ORIGINAL PAPER

Physician–patient relationship and medical accident victimcompensation: some insights into the French regulatory system

Lydie Ancelot • Cornel Oros

Received: 10 September 2013 / Accepted: 17 April 2014

� Springer-Verlag Berlin Heidelberg 2014

Abstract Given the growing amount of medical litigation

heard by courts, the 2002 Kouchner law in France has

created the Office National d’Indemnisation des Accidents

Medicaux (ONIAM), whose main aim is to encourage out-

of-court settlements when a conflict between a physician

and the victim of a medical accident occurs. More than

10 years after the implementation of this law, the statistics

analysing its effectiveness are contradictory, which raises

the question of the potential negative effects of the ONIAM

on the compensation system. In order to address this

question, the article analyses the impact of the ONIAM on

the nature of settlement negotiations between the physician

and the victim. Using a dynamic game within incomplete

information, we develop a comparative analysis of two

types of compensation systems in case of medical acci-

dents: socialised financing granted by the ONIAM and

private financing provided by the physician. We show that

the ONIAM could encourage out-of-court settlements

provided that the hypothesis of judicial error is relevant.

On the contrary, in the case of a low probability of judicial

errors, the ONIAM could be effective only for severe

medical accidents.

Keywords French insurance system �Medical accidents �Victims–physician conflict � Judicial errors

JEL Classification I13 � I18 � K32 � K41

Introduction

The compensation of victims who have suffered thera-

peutic accidents has been a constant topic of economic and

social debate in developed countries for several decades.

The issues dealing with the effectiveness, equity and

transparency of the compensations as well as the behav-

iour, incentives and responsibility of different players

involved in this process (physicians, patients, insurers,

public authorities) have not yet found any clear and per-

fectly satisfactory answers, thus justifying the use of

complex analyses at the confluence of different fields of

economics such as health economics, public economics,

and law and economics. Moreover, the development and

implementation of this type of compensation have been

changing constantly, preserving the relevance of the

debates. In the French case, for example, we have wit-

nessed a very important increase in the number of medical

litigations1 in the last 20 years, mainly at three levels. First,

the frequency of medical accidents doubled between

L. Ancelot � C. Oros (&)

IRIAF- CRIEF, University of Poitiers, 2, Rue Jean Carbonnier

Bat A1 (BP 623), 86022 Poitiers Cedex, France

e-mail: cornel.oros@univ-poitiers.fr

L. Ancelot

e-mail: lydie.ancelot@univ-poitiers.fr

L. Ancelot

BETA, UMR CNRS 7522, University of Strasbourg, Strasbourg,

France

L. Ancelot

BETA, UMR CNRS 7522, University of Lorraine, 13, place

Carnot, 54035 Nancy, France

C. Oros

LEO, University of Orleans, Rue de Blois - BP 26739,

45067 Orleans, France

1 As showed by Helmlinger and Martin [16], ‘‘several resounding

trials as for instance that of the infected blood or that of the growth

hormone have largely popularised the idea that medicine is also

exposed to legal investigation’’ (translation from French).

123

Eur J Health Econ

DOI 10.1007/s10198-014-0606-4

1992–1996 and 1997–2001. Second, there has been a

constant increase in the number of cases brought to court

and the development of the phenomenon called ‘‘medical

prosecution’’2 (805 medical liability claims processed in

1990 against 3,906 in 2002 according to the Annuaire

Statistique de la Justice, 2003 edition [2]). Third, the

average cost of the settlement of an insurance claim rose by

about 50 % in 1990 according to the 2002–2003 Activity

Report of the Commission de controle des assurances [8].

In order to reduce the number of trials—as well as the

costs they involve—the 2002 Kouchner law3 stipulates

facilitating negotiation, which is considered less expensive

than a trial. At the same time, the purpose of the law is to

compensate the acknowledged victims of medical acci-

dents irrespective of the existence or not of a physician’s

fault. More precisely, this law modifies the compensation

process of the victims of medical accidents and thus creates

three possibilities for compensation:

• Compensation by the physician through the premium

paid to the insurer.

• Compensation by the State through the Office National

d’Indemnisation des Accidents Medicaux (ONIAM).4

• Compensation by a hybrid system in which the insurer

and the ONIAM share the costs of compensation.

A few years after the implementation of the Kouchner

law, two important trends can be identified: an increase in

the percent of cases solved by settlement and also in the

amount of compensation incurred by the physician.5 Thus,

according to the 2010 Report of the Observatoire des

Risques Medicaux, in 2009 the out-of-court settlements

represented 70 % of the solved medical accidents with a

clear distinction according to the origin of the proposition

(98 % by ONIAM against 52 % by the physician). At the

same time, we can notice an increase in the amount of

compensation: 20.5 million euros for the ONIAM in 2006

against 88 million euros in 2009, whereas for the insurers

the figures vary from 30 million euros in 2006 to

61.5 million euros in 2009 (Report of Observatoire des

Risques Medicaux, edition 2010).

These facts raise questions about the relevance of the

Kouchner law. We can thus ask the question of the

potential negative effects that the ONIAM could generate.

Facilitating the settlements on one hand and enabling

victims to get compensation on the other may seem two

contradictory objectives. Indeed, making the settlement

easier allows for a reduction in the number of cases brought

to court,6 whereas the certainty of the compensation when

the medical accident is proved7 could encourage the vic-

tims to take legal proceedings in order to benefit from a

bigger compensation if the physician is convicted, which

thus raises the number of cases brought to court.

In order to answer this question, the aim of the article is to

propose an analysis of the physician-patient relationship by

taking into consideration the public compensation granted by

the ONIAM. We thus examine the impact of the presence of

the ONIAM on the behaviour of the physician who, according

to whether he/she is negligent or not, can choose to propose an

out-of-court settlement to the victim or not. Is not the tradi-

tional separating equilibrium supposing that the physician

will reveal his/her real type8 put into question by the presence

of this public institution? The article thus has a normative

dimension and provides support for the public authorities in

the decision-making process by studying the effects of the

two possible compensation types in case of medical acci-

dents: the public state funding by the ONIAM and the private

funding via the physician’s insurance company.

