multiple equilibria and win-win strategies for climate

policy sketched above.

Further work on simple economic ABMs, in par-

ticular on a completely deterministic version of the

heliotropic model as a benchmark and on these mod-

els as dynamical systems in the mathematical sense,

seems worthwhile.

REFERENCES

Balbi, S. and Giupponi, C. (2009). Reviewing agent-based

modelling of socio-ecosystems: a methodology for

the analysis of climate change adaptation and sustain-

ability. Working Papers Department of Economics,

Ca’ Foscari University of Venice No. 15/WP/2009.

ISSN 1827-3580.

Boero, R. and Squazzoni, F. (2005). Does Empirical Em-

beddedness Matter? Methodological Issues on Agent-

Based Models for Analytical Social Science. Journal

of Artiﬁcial Societies and Social Simulation, 8(4).

Capros, P., Georgakopoulos, T., Filippoupolitis, A., Kot-

somiti, S., Atsavesand, G., Proost, S., Van Rege-

morter, D., Conrad, K., and Schmidt, T. (1999). The

GEM-E3 model: reference manual.

Dawid, H., Gemkow, S., Harting, P., and Neugart, M.

(2011). Labor market integration policies and the con-

vergence of regions. Journal of Evolutionary Eco-

nomics. Online ﬁrst.

Epstein, J. M. (2006). Remarks on the foundations of agent-

based generative social science. In Tesfatsion, L. and

Judd, K., editors, Agent-Based Computational Eco-

nomics. Elsevier, North-Holland.

Fagiolo, G., Windrum, P., and Moneta, A. (2006). Empirical

Validation of Agent-Based Models: A Critical Survey.

LEM Working Paper Series, 14.

Gintis, H. (2007). The Dynamics of General Equilibrium.

Economic Journal, 117(523):1280–1309.

Jaeger, C. C. (2012). Scarcity and coordination in the global

commons. In: see right below. pp. 85–101.

Jaeger, C. C., Hasselmann, K., Leipold, G., Mangalagiu, D.,

and T

abara, J. D. (2012). Reframing the Problem of

Climate Change: From Zero Sum Game to Win-Win

Solutions. Routledge.

Jaeger, C. C., Paroussos, L., Mangalagiu, D., Kupers, R.,

Mandel, A., and T

abara, J. D. (2010). The Europe

Mitigation Project – Assessing the growth and job im-

plications of moving the European climate target from

-20% to -30%. German Federal Ministry for the En-

vironment, Nature Conservation and Nuclear Safety,

Berlin. see www.newgrowthpath.eu.

Kirman, A. P. (1992). Whom or what does the representa-

tive individual represent? The Journal of Economic

Perspectives, 6(2):117–136.

Mandel, A., F

urst, S., Lass, W., Meissner, F., and Jaeger,

C. C. (2009). Lagom generiC: an agent-based model

of growing economies. ECF Working Paper, 1.

Mathieu, P. and Secq, Y. (2012). Environment updating and

agent scheduling policies in agent-based simulators.

ICAART, 2:170–175.

Nordhaus, W. (2008). A question of balance: Weighing the

options on global warming policies.

Ormerod, P., Rosewell, B., and Phelps, P. (2009). Inﬂa-

tion/unemployment regimes and the instability of the

philipps curve. Economics E-Journal Discussion Pa-

per, No. 2009-43.

Shi, H. and Zhang, Y. (2011). How Carbon Emission Mit-

igation Promotes Economic Development – A Theo-

retical Framework. Draft.

Stern, N. (2007). The Economics of Climate Change. The

Stern Review. Cambridge University Press, Cam-

bridge, UK.

Tesfatsion, L. (2006). Agent-based computational eco-

nomics: A constructive approach to economic theory.

In Tesfatsion, L. and Judd, K., editors, Agent-Based

Computational Economics. Elsevier, North-Holland.

Wolf, S., F

urst, S., Mandel, A., Lass, W., Lincke, D., Pablo-

Mart

ı, F., and Jaeger, C. (2012). A multi-agent model

of several economic regions. Submitted to Environ-

mental Modeling and Software.

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