Régis Blazy
email: regis.blazy@unistra.fr

Bertrand Chopard
email: bertrand.chopard@univ-nancy2.fr

Eric Langlais
email: elanglais@u-paris10.fr

Ydriss Ziane

Personal Bankruptcy Law, Fresh Starts, and Judicial Practice

Keywords: Personal bankruptcy, over-indebtedness. JEL: G33, K29

We explore the ways French judges respond to the possibility of discharging personal debts in exchange for liquidation of debtors' assets. We present empirical results on the determinants of judicial selection between debtors whose debts are wiped out and those who have to reimburse them. We find that French judges tend to disqualify debtors with multiple creditors from debt discharge, and are sensitive to regional labor market conditions. These empirical results help us understand better how French personal bankruptcy laws perform compared to other national systems. Finally, our results serve to fill the gap between bankruptcy rules and judicial practice.

INTRODUCTION

France, like other European countries, faces a recent and substantial increase of personal bankruptcy filings. The annual number of filing records increased from 188,485 in 2008to 226,582 in 2009(BANQUE DE FRANCE [2008]). Several factors are thought to be responsible for this steady rise: the development of credit debt and revolving debt with high interest; an increase in major expenses, such as domestic rental and personal costs (especially following divorce or separation); and significant job losses. When such an adverse event occurs, some people are unable to repay the debts (which are often revolving debts) they have accumulated with their creditors. In this kind of financial context, it is necessary to understand (and test) whether personal bankruptcy law may have an impact on debtors' and creditors' incentives before the events that provoke financial distress. For instance, let's assume that the prime objective of bankruptcy law is to protect creditors' interests against debtors': the rules stress that debtors must repay their debts with their future incomes and assets. This would be a means of reducing the risk of over-indebtedness, as it may discourage consumers from over-borrowing, with loans issued against borrowers' rational anticipation of the future evolution of their income.

Alternatively, we might assume that a stronger level of creditor protection against bankruptcy filing might give them an incentive to offer more credit, as credit becomes more profitable. So, a solution to the problem of growing personal debt might be to penalize lenders who take advantage of consumers' tendency to over-borrow and their ignorance of credit conditions and prices. The current focus of empirical studies in the area of personal bankruptcy law is mainly on (1) whether the design of U.S. personal bankruptcy law (especially the difference in bankruptcy exemptions across U.S. states) plays a role in the evolution of consumers' bankruptcy filings; and (2) whether and how U.S. bankruptcy law may affect the supply of credit.

In the first strand of research, FAY, HURST, AND WHITE [2002] explore whether, before filing for bankruptcy, debtors would compare their financial benefit from filing under Chapter 13 (a debt reschedule plan) to their financial benefit from filing under Chapter 7 (a liquidation). As American debtors can freely choose between these two procedures, they would a priori file for the one that gives them the higher financial benefit. In fact, FAY, HURST, AND WHITE give some empirical evidence that such strategic behavior has an impact on the number of bankruptcy filings, all else being equal. For instance, the more debtors' assets are exempted from liquidation under Chapter 7, the more financially distressed debtors are motivated to file for such a bankruptcy procedure. 1 More interestingly, the authors also find little support for the assumption that debtors would rather file for 1 More extremely, FAN AND WHITE [2003], WANG AND WHITE [2000], WHITE [1998aWHITE [ , 1998b[START_REF] White | Abuse or protection? Consumer bankruptcy reform under BAPCPA[END_REF]] look at the risk of an opportunistic use of U.S. personal bankruptcy law. For instance, anticipating lenient treatment of their financial distress, some debtors might divert their assets prior to the bankruptcy filing in order to obtain partial debt clearance without any liquidation of their assets. Debtors could also accumulate credit cards by anticipating that their future financial distress would force creditors to accept some debt discharge. Furthermore, some borrowers might raise new, unsecured credit in order to reimburse other secured debts that would have to be repaid whatever the bankruptcy process initiated. Finally, some American debtors might choose their state of residence according its personal bankruptcy rules.

