How to Build an Agent-based Model to Assess the Impact

of Co-payment for Health Services

Angela Testi, Michele Sonnessa and Elena Tànfani

Department of Economics, University of Genova, Via Vivaldi 5, Genova, Italy

Keywords: Agent-based Models, Economic Simulation, Health Care Financing.

Abstract: Some forms of co-payment are required in insurance markets to avoid moral hazard that in health sector

entails excessive consumption and costs. Literature and empirical findings, however, do not agree about the

effectiveness of co-payment in practical situations. Moreover, in health systems co-payment seems to be

more aimed to help in financing than to reduce moral hazard. The final impact of co-payment is rather

difficult to predict due to these conflicting aims. Assessing the impact of a co-payment policy is, however,

very important, because it affects also the principles of universalistic health systems threatening equity

attainment. The specific aim of this paper is to propose an Agent-based simulation model that allows both i)

to take into account all these contradictory effects at the same time, ii) to compare different co-payment

models. The model development is presented mixing empirical data with some stochastic assumptions the

authors intend to test.

1 INTRODUCTION

Insurance companies use co-payments to share

health care costs and prevent moral hazard, that is

post contractual opportunistic behavior to transfer

more risks to insurance company. In absence of

some co-sharing tools, this behavior leads to

inefficient situations, excessive consumption and

higher costs. Though co-payment is often a small

portion of the actual cost of the medical service, it is

meant to prevent people from seeking medical care

that may not be necessary. The underlying

philosophy is that with no co-payment, people will

consume much more health care services than they

otherwise would if they were paying for all or some

of them. Co-payment may, however, be ineffective

in presence of relevant Supply-Induced-Demand

effect, i.e. when services are not demanded directly

by the patient, but by the physician, acting as patient

"agent". In this case excessive consumption, due to

moral hazard, will not be reduced and even we could

predict a further increase (Ellis and McGuire, 1993).

However, also in case of moral hazard reduction, the

crucial issue is that co-payment should reduce only

not essential consumption, without discouraging

people from seeking necessary medical care. This

can be done, applying co-sharing measures (e.g.

tickets or ceiling, or caps) on more elastic

consumption items.

The above described mechanism is, however,

based only on a theoretical model. From an

empirical point of view, co-payment acts as a

rationing device preventing access to care in

universalistic systems as literature shows (Louckx,

2002). And even if no definite result is given, many

empirical papers, from the more complete and cited

(Manning et al, 1988), predict effects of

consumption restriction of the more frail and

deprived people, engendering negative effects on

their health status. It seems that co-payment gives

rise to the classical trade-off between equity and

efficiency, where the only demonstrated effects are

the negative ones on equity, because gains in terms

of efficiency and cost containment are not clearly

verified by empirical literature (Carrieri, 2010).

What makes things more difficult is, however,

that in practical application, co-payment is not

utilized, as theory prescribes, to reduce moral

hazard, but almost exclusively as a tax to finance

public budget. This is, however, a practical aim

opposite to the theoretical one, entailing that to be

more effective, co-payment should not change

consumption, which is exactly the opposite of co-

payment intended to reduce moral hazard.

If co-payment should improve public balance, it

should be imposed on the "less" elastic items, not to

556

Testi A., Sonnessa M. and Tànfani E..

How to Build an Agent-based Model to Assess the Impact of Co-payment for Health Services.

DOI: 10.5220/0004166205560563

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

556-563

ISBN: 978-989-8565-20-4

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

the "more" elastic ones: this means on the more

essential services, the ones that patient do not reduce

even if their price increases. In this case negative

effects on equity are still larger, because being a

form of financing not linked to the ability to pay, but

rather to the use of services, it requires greater

contribution from the least well-off (Wagstaff et al.,

1999), even if to attenuate partially this undesirable

effect some exemption rules are usually

implemented.

As far as we know the impact on the public

budget of the introduction of a co-payment system

has never been studied in detail, nor who bears the

greatest disadvantage. We can predict that as co-

payment is perceived as a price by the patient, a

price increase means reducing demand, but how

much demand reduces depends on elasticity.

Following traditional microeconomics, we know that

elasticity depends on price effect, which, in its turn

is composed by a substitution and an income effect.