The first section of the article briefly presents the

functioning of the ONIAM. The second section presents

the model that we have used and describes the strategies

and payoffs of the players. The third section presents the

different Bayesian equilibriums identified and provides a

comparative analysis of physicians’ incentives to propose a

2 Helmlinger and Martin [16], Naatowicz-Laurent [22], Kouchner

et al. [18], Lecocq et al. [20].3 The 2002-303 law from 4 March 2002 relative to the patients’

rights and to the quality of the health system.4 ONIAM was created in the context of the Kouchner law in 2002

and can be considered as a substitute for the insurers. It intervenes

when a medical accident occurs if the responsibility of the physician

is not recognised, i.e. lack of medical malpractice liability or if there

is no proposal for out-of-court settlement by the insurer. The creation

of ONIAM is specifically French, but other European countries

(mainly Germany, the UK, Denmark, Sweden and Italy) have

developed a similar approach trying to encourage out-of-court

settlements when medical accidents occur. As mentioned by the

Senate Report in November 2000 [25], ‘‘the analysis of the systems of

medical accident compensation puts forward that except Italy, all the

analysed countries have developed specific procedures allowing the

victims of medical accidents to obtain a compensation without going

to court’’ (translation from French). This report also describes the

specific procedures implemented in each country.5 Inspection Generale des Affaires Sociales (2007): ‘‘contrary to what

was feared, there has been no important rise in the number of

complaints as a consequence of the introduction of an obligation to

inform the patient or of the creation of CRCI (Commission Regionale

de Conciliation et d’Indemnisation)’’ (translation from French).

Report of the Office National d’Indemnisations des accidents

medicaux (2010): ‘‘the number of medical litigations handled by the

legal system has remained stable, i.e. around 7,000 new cases each

year throughout all jurisdictions’’ (translation from French).

6 The risk with ONIAM is that some conflicts may not be brought to

court where the judge could award a better compensation to the

victim. Another risk is that in the absence of court judgments, we may

lack references relative to similar conflicts [29].7 We will later see that the presence of ONIAM implies that the

victim is always compensated if a medical accident is proved,

whether the physician is negligent or not.8 The guilty agent recognises his/her negligence, whereas the not

guilty agent declares him/herself not negligent [5].

L. Ancelot, C. Oros

123

settlement to the victim according to the existence or not of

the ONIAM.

The role and functioning of the ONIAM

Given the fact that our article aims at analysing the impact

that the ONIAM could have on the nature of the physician–

patient relationship, a description of the operating princi-

ples of the ONIAM will provide a better grasp of our

institutional framework.

Traditionally, before the creation of the ONIAM, there

were two ways for victims of medical accidents to obtain

compensation9:

• A direct settlement between the physician and the victim.

Once the victim has made the complaint, the physician

makes a compensation offer on his/her insurer’s advice.

The victim can accept the proposal or not.

• A decision by the court stipulating the compensation of

the victim. This case occurs when the physician does

not make any settlement offer or if the victim refuses

the offer made by the physician, thus deciding to go to

court. If the physician is found guilty, he/she will be

convicted as negligent and his (her) insurer will have to

pay compensation.

The 2002 Kouchner and About laws introduced an

additional way to compensate the victims of medical

accidents.10 Two innovative principles characterise this

compensation alternative:

• It admits that a medical accident may be generated by a not

negligent act. In this case, the medical accident is

recognised but the physician is not considered negligent.11

and the victim’s compensation is paid by the ONIAM.

• The victim is always compensated if the medical

accident is proved.

The topic of our article is in line with this alternative

compensation whose operating mechanisms can by summa-

rised as follows. The persons who consider themselves victims

of medical accidents can refer to a regional commission, i.e. the

Commission Regionale de Conciliation et d’Indemnisation

(CRCI), in order to obtain compensation. The role of the CRCI

is to encourage the out-of-court settlement of conflicts and to

Complaint against the physician made by the victim of a medical accident

The physician makes an offer on the insurer’s advice

The physician does not make any offer on the insurer’s advice

The victim accepts the proposal =

compensation

The victim refuses the proposal

The physician is convicted = total compensation for the victim = negligence rule

The physician is acquitted = lack of compensation for the

victim = the medical error is not recognized

Changes generated by the Kouchner and About laws

1. It is admitted that the act may not be negligent.

2. The victim is always compensated if the medical accident is proved.

Court

The physician is convicted = total compensation for the victim =

negligence rule

The physician is acquitted = compensation paid by ONIAM = strict

liability

The physician is partially convicted = compensation paid by the physician’s insurer and by ONIAM: impossibility to prove the complete negligence of

the physician

Fig. 1 Ways of compensation for the victims of medical accidents

9 We thank the referee for suggesting this description.

10 See Fig. 1 for a synthetic description of the different ways for a

victim of medical accidents to obtain compensation.11 For instance, we can mention iatrogenic infections.

Physician–patient relationship

123

allow compensation to the victims whose damage presents a

degree of severity that is superior to a legal threshold.

If the request is admissible,12 the Commission will

transfer the case to an expert who will conduct an inves-

tigation.13 The Commission has 6 months from the date of

receipt of an admissible request to deliver its judgement on

the circumstances, the causes and the amount of the dam-

age suffered by the victim.

If the Commission recognises the existence of a right to

compensation, it will name the agent who will pay the com-

pensation, either the physician’s insurer if the physician is

considered as negligent or the ONIAM in the case of strict

liability.14

The designated agent has to present a compensation

offer to the victim within 4 months according to the indi-

cations provided by the CRCI. In practice, it is possible that

the physician’s insurer does not answer or refuses to make

a compensation offer to the victim. In this case, the victim

can choose to go to court but he/she also has the possibility

to make a demand requesting that ONIAM replaces the

deficient insurer.15 If ONIAM accepts the demand, it can

pursue the physician afterwards.

The model

The model that we develop falls within the scope of two

important types of microeconomics models: the bargaining

models with asymmetric information [19] applied to health

problems [21] on the one hand and the economic analysis

of law and economics on the other hand.