bankruptcy when an adverse event occurs (i.e. the non-strategic view of bankruptcy law). This is quite surprising because we know that over-borrowing results mainly from an exogenous shock (such as loss of job, illness, or divorce-see [START_REF] Gan | A simple test of adverse events and strategic timing theories of consumer bankrutpcy[END_REF]), the misuse of credit debt, or debtors' inability to manage their budget [START_REF] Lusardi | Debt literacy, financial experiences, and overindebtedness[END_REF]. Further, in the time series, DICK AND LEHNERT [2010] shed light on the fact that evolution in bankruptcy exemptions is too small to explain the rise in U.S. bankruptcy filings. Rather than the design of personal bankruptcy law, DICK AND LEHNERT explore the extent to which consumers file in response not only to adverse events but also to changes in lending practices (credit card, technology to estimate credit risk, or commercial practices) encouraged by bank deregulation.

The second strand of empirical research explores the links between U.S. personal bankruptcy and the credit market. GROPP, SCHOLZ AND WHITE [1997] demonstrate that American debtors, who live in states with the higher exemption levels on assets and future incomes (i.e. the most prodebtor states), have logically more difficulty accessing credit than others and pay a higher price for it. Now, if we focus only on debtors who have been quick to file for bankruptcy in the past, there are no clear-cut empirical results. On the one hand, [START_REF] Musto | What happens when information leaves a market? Evidence from postbankruptcy consumers[END_REF][START_REF] Filer | The consumption effects associated with filing for personal bankruptcy[END_REF][START_REF] White | Bankruptcy reform and credit cards[END_REF] provide some evidence that American debtors who file for bankruptcy suffer from credit rationing later. On the other hand, COHEN-COLE, DUYGAN-BUMP AND MONTORIOL-GARRIGA [2009] use U.S. micro-econometric data to demonstrate that the most reckless American borrowers, who benefited from a debt reschedule payment after their bankruptcy filing, would have quickly access to credit afterward.

It is more complex to address these questions in European countries, and more particularly to produce cross-country empirical analysis, because each European country has developed its own policy toward over-indebtedness. One solution to the problem of heterogeneity among European countries might be to evaluate the specific laws for each individual country. Here, there is a risk of misrepresenting some laws, in particular the gap between the rules and practices of bankruptcy courts.

For instance, when the World Bank ran cross-country comparisons in the area of corporate bankruptcy law, its legal index (based on a set of four variables) did not cover all the legal possibilities of resolving firms' financial distress, in particular the ways that bankruptcy courts worked. Further, to our knowledge, there are neither legal indicators nor specific cross-country comparisons that could serve to test the expected effects of personal bankruptcy law on credit markets or bankruptcy filings in Europe. Only JAPPELLI, PAGANO, AND DI [START_REF] Jappelli | Households' Indebtedness and Financial Fragility[END_REF] try to link empirically household default rates to some institutional factors in a sample of European countries (by using World Bank indicators on the extent of credit information sharing between lenders, and judicial efficiency). [START_REF] White | Bankruptcy reform and credit cards[END_REF] initiates a more precise comparison between the U.S., Canada, England, France, and Germany. Her work relies on seven variables: the amount of debt discharged, the level of asset exemption, the level of income exemption, the fraction of income above the exemption that debtors must use to repay their debts, the length of the repayment obligation, bankruptcy costs, and the bankruptcy punishment (for example, debtors' inscription on default records that could limit their future access to credit).2 According to these variables, a personal bankruptcy law is said to favor creditors if (1) the amount of debt discharged is lower, (2) the exemption levels on debtors' future incomes (or assets) are lower, (3) debtors' penalties are higher, (4) the length of the repayment period is shorter, or (5) fewer assets are exempted from liquidation or debt collection.