The first effect depends on how many substitutes

exist, while the income effect on how large the

income is in absolute term and how large health

expenses are in relative term with respect to other

goods. If the aim is to finance health services, co-

payment should be applied to services with a rigid

demand, that is were no substitution effect exists and

health expenses are high during a year, for instance

in chronic conditions. This is, of course,

contraindicated for equity, so, before recurring to co-

payment in universalistic systems, decision makers

should know in advance: i) whether increasing co-

payment will make people reduce their demand for

services and / or getting no consistent fiscal return

and ii) what is the best exemption structure to

correct excessive payment from chronic or deprived

patients.

In particular, since 2000, the Italian experience,

developed in some different ways following the

regional policies, includes diverse experiences of co-

payment on drugs, diagnostic and specialist visits,

differently designed in the Italian regions. From a

point of view aggregate and almost exclusively for

drugs there are some data showing what has been the

impact (http://www.agenziafarmaco.gov.it/it/content

/osservatorio-sull%E2%80%99impiego-dei-medici

nali-osmed). Data on specialist visits, diagnostic and

revenue that has been obtained during the years are,

however, missing, even if some preliminary

information were given during a national Conferen-

ce in Rome, last May (http://www.agenas.it/agenas_

pdf/Dossier%20Co-payment_aprile2012.pdf). The

same happens for the effects on different categories

of exempt people. In this research still in course, it

appeared that, generally, the patients who cannot

profit by exemption consume less medicines,

diagnostic and specialist visits than the exempted

ones. From this strong, and not yet published

evidence of under treatment, the empirical aspect of

this study took start.

In this paper, we propose an Agent-based

modeling framework aimed at investigating the

effects of different co-payment rules.This model can

represent a useful support to decision makers,

increasing the capacity to control the adverse

consequence of co-payment on equity of access.

The reminder of the paper is as follows. In

Section 2 an agent-based simulation model is

described intended to be a tool for better decision

making about definition of more effective co-

payment policy. Section 3 provides an overview of

the LigurNet database the model is built upon.

Section 4 indicates conclusion and further work.

2 AGENT-BASED MODEL

In economic research increasing attention is given to

agents' characteristics and their interaction to

determine aggregate results. This is crucial in

complex situation as co-payment is. Since it is

impossible to verify single economic theory, agent

based models seem to be preferable because they

can predict the results of conflicting aims and

behaviors. Aggregate levels of the main decision

variables, such as total expenditure, co-payment

returns, consumption, and so on, are derived starting

from the individual behaviors.

In fact, as stated in Ostrom (1988), and to some

extent in Gilbert and Terna (2000), computer

simulation can combine the extreme flexibility of a

computer code where we can create agents who act,

make choices, and react to the choices of other

agents and to the modifications of their environment

and its intrinsic computability.

Economic policy advice requires a thorough

understanding of the relevant individual choices that

are responsible for the effects of policy measures in

the economy, as well as in the public health system.

Theoretical work based on certain model

structures accompanied by empirical evidence aims

at giving us guidance on the causal relationship of

key economic variables.

Agent-based models can improve the

possibilities of a modeler to capture economic

phenomena that seem relevant to policy makers and

extend the set of questions that can be asked about

policy effects.

How to Build an Agent-based Model to Assess the Impact of Co-payment for Health Services

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The choice of agent based paradigm for studying

the co-payment system is mainly due to two reasons:

its algorithmic flexibility and the need for a

multilevel interaction.

The rules to value the co-payment of each

prescription are based on algorithms and legislators

often change them deeply. So in order to effectively

adapt the model to different co-payment scenarios,

we opted out for the agent based modeling

technique. Moreover, we are interested in

understanding how interaction phenomena can affect

the individual choices, in terms of selection of public

or private health provider by citizens. As also stated

in Howitt et al. (2008), an agent-based model is a

way to create virtual worlds that can be used as test

beds to study macroeconomic phenomena,

considering interactions among agents

simultaneously with agent decisions.

2.1 General Structure of the Model

The Agent-based modeling is a strongly micro-

founded approach to study economic dynamics. It is

interested in detecting the patterns at aggregated

levels of analysis that origin from the interaction of

agents, who follow particular behavioral rules and

may be constrained in their choices by various

institutional arrangements.

Nevertheless, the aggregate behavior of the

system can be well depicted in terms of cause-effect

structure, where the final result depends on agents

characteristics, their incentive design mechanism

and co-payment structure.