The literature on bargaining games with asymmetric

information in health economics is quite vast, which is

mainly due to the multiplicity of actors generating the

analysis of a large number of strategic behaviours.16 In this

context, our model aims to examine the impact on the

physician–patient relationship of the presence of the public

regulatory authority specific to the French system of

compensation, namely the ONIAM. Beyond the introduc-

tion of this specific public actor, the originality of our

framework is based on the fact that the physician-patient

relationship is developed in the context of a legal dispute

between these two actors.17 Thus, both of the models used

in the resolution of legal disputes and of the models ana-

lysing the role of information asymmetries in health sys-

tems being close,18 our own model examines the

effectiveness of the impact of the ONIAM on the devel-

opment of the out-of-court settlements.

The methodology uses game theory tools and involves

the construction of a dynamic game model with incomplete

information between two players: the physician and the

victim. The judge is also present in our model and influ-

ences the conviction or not of the physician, the behaviour

of the latter and of the victim through his/her decision.

When the case is referred to the judge, we consider that the

latter may commit two types of judicial errors: (1) declare

the physician guilty when he/she is not negligent or (2)

declare the physician not guilty when he/she is negligent.

Our approach is in line with P’ng’s model [24] sup-

posing a signaling model where the informed party (the

physician) makes an offer to a non-informed party (the

victim). Nevertheless, our model is different as we consider

the hypothesis of a lack of perfect information from the

judge, thus generating the potential existence of the two

judicial errors (type 1 and 2) previously mentioned.19

We chose to focus only on the physician-patient relation-

ship and thus to ignore the role of the physician’s insurer in the

victim compensation process. As we have already indicated,

the insurer plays a technically specific role in the compensation

process mainly by paying the compensation when the judge or

the CRCI declare the physician negligent. Nevertheless, in

practice, the exact type of these compensations and thus the

role of the insurer in this process are very heterogeneous and

complex depending essentially on the specific nature of the

contract between the insurer and the physician, specificity that

depends on the physician’s specialty. The latter highly

12 The request is admissible if the medical procedure generating the

accident took place after September 2001 and if it generated damage

that is superior to a threshold fixed by the law.13 The expert investigation is free of charge for the victim.14 We could draw a parallel with the 1985 Badinter law for traffic

accidents within a system of strict liability. This law creates an

obligation for the insurers to make an offer to the victims. In this type

of conflict, only the most severe injuries or the most complex cases go

to court.15 We can thus conclude that the ONIAM has two main objectives.

First, it generates a victim compensation process when the physician

is not negligent. Second, it represents a substitute to the negligent

physician if he/she does not make an offer.16 Rochaix [26] provides a survey of the literature and presents the

various strategic behaviours that can be analysed in health economics.

The articles of Bejean and Gadreau [6] and Bejean et al. [7] describe

the specific relationships that could be identified among the different

regulatory authorities (health insurance system, government), insurers

(private and public) and thealth care providers (hospitals, physicians,

pharmacists, etc.).

17 The economic analysis of the legal system draws a distinction

between two main categories of models [14]: the screening models [5]

and signal models [13, 28]. It has grown in popularity as a result of

the implementation of alternative dispute resolution. This field of

research aims to study the effectiveness of legal rules and to provide

innovative measures allowing improving the current juridical system.18 Our approach refers also to the literature about medical malprac-

tice. For some important references on the topic, see for instance

Danzon and Lillard [12], Danzon [9–11].19 Contrary to the P’ng [24] model, we do not take the existence of

the nuisance suits explicitly into consideration, supposing that the

victim’s expected gain from the legal proceedings could be inferior to

his/her cost.

L. Ancelot, C. Oros

123

influences both the number of compensated cases and amount

of the compensation.20 Moreover, the insurance system itself

can generate important compensation heterogeneities. Certain

specialties pay very important premiums because in case of a

medical error, the compensation amount cannot be covered

only by the physician and an intervention of the insurance is

thus necessary.21 An important distinction thus exists between

the full insurance and the co-insurance: the insurer has a par-

ticularly important role in the compensation process only when

the physician benefits from a full insurance contract. On the

contrary, the role of the insurer becomes relatively less

important for the co-insurance contracts. At the same time, the

status of the physician (professional of a public or private

sector) highly influences the type of the liability and thus the

compensation.22

Another element leading us to ignore the physician’s

insurer relies on the specificity of ONIAM as a public

institution specialised in the compensation of the victims of

medical accidents. Indeed, as we have already mentioned,

the physician’s insurer is a central player in the resolution

of the medical conflicts for which the physician’s respon-

sibility is recognised. On the contrary, as the presence of

the ONIAM is justified by the potential existence of the

physician’s strict liability, the role of the physician’s

insurer is consequently relatively less important.23

In the context of a medical compensation system that is

particularly complex, involving a large number of actors [health

institutions (public or private), health professionals, insurers,

medical experts, victims] and taking into consideration that the

objective of the article is to analyse the potential impact of the

creation of a public compensation institution on the physician’s

behaviour, the role of the insurance is thus isolated in order to

focus on the physician–patient relationship.24

The game is developed according to the following steps:

1. The physician is negligent or not. This characteristic

represents his/her type.

2. The physician knows perfectly his/her type and decides

to propose or not a settlement to the victim. The

negligent physician proposes a settlement with a

probability bN, whereas the non-negligent physician

proposes a negotiation with a probability bN .

3. The victim decides to accept or not the settlement

proposed by the physician. The victim accepts with a

probability cN when he/she considers that the physician is

negligent. On the contrary, when the victim considers

that the physician is not negligent, he/she accepts the

arrangement with a probability cN . The victim’s a priori

beliefs on the type of the physician are the following: the

physician is negligent with a probability a and non-

negligent with a probability 1 - a.

4. If the victim accepts, the case is closed.

5. If the victim refuses the settlement, the case is brought to

court, and the judge decides to convict the physician or

not.25 The judge may commit judicial errors (type 1 or 3)

and the negligent physician is acquitted or convicted with

a probability (1 - pN) or (pN). The non-negligent physi-

cian is convicted or acquitted with a probability (pN) or

(1� pN). Concerning the relationship between these

probabilities, we have pN [ pN , which means that the

probability for a physician to be convicted is higher when

he/she is negligent than when she (he) is not negligent.