The agent-based model introduced in present

work is aimed at modeling individual behavior and

interactions among three classes of agents (patients,

physicians and public decision-makers). The general

macro structure of the model can be described by the

cause-effect diagram in Figure 1.

The model controls three relevant variables:

public budget, prescription level and co-payment

level.

Public Budget depends on prescription level and

is defined by two tools: "moral suasion" exerted by

Health Authorities on physicians" and "co-payment

level". It represents the key driver in the policy

maker decision function.

Prescription Level depends on the behavior of

two agent types: the physician (propensity to

prescribe) and the patient rate of demand for

prescription. The level of prescription determines

both the public budget level as well as the patient

utility.

Co-payment Level depends on the policy maker

decision, taking into account public budget as

budgetary constraint and the patient utility, as

directly connected with public consensus. Given the

health status of the patient, the co-payment level

determines the propensity to demand health services;

the difference between what the patient expects on

the basis on his health status and what the doctor

prescribes determines the patient utility.

The patient utility depends on the number of

prescriptions requested (the so called "expressed

demand"), following their perceived "want", and on

the number of prescriptions really delivered by

physicians, following what they think is the patient's

"need" (Culyer and Wagstaff, 1993).

Public

balance

Moral

suasion+

Prescription

propensity

Prescription

demand rate

Prescriptions

Co-payment

Prescription

demand propensity

Patient

utility

Patient

expense

Figure 1: Cause-effect diagram.

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2.2 Model Implementation

The model is closely linked to a large empirical

dataset (see Section 3), so it has been implemented

in native Java language using JAS libraries

(described at http://jaslibrary.sourceforge.net). This

choice grants an efficient interaction with the

database, containing the population and the

prescriptions of the last ten years. In fact, as stated in

Boero and Squazzoni (2005), "...attention has been

paid to the need of integrating ABMs (and

simulation models generally speaking) and methods

to infer data from empirical reality, such as

qualitative, quantitative, experimental and

participatory methods […]. The link between

empirical data, model construction and validation

needs to be thought and practicised as a circular

process for which the overall goal is not merely to

get a validation of simulation results, but to

empirically test theoretical mechanisms behind the

model. Empirical data are needed both to build

sound micro specifications of the model and to

validate macro results of simulation. Models should

be both empirically calibrated and empirically

validated. This is the reason why we often enlarge

our analysis to the broader quest of the use of

empirical data in ABMs, with respect to the narrow

quest of the empirical validation".

The approach we follow in implementing the

model consists in utilizing both current empirical

data and integrating them with strong hypothesis for

variables that cannot be directly observed from

available data.

According to the methodology proposed in

Richiardi et al. (2006), the general structure of

classes, entities and schedule is represented in terms

of class diagram (Figure 2) to represent the agent

characteristics as well as the information/documents

they create and exchange and in terms of time-

sequence diagram to describe when things happen

within a simulation experiment (see Section 2.3).

Taking into account the general structure of the

model, three classes of agents are introduced. The

characteristics and properties of each agent class are

described in the next subsections. The model also

defines the list of the patient’s pathologies with

corresponding exemptions if any and a collection of

PrescriptionRequests, i.e. objects that trace the

lifecycle of a single prescription request, to collect

aggregate variables such as patients’ utility, patient

expense and general regional expenditure.

The prescription request object is characterized

by the following properties:

 Prescription type (Medicine, Specialist Visits,

Exams and controls);

 Final price for National Health Service;

 Price for patient (taking into account co-

payment amount);

 Prescribed (boolean value).

Moreover, the following general parameters are

defined:

 Number of patients;

 Number of physicians;

 Co-payment level and design (e.g. fixed

amount, percentage of the price of the service,

Figure 2: Class diagram of the model.

How to Build an Agent-based Model to Assess the Impact of Co-payment for Health Services

559

ceiling, etc.)

 Income distribution of patients.

 : it is a parameter of the patient: it defines the

share of health spending relative to income,

which represents utility of 0. In other words, it

is the sum of what has been paid within a year

compared to one's income that is considered

acceptable. This coefficient is assumed to be

equal for all patients.

 

is a parameter of the physician. It represents

the tendency to meet patient demand for

prescription.