The payoffs of the players are the following:

D amount of the compensation if the victim accepts the

settlement. Taking into account that our approach

ignores the presence of the insurance and focusses

exclusively on the physician–patient relationship, we

consider that the compensation proposal is made

directly by the physician. In this case, if the victim

accepts, the amount of this compensation will be

entirely incurred by the physician. 26

20 According to the Observatoire des Risque Medicaux [23] for the

period 2006–2009, the surgical disciplines represented 59.4 % of the

compensated cases, which corresponds to 280 million euros. Anaes-

thesia, resuscitation, emergency and regulation procedures represent

6.4 % of the compensated cases, which corresponds to 41 million

euros.21 We can mention for instance the important differences between the

premiums paid by a general practitioner and by an obstetrician-

gynecologist.22 According to the Observatoire des Risques Medicaux [23], in

private health institutions, it is the liability of the practitioners that is

largely questioned (58 % of cases for all the private institutions),

whereas in public health institutions, it is the institution itself (more

than 90 % of cases).23 An interesting extension of our model could be to consider a different

framework supposing that the proposal is made either by the insurer or by

ONIAM according to whether the case is initially considered as a

negligent or not negligent act. The victim’s incentives to accept or refuse

the offer could thus be different according to the origin of the offer.24 The Kouchner law implementing the ONIAM insists on the role of the

physician in the physician-patient relationship and imposes an obligation

for the physician to inform the patient about his/her medical file.

25 The game is identical regardless of the presence or not of the

ONIAM. The differences concern the players’ payoffs.26 When there is an insurance, the proposal will be made by the insurer on

behalf of the physician. In this case, the insurance can cover the

compensation if the victim accepts the proposal. The type of this proposal

depends on the nature of the contract between the insurer and the

physician. It is thus particularly difficult given the complexity and the

diversity of these contracts to be able to capture a representative insurer-

physician relationship in order to explicitly formalise it in our model.

Moreover, if we consider that it is the insurer who makes a proposal to the

victim and pays it, the physician–patient relationship, which we aim at

focussing on in our article, will be biased as it will be highly conditioned

by the nature of the contract between the insurer and the physician.

Physician–patient relationship

123

D amount of the compensation of the victim if he/she

refuses the settlement in the case in which the

physician is convicted.

DI amount of the compensation paid by the physician if

the victim refuses the settlement and if the physician

is convicted (in presence of the ONIAM).

CV cost supported by the victim who goes to trial if there

is no settlement proposal.

CV cost incurred by the victim if he/she decides to go to

trial and refuses the proposal.

CM cost of the trial incurred by the physician if he/she

makes a proposal.

CM cost of the trial incurred by the physician in case of

lack of proposal.

DIamount of the compensation paid by the physician if

he/she did not make any proposal and is convicted by

the judge (in presence of the ONIAM).

The Table 1 sums up all the payoffs both for the phy-

sician and the victim according to the presence or the lack

of the ONIAM:

Concerning the payoffs of the players, several assump-

tions must be taken into account:

If ONIAM is not present, we consider that:

• the judge does not intervene to impose sanctions on the

physician who did not make any proposal. Conse-

quently, the compensation D paid to the victim is the

same when the physician is convicted whether the latter

made a proposal or not. On the contrary, his/her trial

costs are different: the fact of making a settlement

proposal implies an additional cost accounted for by the

existence of a supplementary step in the conflict

resolution. We thus have: CM [ CM .

• the trial costs charged to the victim are more important

if he/she refuses the proposal and goes to trial:

CV [ CV . Our approach takes into consideration the

French rule of allocation of litigation costs (‘‘regle de

condamnation aux depens’’), according to which the

loser pays a part of the winner’s litigation costs. Indeed,

the convicted physician pays the victim’s litigation

costs.

• the compensation paid by the physician is more

important when there is no settlement (D [ D). We

follow here the principle of an out-of-court settlement

supposing that the sanction (compensation and trial

costs) is always less important in the case of a

settlement than in the case of a trial.

In the presence of the ONIAM, the specificity of the

hypothesis concerns the following elements:

• the presence of the ONIAM does not influence the

physician payoffs when the latter is convicted after

having made a proposition (DI ¼ D). Indeed, since the

physician makes a proposal, we consider that a higher

degree of sanction is not appropriate.27

• when the physician is convicted, the monetary costs he/

she incurs are identical between the situation supposing

the presence and the lack of the ONIAM. Indeed, we

consider that the financial burden incurred by the

physician in order to prove its innocence is identical

regardless of the nature of the defence, i.e. in front of

the victim’s lawyer or in front of the ONIAM.

• if the physician is acquitted, his/her payoff is zero

when the ONIAM is present, which means that the

public authority bears the trial costs in this case.

The explanation is based on the fact that if the

physician is acquitted, the victim did not have to

take legal proceedings and consequently the physi-

cian will not incur any costs. The ONIAM plays a

protective role here with regard to the physician by

paying the trial costs when the physician is not

convicted.

• the French rule of allocation of litigation costs (‘‘regle

de condamnation aux depens’’) is applied, and the

victim bears the costs of the trial only when the

physician is acquitted28 whereas the convicted physi-

cian pays for the victim’s litigation costs.

We consider that all these variables that influence the

payoffs of the players are exogeneous.

The Kuhn tree (extensive form game) is described in

Fig. 2 (the payoffs in the case where the ONIAM is not

present are represented on the first line, whereas the dif-

ferences between the payoffs generated by the presence of

ONIAM are represented on the second line).

Equilibrium of the game

We will identify the Bayesian equilibriums of the game

according to the presence or not of the ONIAM. Even if our

approach is close to the signalling models proposed by

P’ng [24], a major distinction compared to this model

concerns the manner of analysing the game equilibriums.

Our objective is not to identify all the equilibriums of the

game (pure and mixed strategies) but to analyse the impact

on the equilibrium physician’s behaviour of the existence

27 We will see further on that ONIAM has the possibility to sanction

the physician more severely when he/she did not make any proposal

as this behaviour is inconsistent with ONIAM’s objective of

developing a settlement agreement.28 The victim bears the costs of the trial when the physician is

acquitted regardless of the physician’s decision (i.e. to propose a

settlement or not). This hypothesis is justified by the fact that the

victim is the first actor to take legal proceedings.

L. Ancelot, C. Oros

123

or not of a public compensation institution (ONIAM). This

is the reason why we have identified the conditions

allowing the existence of a benchmark equilibrium (sepa-

rating equilibrium) and analysed the evolution of this

equilibrium according to the two configurations.29 A

modification of the benchmark equilibrium according to

the presence or not of the ONIAM allows capturing the

nature of the modification of the physician’s behavior in a

relatively easy manner.

Game configuration when the ONIAM is not present

We take as a reference a specific separating equilibrium

supposing that contrary to the negligent physician, the non-

negligent physician does not make any proposal. This

hypothesis seems relevant as it is more advantageous for a

negligent physician to compensate the victim following an

out-of-court settlement that is less costly (in terms of

compensation and legal fees) compared to a trial convicting

the physician. On the contrary, the non-negligent physician

does not have to make any proposal and thus goes to trial in

order to prove his/her innocence.

This situation will be used as a benchmark allowing to

compare the different strategies of the players according to

the specific game configuration, i.e. with/without ONIAM.

The conditions that allow this type of behaviour on the

part of the physician are the following:

The non-negligent physician does not make a proposal:

�pN Dþ CM þ CV

� �� CM 1� pN

� �[ � cND

� 1� cN

� �ðDþ CM þ CVÞpN þ CM 1� pN

� �� �:

We thus have:

D [ pN Dþ CV

� �þ CM �

pN CV � CV

� �þ CM � CM

cN

¼ A:

The negligent physician makes a proposal:

� cND� 1� cNð Þ Dþ CM þ CV

� �pN þ CM 1� pNð Þ

� �

[ � pNðDþ CM þ CVÞ � CM 1� pNð Þ:

We thus have:

Fig. 2 The extensive form of the game

29 A close approach developing a bargaining model with asymmet-

rical information and supposing an initial separating equilibrium is

proposed by Baker and Mezzetti [3]. We can thus identify a

difference compared with the results of P’ng [24] who, according to

the parameters of its model, has identified only pooling equilibriums.

In our approach, the existence of a separating equilibrium used as a

benchmark in order to compare the physician’s incentives to make a

proposal according to the presence or not of the ONIAM does not

exclude the existence of pooling equilibriums.

Physician–patient relationship

123

D\pN Dþ CV

� �þ CM �

pN CV � CV

� �þ CM � CM

cN

¼ B:

The victim accepts the proposal if:

p NNjPð ÞDþ p NjPð ÞD [ p NNjPð Þ pND� 1� pN

� �CV

� �

þ p NjPð Þ pND� ð1� pNÞCV

� �:

We obtain:

D [ p NNjPð ÞðDþ CVÞ pN � pN

� �þ pND� ð1� pNÞCV

p NjPð Þ\T ¼Dþ 1� pN

� �CV � pND

ðDþ CVÞ pN � pN

� � :

When we have a separating equilibrium, the negligent

physician makes a proposal (p NjPð Þ ¼ 1) and the behav-

iour of the victim can thus be analysed. The victim refuses

the proposal if Dþ CV\pN Dþ CV

� �) Dþ ð1� pNÞ

CV\pND, which implies a relatively low value for CV

because we have D\D. This strategy is not compatible

with the physician’s strategy and consequently the game

equilibrium is not stable in this case.

On the contrary, the acceptance is optimal for the victim

if Dþ CV [ pNðDþ CVÞ ) Dþ ð1� pNÞCV [ pND. We

observe that the victim’s switching toward an acceptance

strategy is conditioned by the costs of the trial (CV ), which

becomes a crucial factor for the stability of the equilib-

rium.30 When the trial costs incurred by the victim are

relatively high as well as the probability of the judicial

error of type 2 (pN low), negotiation is encouraged even if

the compensation is bigger when the victim obtains it

following a trial. We can thus raise the question of the

effect of the ONIAM on the negotiation when the victims

do not incur the trial costs (the case of the agents who are

subject to legal proceedings and who benefit either from

the legal aid or from the legal expenses insurance).

According to the literature,31 there is a bigger probability

of refusal from the individuals benefitting from the

reduction of their trial costs because of the presence of

ONIAM.

The victim’s acceptance strategy is compatible with the

physician’s behaviour if the two following conditions are

satisfied:

D [ pNðDþ CVÞ þ CM ) pN\D� CM

Dþ CV

D\pNðDþ CVÞ þ CM ) pN [D� CM

Dþ CV

:

The acceptance by the victim thus insures the stability of

the separating equilibrium whose strategies are:

sMðNNÞ; sMðNÞ; sV� �

Without ONIAM

¼ sMðNNÞ ¼ No Proposal; sMðNÞ ¼ Proposal;sV ¼ Accepts

� �:

Game configuration when the ONIAM is present

We keep the separating equilibrium as a benchmark suppos-

ing that the non-negligent physician does not make a proposal:

D [ pN Dþ CM þ CV

� �

þ pN

cN

DI � D� CM � CM

� �� CV � CV

� �h i¼ A0

contrary to the negligent physician who makes a

proposal:

Table 1 The physician and the

victim’s payoffs according to

the presence or the lack of the

ONIAM

Situation Without ONIAM With ONIAM

Victim payoff Physician payoff Victim payoff Physician payoff

Victim accepts settlement D -D D �D

Victim refuses settlement,

the physician is convictedD - Dþ cM þ cV

� �D � DI þ cM þ cV

� �

Victim refuses settlement, the

physician is acquitted

�cV �cM �cV 0

Lack of proposition and

discharge of the physician

-cV �cM -cV 0

Lack of proposition and

conviction of the physicianD � Dþ cM þ cV

� �DI � DI þ cM þ cV

�

30 We notice that the acceptance by the victim can also be explained

by the existence of a type 2 judicial error supposing that the

responsible physician is acquitted (pN\1). Thus, the higher the

probability of this erroris (pN goes down), the higher the victim’s

incentive to accept the physician proposal. Indeed, faced with the risk

of undergoing a judge’s wrongful decision, which diminishes

compensation by acquitting the responsible physician, the victim

prefers to accept the physician’s proposal.

31 Indeed, as shown by the literature on public aid [1], [4], [15], [17]],

[27], the persons subject to legal proceedings are encouraged to go to

trial by refusing the proposal from the accused as their trial costs are

paid by the insurer but also because the assistance received could

represent a credible threat.