2.2.1 Patient Agent Class

Every patient agent is characterized by following

own properties:

 Age [E];

 Income [R];

 Pathologies [M];

 Exemptions [Me];

We assume that agents require prescriptions

depending on their health status (i.e. the number of

pathologies directly influences the number of

required prescriptions) and their level of income.

The individual demand function, for a given class of

patient age and health status, has the form shown in

Figure 3.

Figure 3 Individual demand function.

For different combinations of ages and number

of pathologies we can define different demand

functions and test their correspondence in empirical

data.

The demand for prescription depends on: i) the

health status (proxied by the number of pathologies)

which is introduced into the model using empirical

data and can change over simulation time; ii) the

yearly income.

The particular form of the demand curve

depends on the trade-off between the two

components: the level of pathologies increases the

prescription demand, while the level of income

decreases it, since rich people are supposed to use

more private health services than poor ones. The

position of the demand curve depends on the

individual exemption regime: different exemption

facilities may have different impact on the individual

income and, therefore, at parity of total income

increase or decrease the number of required

prescription (shift the curve upwards or downwards),

given the same health status.

Every simulated year, agents compute their own

utility level, depending, negatively, on the

expenditure and, positively, on the prescriptions

received by the physician. More in detail, the utility

level for patient i at time t is computed by the

following equation:













rqop



(1)

Note that, the utility is made up of two components:

 the difference between



(percentage of health

expenditure, giving a null level of utility) and

the individual expenditure quota for health

services, computed as the ratio between





, where P

is the price paid for

prescription j by patient I, and the total income



of patient i;

 the percentage difference between the obtained

prescriptions (op). and the requested ones (rp).

The price P

is intended as the final price for patient,

including the effect of co-payment and exemptions.

We assume that, the percentage  does not depend

on the individual level of income. Moreover, it

possible to relax this assumption and modeling the

relationship between the parameter  and the

individual income. On the contrary, patient

behaviour evolves over simulation time, since its

status in terms of pathologies and exemptions can

change over time.

The agent population is built from empirical data

collected in the GP LigurNet database (see next

section for detailed description). The data set

provides identities of agents, with the list of

pathologies and exemptions they obtained in the

past. Unfortunately, the income level is not available

in database, so it is randomly assigned by the

simulation model based on a normal distribution

according official data of ISTAT Multiscopo Survey

(www.istat.it) and Banca Italia Survey on Income of

the Italian families (www.bancaditalia.it/statistiche

/ibf).

At each simulation step, the agent decides if a

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560

new prescription should be asked to its physician.

This choice is mainly driven by the empirical

dataset. The prescription request is communicated to

the patient’s physician and internal accounting is

modified according to its response.

2.2.2 Physician Agent Class

Physician is characterized by the tendency to go

along with patient demands [

]. The agent is able to

react to patients’ prescription requests. For each

request, the physician has to decide if to prescribe it

or not.

Prescription rate depends on physician individual

tendency to go along with patient requests, affected

by general level of moral suasion coming from the

policy maker. For each prescription request a

uniform random sample is generated in the range

[0,1]. If the sample is greater than the threshold

level, computed as 

, the prescription is granted.

The 

parameter is introduced according the

principle of “defensive medicine” leading to

"supply-induced demand": the physician generally

tends to give into patients requests, to avoid legal

risks. This phenomenon is modified by moral

suasion level  applied by legislator. We assume that

physician behaviour does not evolve over simulation

time. The individual values of the 

parameter are

randomly generated from a normal distribution.

Physician agents react to external stimuli. In

particular, they are waiting for patients’ requests and

decide if according them or not. This

implementations reflects real physician strategy. In

fact they respond to the so called “waiting medicine”

criteria. They are not supposed to be active in

contacting patients and stimulating care.

2.2.3 Policy Maker Agent Class

The policy maker represents a single agent instance

able to influence the whole system with its actions.

It modifies its choices observing aggregate

endogenous variables deriving from other agents’

behaviour, in particular by the patients’ utility.

Policy maker is characterized by own following

properties:

 yearly budget [B];

 moral suasion level [].

In the first version no evolutive behaviour are

provided. This means that Policy maker does not

change its parameters during each simulation run.

Different parameter combinations are tested

comparing different simulation run outcomes.