L. Ancelot, C. Oros

123

D\pN Dþ CM þ CV

� �

þ pN

cN

DI � D� ðCM � CMÞ � CV � CV

� �h i¼ B0:

Concerning the behaviour of the victim, the acceptance

condition is the same as in the case of the game without

ONIAM:

p NNjPð ÞDþ p NjPð ÞD [ p NNjPð Þ pND� 1� pN

� �CV

� �

þ p NjPð Þ pND� ð1� pNÞCV

� �:

We thus have:

p NjPð Þ\T ¼Dþ 1� pR

� �CV � pND

Dþ CV

� �pN � pN

� � :

The acceptance by the victim is compatible with the

separating equilibrium if:

D [ pNðDI þ CM þ CVÞ ) pN\D

DI þ CM þ CV

D\pN DI þ CM þ CV

� ) pN [

D

DI þ CM þ CV

:

As in the previous case, the decision of the victim to

refuse the proposal is not compatible with the physician’s

strategies described by the separating equilibrium.

The separating equilibrium is thus the same as that

identified in the case when the ONIAM is not present:

sM NNð Þ; sM Nð Þ; sV� �

ONIAM

¼ sM NNð Þ ¼ No Proposal; sM Nð Þ ¼ Proposal;

sV ¼ Accepts

� �:

Using the equilibriums previously identified, we develop

a comparative analysis of the behaviour of the physician

according to the presence or the absence of the ONIAM.

Taking as a benchmark the separating equilibrium allowing

the physician to reveal his/her real type, we compare the

relative position of the thresholds A, B, A0, B0, which define

the separating equilibriums for the two situations (pre-

sence/lack of the ONIAM). If we take into consideration

the fact that the separating equilibriums are unstable when

the victim refuses the settlement, we only analyse the sit-

uation supposing the acceptance from the victim

(cN ¼ cN ¼ 1). In this context, the comparison supposes:

A vs A0 , CM 1� pN

� �vs pNðDI � DIÞ

B vs B0 , CM 1� pNð Þ vs pNðDI � DIÞ:

The relative position of these thresholds is conditioned

by the distinction existing when the ONIAM is present

between the payoff of the physician when he/she makes a

proposal and is convicted (DI) and the payoff when the

physician is convicted without making any proposal (DI).

We can thus identify two configurations according to the

guidance provided by the public authorities to the role of

the ONIAM.

A. DI �DI : the ONIAM pays a part of the compensation

because the responsibility of the physician is not

entirely proved by the judge.

B. DI\DI : the ONIAM penalises the physician who does

not make any settlement proposal more severely.

The comparative analysis of the equilibriums is done

according to the relative position of variable D (amount of

the compensation of the victim if he/she accepts the set-

tlement) compared to the thresholds A, B, A0 and B0. Var-

iable D is considered exogeneous as in our model we

analyse the role of the public authorities in developing the

out-of-court settlement. In this case, the physician is free to

propose a settlement or not, but does not have the possi-

bility to influence the amount of the compensation pro-

posed. To put it differently, the amount proposed by the

physician depends on the damage incurred by the victim,

this amount being defined by the legal framework.32

The ONIAM pays a part of the compensation

This case corresponds to a subsidy provided by the public

authorities to the physician whose responsibility is not

entirely proved. We have decided to analyse this situation

as one of the roles of ONIAM is to pay to the victim a part

of the compensation in the case of strict liability.

Taking into consideration the hypothesis defining this

configuration, we have A [ A0 and B [ B0.We can thus identify three intervals of analysis.

a. D 2 ðA0; AÞ implying a pooling equilibrium with a

proposal from the physician in the case where the

ONIAM is not present and a separating equilibrium in

the case with ONIAM.

b. D 2 ðA; B0Þ implying a separating equilibrium

regardless of the presence of the ONIAM or

not.33

c. D 2 ðB0; BÞ implying a separating equilibrium in the

case where the ONIAM is not present and a pooling

equilibrium without a proposal when ONIAM is

present.

These three intervals are represented in the figure below:

32 ONIAM has created a reference system that gives the guidelines

applied for the compensation of the victim according to the type of

damage suffered (http://www.oniam.fr/infos-et-documents/referen

tiels-d-indemnisation/).33 This case implies the same type of separating equilibrium

according to the presence/lack of ONIAM. This does not allow

refining our comparative analysis relative to the two other configu-

rations and consequently will not be developed here.

Physician–patient relationship

123

When D rises and moves from A0 to B, the physician’s

incentive to avoid the proposal rises. At the same time, for

a given value of D, the physician’s incentive to avoid the

proposal is more important when ONIAM is present

compared to the situation when ONIAM is absent. To put it

differently, D can be interpreted here as a threshold con-

sidered as acceptable by the physician to make a proposal.

This threshold is smaller in the presence of ONIAM, which

thus reduces his/her incentive to propose. A moral hazard

problem can thus appear because of the presence of ON-

IAM34 as the negligent physician is encouraged to avoid

the proposal and thus conceal his/her real type.

In the first configuration, the separating equilibrium with

ONIAM is:

sM NNð Þ; sM Nð Þ; sV� �

ONIAM

¼ sM NNð Þ ¼ No Proposal; sM Nð Þ ¼ Proposal;

sV ¼ Accepts

� �:

The pooling equilibrium in the case without ONIAM is

described by the following strategies:

sM NNð Þ; sM Nð Þ; sV� �

WithoutONIAM

¼ sM NNð Þ ¼ Proposal; sM Nð Þ ¼ Proposal;

sV ¼ Accepts

� �

if Dþ CV [ D apN þ ð1� aÞpN

� �or

sM NNð Þ; sM Nð Þ; sV� �

WithoutONIAM

¼ sM NNð Þ ¼ Proposal; sM Nð Þ ¼ Proposal;sV ¼ Refuses

� �

if Dþ CV\ D apN þ ð1� aÞpN

� �:35

In the third situation, the separating equilibrium in the

case where the ONIAM is not present is written as follows:

sM NNð Þ; sM Nð Þ; sV� �

WithoutONIAM

¼ sM NNð Þ ¼ No Proposal; sM Nð Þ ¼ Proposal;sV ¼ Accepts

� �

whereas the pooling equilibrium supposing the lack of a

proposal by the physician when the ONIAM is present is

given by:

sM NNð Þ; sM Nð Þ; sV� �

ONIAM

¼sM NNð Þ ¼ No Proposal; sM Nð Þ ¼ No Proposal;

sV ¼ Accepts

� �

if Dþ CV [ D apN þ ð1� aÞpN

� �.