Through the collection of system responses to

changes in policy parameters, we can provide a

sensitivity analysis of the key variables the policy

maker can act upon, to reduce public expense and

increase overall patients’ utility.

It the first model configuration policy maker is

characterized by a fixed behaviour which is initially

determined as a simulation parameter. Future model

improvements should take into account the

possibility that policy maker’s choices, in terms of

moral suasion and co-payment, can change over

Figure 4: Time-sequence diagram of the model.

How to Build an Agent-based Model to Assess the Impact of Co-payment for Health Services

561

simulation time according to balance trends and

aggregate patient utility.

2.3 Simulation Time Schedule

The dynamic of the model (Figure 4) is trivial. For

each simulation step all patients decide whether to

require a prescription, according the general

probability and their own individual characteristics.

In case a request is generated it is processed by the

physician, who can approve it or not.

Every simulated year of simulation, the model

updates the statistics and eventually asks the policy

maker to guess changes in regulation.

3 DATA COLLECTION

As said above, the model is closely linked to a large

empirical dataset available thanks to the

collaboration of GP-LIGUR.net, the Primary care

Observatory of Regione Liguria, collecting clinical

and prescription data of 188,568 citizens, by 134

physicians for the period June 2000-June 2011.

In Italy to accede the second and third level of

publicly delivered care, the prescriptions of family

doctors, or General Practitioners (GP), are required.

They record prescriptions by using the same

software (www.Millewin.it). Even if the registration

does not constitute compulsory information debt by

GP, therefore, the database is a huge mine of

information, that until now, have never been used by

policy makers. Moreover, data are particularly

valuable as it is possible to build the history of every

patient, which is important for implementing our

model.

The original database was corrected according to

quality requirements following a set of indicators

fixed with the help of the physicians. This meant

reducing the number of doctors from 134 to 81 and

the prescriptions from about 37 millions to about 12

millions.

3.1 Methodology of Data Extraction

Three groups of pathologies were taken into

consideration.

 Oncological diseases - breast K, K prostate

 Chronic cardiovascular and metabolic diseases

 Depressive syndromes

The first two groups (oncologic and

cardiovascular) may give right to exemptions from

ticket payment in particular conditions of income

and age, as specified in (Table 1), that are a mix of

income, age, and pathology conditions. The third

group, is a chronic pathology not recognized by

exemption rules except for a tiny subgroup

(psychosis).

Note that exemption conditions reported are the

ones currently applied in Regione Liguria. Italian

citizens, in fact, can benefit of different conditions

depending on which Region they live (Il

sole24oreSanità, 2012).

3.2 Database Role for the Model

The database allows to define a population of agents

characterized by all those properties that are

important for the construction of the agent-based

simulation model. In particular, the propensity to

demand prescription of patients, the exemption

choices that reduce the expected return from co-

payment, the prescription policy of the physician

and so on.

From a first inspection of database, we can

affirm that current situation is affected by a deep

iniquity that should be corrected. There is strong

evidence, for instance, of "foregone" care at the

expenses of not exempted. The last have

systematically less access to essential care. This is

particularly serious for cancer patients, who require

maximum adhesion to treatment and could, in the

event of noncompliance, have an immediate and

serious impact on their health. It is, however, serious

also for chronic cardiovascular and metabolic

Table 1: The current situation of exemption in Regione Liguria.

POOR: Family income <36.150 Euro

RICH: Family income >36.150 Euro

YOUNG: age <65

Co-payment is due on every prescription

OLD: age > 65

No co-payment on every prescription

Co-payment is due on every prescription

ILL+YOUNG: Recognized chronic pathology and

age < 65

No co-payment on every prescription

Co-payment is due only on drug.

No co-payment on specialist and exams

ILL+OLD: Recognized chronic pathology and age

> 65

No co-payment on every prescription

Co-payment is due on every prescription

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

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562

diseases, even if as we expect that patient affected

by the three prevalent chronic diseases (diabetes,

hypertension and ischemic heart disease) are less

adherent with respect to the first group as they may

perceive their pathology less important than cancer.

In addition, with regards to this third group, the

database proves large undertreatment, which

indicates that probably most of them exit the public

system, given that they not only cannot be exempted

but also they are consumer of class C drug (that is

not supplied free by NHS). We can imagine that a

further utilization of the model could be assessing

the impact on public budget of enlarging the list of

the recognized chronic pathologies. At present, there

are, due to population aging, other pathologies that

could be included, such as, for instance, depression,

arthritis, venous insufficiency.