In this first configuration, which supposes that the ON-

IAM pays a part of the compensation, the settlements are

not encouraged by the presence of the ONIAM. Thus, the

objective of the public authorities to encourage the out-of-

court settlements through the ONIAM is not achieved.

The intuition of this result relies on the fact that the trial

sanction is reduced by the subvention provided to the

physician who becomes more tempted to go to court, tak-

ing the risk of being convicted. His/her incentives to make

a proposal will be thus reduced.

The ONIAM sanctions the lack of a proposal more severely

In this configuration, the objective of the ONIAM to

develop the negotiation is clearly put forward. We can

identify three distinct situations that allow us to refine the

analysis of the role of the ONIAM.

1. A \ A0 and B \ B036

We thus have:

CM 1� pN

� �\pNðDI � DÞ

CM 1� pNð Þ\pNðDI � DÞ:

A B

A’ B’

Without ONIAM

With ONIAM

PoolingProposal

Separating PoolingLack of Proposal

D

D PoolingProposal

Separating PoolingLack of Proposal

34 This moral hazard problem can be identified on the segment B0B of

the above diagram.35 Contrary to the separating equilibrium, the rejection of the

proposal by the victim is a strategy that is compatible with the

physician’s behaviour in the case of a pooling equilibrium. Never-

theless, our comparative analysis is concerned with the physician’s

behaviour whose benchmark is the separating equilibrium. Thus, even

in the case of pooling equilibriums, we will retain only the acceptance

strategies from the victim as solution.

36 Condition A \ A0 implies B \ B0. It is thus impossible to have the

case A \ A0 and B [ B0.

L. Ancelot, C. Oros

123

In order to verify the condition A \ A0, we must have

pN [ 0. This latter condition implies the existence of a

type 1 judicial error, triggering the conviction of the non-

negligent physician.

In this configuration, we can identify three analysis

intervals represented as follows:

a. D 2 ðA; A0Þ implying a separating equilibrium in the

case where the ONIAM is not present, associated with

a pooling equilibrium with a proposal when the

ONIAM is present.

b D 2 A0;Bð Þ supposing a separating equilibrium with-

out and with the ONIAM.

c. D 2 ðB; B0Þ supposing a pooling equilibrium without

a proposal from the physician when the ONIAM is not

present and a separating equilibrium with the ONIAM.

For the first configuration, the separating equilibrium in

the case where the ONIAM is not present corresponds to

the strategies previously identified:

sM NNð Þ; sM Nð Þ; sV� �

WithoutONIAM

¼ sM NNð Þ ¼ No Proposal; sM Nð Þ ¼ Proposal;sV ¼ Accepts

� �

whereas the presence of the ONIAM generates the fol-

lowing equilibrium strategies:

sM NNð Þ; sM Nð Þ; sV� �

ONIAM

¼ sM NNð Þ ¼ Proposal; sM Nð Þ ¼ Proposal;

sV ¼ Accepts

� �

if Dþ CV [ D apN þ ð1� aÞpN

� �.

The presence of the ONIAM encourages the physician to

make a proposal that corresponds to the objective pursued by

the public authorities. Nevertheless, this type of behaviour

from the physician depends on the judicial error of type 1, i.e.

‘‘conviction of an innocent’’ (pN [ 0) and not only on the

existence of a more severe sanction in the case of a lack of

proposal. Indeed, the results point out that the non-negligent

physician, knowing that the justice may wrongly convict him/

her, always prefers to make a proposal in the presence of the

ONIAM, thus avoiding a more important sanction. In this case,

the ONIAM can be seen as an entity that replaces a failing

judicial system, thus allowing reducing the sanctions wrongly

imposed on the non-negligent physician.

In the case of the third situation, the pooling equilibrium

in the case where the ONIAM is not present becomes:

sM NNð Þ; sM Nð Þ; sV� �

WithoutONIAM

¼ sM NNð Þ ¼ No Proposal; sM Nð Þ ¼ No Proposal;sV ¼ Accepts

� �

if

Dþ CV [ D apN þ ð1� aÞpN

� �:

In the presence of ONIAM, the separating equilibrium is

written as:

sM NNð Þ; sM Nð Þ; sV� �

ONIAM

¼ sM NNð Þ ¼ No Proposal; sM Nð Þ ¼ Proposal;

sV ¼ Accepts

� �:

In this case, the physician’s incentive to avoid the pro-

posal is relatively more important in the case where the

ONIAM is not present. The comparative analysis relative

to case A allows us to observe that the economic policies

can make the ONIAM effective even if there are not any

judicial errors. Indeed, the supplementary sanction

imposed by the ONIAM on the physician who avoids the

proposal encourages the negligent physician to make a

proposal, whereas without the ONIAM, other things being

equal, this type of physician would not make any proposal.

2. A [ A0 and B [ B0

We find the same results as in the case A showing the

ineffectiveness of the ONIAM, which did not encourage the

settlements. Nevertheless, in case A, the lack of incentives to

make a proposal was based on the subsidy provided by the

ONIAM to the convicted physician, whereas here the role of

the ONIAM is different and aims at further sanctioning the

A B Without ONIAM

With ONIAM

D

PoolingProposal

Separating PoolingLack of Proposal

A’ B’

PoolingProposal

Separating PoolingLack of Proposal

D

Physician–patient relationship

123

lack of proposal (DI\DI). To put it differently, even when

implementing an explicit policy to fight against the lack of a

proposal, the presence of the ONIAM turns out to be coun-

terproductive as it does not encourage negotiations.