4 CONCLUSIONS AND FUTURE

WORK

In this paper we argue that agent-based modelling

applied to policy making in the public health system

needs a methodological protocol allowing to mix

empirical data with theoretical assumptions about

individual behaviour and preferences.

In this respect, we wish to introduce formalised

approach to mix behaviour modeling, real data

coming from regional health system and co-payment

rule algorithms into an agent based model.

The approach is aimed at showing that feeding a

model with empirical data can improve the

awareness and guide policy makers towards better

choices in terms of co-payment rules, as well as,

connect the model more closely to the real world

that it intends to simulate.

In further research, we plan to computationally

develop the prototype and use the appropriate

techniques to explore changes into the structure of

the prototype, in order to find more deep theoretical

insights and validate assumption about correlation

between patient income and their behavior in terms

of exemption and the possibility they look at private

health system.

Throughout an appropriate validation of

individual behaviour, more reliable assuptions about

the right co-payment system can be provided.

ACKNOWLEDGEMENTS

We wish to thank GP Ligurnet and, in particular, Dr

Pierclaudio Brasesco for collaboration in supplying

data. All the authors participate and acknowledge

support from the Italian Ministry of Education,

University and Research (MIUR), under the grant n.

RBFR08IKSB - FIRB PROJECT.

REFERENCES

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

Embeddedness Matter? Methodological Issues on

Agent-Based Models for Analytical Social Science.

Journal of Artificial Societies and Social Simulation,

8(4). Retrieved from: http://jasss.soc.surrey.ac.uk/8/4/

6.html.

Carrieri, V. (2010). The Effects of Cost-Sharing in Health

Care: What Do We Know From Empirical Evidence?.

Economia Politica:Journal of Analytical and

Institutional Economics, 27(2), 351-374.

Culyer, A. J. and Wagstaff, A. (1993), Equity and equality

in health and healthcare. Journal of Health Economics,

12(4), 431-457.

Ellis, R. P. and McGuire, T. G. (1993). Supply-Side and

Demand-Side Cost Sharing in Health Care. The

Journal of Economic Perspectives, 7(4), 135-151.

Gilbert, N. and Terna P. (2000). How to build and use

agent-based models in social science. Mind & Society,

1(1), 57-72. http://www.agenas.it/agenas_pdf/Dossier

%20Co-payment_aprile2012.pdf

Howitt, P., Kirman A., Leijonhufvud A., Mehrling P. and

Colander D. (2008). Beyond DSGE Models: Toward

an Empirically Based Macroeconomics. Middlebury

College Economics Discussion Paper No. 08-08.

Il sole24oreSanità, (2012), Focus, 24-30 april 2012 -

pp.11-15- and 17-23 april 2012- Focus pp 9-13

Louckx, F. (2002). Patient cost sharing and access to

healthcare. In Mackenback J., and Bakker M. (eds),

Reducing inequalities in health. A European

perspective. London: Routledge, pp 188-198

Manning, W. G., Newhouse, J. P., Duan, N., Keeler, E. B.,

Benjamin, B., Liebowitz, A. et al. (1988). Health

insurance and the demand for medical care. Evidence

from a randomized experiment. Santa Monica, CA:

RAND Corporation, 1988. Report R-3476-HHS. ISBN

0-8330-0864-1. An abridged version of this report.

was published in Manning, W.G. et al.(1987) Health

insurance and the demand for Medical Care: evidence

from a randomized experiment. American Economic

Review, 1987, 77, 3:251-277

Ostrom, T. (1988). Computer Simulation: the Third

Symbol System. Journal of Experimental Social

Psychology, 24, 381-392.

Richiardi M., Leombruni R., Saam N. and Sonnessa M.

(2006). A Common Protocol for Agent-Based Social

Simulation. Journal of Artificial Societies and Social

Simulation, 9(1). Retrieved from http://jasss.soc.

surrey.ac.uk/9/1/15.html

Wagstaff A. et al. (1999). Equity in the finance of health

care: some further international comparisons, Journal

of Health Economics, 1999, 18, 3:263-290.

How to Build an Agent-based Model to Assess the Impact of Co-payment for Health Services

563