This case relies also on the existence of a judicial error,

i.e. the type 2 error, supposing that the negligent physician

could be acquitted (pN \ 1).37

In this configuration, the fact that the negligent physi-

cian could be acquitted implies the lack of effectiveness of

the ONIAM, as the incentive for the negligent physician to

make a proposal is reduced (compared to the case where

the ONIAM is not present). More precisely, the negligent

physician avoids proposing and accepts the risk of a sup-

plementary sanction as he/she is counting on a judicial

error, indicating his/her false innocence, whereas the same

physician would make a proposal if the ONIAM were

absent.

3. A C A0 and B \ B0

This situation is interesting because it is no longer

conditioned by the existence of a judicial error. Indeed, the

condition A [ A0 does not imply that the non-negligent

physician is convicted (pN [ 0). On the contrary, the more

correct the decision of the judge (pR goes down), the higher

the probability is to have A [ A0. In the same way, the

condition B \ B0 excludes the possibility to acquit the

negligent physician (pN \ 1). In contrast, the more correct

the decision of the judge (pN rises) is, the higher the

probability to have B \ B0.The differences between the configurations with and

without the ONIAM are represented below:

The configurations are:

a. D 2 ðA0; AÞ implying a pooling equilibrium with a

proposal if the ONIAM is not present and a separating

equilibrium with the ONIAM.

b. D 2 ðA; BÞ supposing a separating equilibrium

regardless of the presence or not of the ONIAM.

c. D 2 ðB; B0Þ supposing a pooling equilibrium without

a proposal if the ONIAM is not present associated with

a separating equilibrium with the ONIAM.

For the first configuration, we can identify the separating

equilibrium when the ONIAM is present:

sMðNNÞ; sMðNÞ; sV� �

ONIAM

¼ sMðNNÞ ¼ No Proposal; sMðNÞ ¼ Proposal;

sV ¼ Accepts

� �:

The pooling equilibrium when the ONIAM is not pres-

ent is described by the following strategies:

sM NNð Þ; sM Nð Þ; sV� �

WithoutONIAM

¼ sM NNð Þ ¼ Proposal; sM Nð Þ ¼ Proposal;

sV ¼ Accepts

� �

if Dþ CV [ D apN þ ð1� aÞpN

� �.

For the third situation, the pooling equilibrium when the

ONIAM is not present is written as:

sM NNð Þ; sM Nð Þ; sV� �

WithoutONIAM

¼ sM NNð Þ ¼ No Proposal; sM Nð Þ ¼ No Proposal;

sV ¼ Accepts

� �

if Dþ CV [ D apN þ ð1� aÞpN

� �.

In the presence of the ONIAM, the separating equilib-

rium is:

sM NNð Þ; sM Nð Þ; sV� �

ONIAM

¼ sM NNð Þ ¼ No Proposal; sM Nð Þ ¼ Proposal;

sV ¼ Accepts

� �:

We observe that if D is relatively small (D [ (A0, A)),

the ONIAM encourages the physician to avoid the proposal

despite the policy implemented by the public authorities

(DI\DI). This policy turns out to be effective only if D is

A B Without ONIAM

With ONIAMD

PoolingProposal

Separating PoolingLack of Proposal

A’ B’

PoolingProposal

Separating PoolingLack of Proposal

D

37 Indeed, the lack of judicial error signifies that the responsible

physician has to be convicted (pN ¼ 1). In this context, the condition

B [ B0 is no longer satisfied.

L. Ancelot, C. Oros

123

relatively high (D 2 ðB; B0Þ), which signifies that the

ONIAM can encourage the settlements if the harm suffered

by the victim is important. This result thus raises the

question of whether the ONIAM is effective in all types of

medical accidents. Indeed, as the ONIAM is effective only

when D is important, we can consider that its effectiveness

will be all the higher as the damage suffered will be high

and thus D will be important.

Conclusion

The 2002 Kouchner law establishes the creation of the

ONIAM as a public authority enabled to compensate the

victims of medical accidents in two specific cases: if the

physician is not negligent and if the insurer does not make

any proposal for settlement negotiations. At the same time,

the ONIAM aims at encouraging the negotiations between

victims and insurers before the beginning of prosecution

requirements. Based on the observation that this law gen-

erates an increase of both the settlements and the com-

pensations, the issue of the effectiveness of this law is even

more relevant as it involves an important financial

responsibility from the state.

This article reconsidered the impact of the ONIAM on the

evolution of the settlement negotiations between the physician

and the victim. Using a dynamic game with incomplete

information, we developed a comparative analysis of the

Bayesian equilibriums identified according to two game con-

figurations supposing the presence or absence of the ONIAM.

We showed that the out-of-court settlement is highly

conditioned by the extent of the costs payable by the actors.

The presence of the ONIAM reinforces the effectiveness of

the settlement negotiations provided that the public

authorities can influence the costs incurred by the patients.

On the contrary, when the public authorities cover a part of

the compensations paid by the physicians, the presence of

the ONIAM becomes counterproductive.

Our study also showed that the ONIAM can be con-

sidered as an authority facilitating the out-of-court settle-

ments when the hypothesis of judicial error is relevant. The

ONIAM’s objective to develop the out-of-court settlements

can sometimes be achieved to the detriment of a potential

conviction of a non-negligent physician. If the judicial

system is reliable supposing a low probability for the

judicial errors, ONIAM encourages the out-of-court set-

tlements only for the medical accidents that are relatively

heavy implying important damage.

Our analysis can be further developed: a different

framework can be considered in which the physician plays

an active role in the definition of the compensation amount.

In this case, the physician will no longer use the referential

imposed by the ONIAM, but he/she could have more

leeway to define the amount proposed to the victim. This

situation was not examined here as we focussed mainly on

the role of the public authorities on the development of the

out-of-court settlements (a crucial role assigned to the

ONIAM). Nevertheless, relaxing this assumption could be

useful in order to better examine the impact on the physi-

cian’s incentives of revealing his/her private information.

The theoretical results of the article could be tested

empirically in order to identify the evolution of the percent

of the out-of-court settlements before and after the creation

of the ONIAM according to the nature of the medical

accidents generating a proposal from the physician or from

the ONIAM.

Acknowledgments The authors thank two anonymous referees as

well as David Crainich, Louis Eeckhoudt and the participants to the

34th JESF, 30th JMA and 2013 AFSE Meeting for their constructive

suggestions and comments.

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