Following [START_REF] White | Bankruptcy reform and credit cards[END_REF], in comparison to the U.S., Canada, U.K., and Germany, French bankruptcy procedure seems to be the most pro-creditor in this set of countries. Indeed, the average duration of repayment plans is quite long, approximately eight years (BANQUE DE FRANCE [2008]). The levels of exemption on assets/future incomes are very low. This means that bankrupts will have to adjust their net income to a minimal poverty-level standard of living during the debt reschedule plan. Moreover, before filing for bankruptcy, individuals will have to sell their assets (if they have any) if they want to benefit from a bankruptcy procedure. However, this approach to personal bankruptcy law is severely limited. For instance, French judges can impose some delays in payment or reduction in interest charges on creditors (the latter possibility is not included in the index indicated above). This applies when financial creditors have made loans to debtors who were already over-indebted, or when they did not sufficiently verify that debtors were able to reimburse their loan.

Further, as [START_REF] White | Bankruptcy reform and credit cards[END_REF] noted, some bankrupts may file for a liquidation procedure, or "procédure de rétablissement personnel" (PRP), in order to obtain a full debt discharge in exchange for the liquidation of their non-exempt assets (similar to the U.S. liquidation process). Here, the crucial point is what determines judges' decisions to discharge (or not) personal debts, that is, judges' practices. So, our paper may also be linked to the behavioral law and economics literature, through our common focus on how judges apply the law. In the area of personal bankruptcy law, RACHLINSKI, GUTHRIE, AND WIRSTRICH [2007] explore whether there is room for emotional influence in judges' decision making in the U.S. They show that debtors' apologies (for excessive accumulation of debts) has little effect on judges' choices whether or not to discharge debts, even after controlling for judges' characteristics (gender, judicial experience, and political affiliation). Instead, they give some evidence that Republican judges are more likely than Democrat judges to make decisions in favor of creditors.

An economic analysis of personal bankruptcy law reveals that there are two procedures for resolving financial distress. The first aims at elaborating a restructuring debt schedule plan through debt renegotiation between the debtor and the main creditors under the supervision of a judge or an administrative authority. This bankruptcy process generally orders an automatic stay on creditors' pursuits in order to protect the debtors. Nevertheless, some creditors (in particular, secured creditors) are far from powerless when individual debtors cannot meet their debt obligations. In France, they can use specific procedures to repossess or foreclose on some assets (such as homes or cars), debit money from debtors' wages, stop debtors' bank accounts, or impose penalties for late credit repayment.

Failing that, if the debt renegotiation succeeds, debtors usually have to reimburse their debt (whole or in part) from their future income within a fixed period. Generally, the law decrees that part of future earnings is exempt from debt reimbursement, depending on family size, location, and so on. In some cases (for example, in France), a judge can also authorize delays in debt repayment when creditors do not reduce their claims sufficiently, or when lenders paid insufficient attention to individual borrowers' ability to repay loans. The second bankruptcy procedure allows for personal debts to be discharged under the supervision of a judge. This alternative procedure is intended to discharge debts and liquidate debtors' non-exempt assets-in other words, it requires bankrupts to repay from the proceeds of liquidation. However, for bankrupts to benefit from this fresh start, a judge has first to gauge whether or not they have a chance of repaying their debts in the future. If they do, the judge may order a new schedule of repayment of creditors, or ask for debtors and creditors to renegotiate a debt reschedule plan.

As [START_REF] White | Bankruptcy reform and credit cards[END_REF] noted, it is generally agreed that France is clearly pro-creditor, in the sense that bankruptcy laws tends to protect creditors' interests rather than debtors'. Although France introduced the possibility of discharging debts in exchange for liquidation of non-exempt assets in 2003, it is debatable whether this modification really does work in favor of borrowers, because debt discharge ultimately depends a judge's ruling on a case. In this paper we explore how French judges decide whether or not debts are discharged and non-exempt assets are liquidated through PRP. To do so, we examine how this move toward a more pro-debtor bankruptcy system is implemented and whether it constitutes a means of promoting a fresh start for bankrupts. We argue that French bankruptcy judges face a particular dilemma, having implicitly to arbitrate between the right of creditors to recover their claims and the right of debtors to ask to benefit from a release from debt.

Based on an empirical study of 1069 French bankruptcy filings in the period 2004-5, we report three observable results. First, we describe how judges allow debt discharge according to the legal criteria of bona fide ("bonne foi") and over-indebtedness ("situation irrémédiablement compromise"). Second, we find evidence that judges not only discharge debts for the most financially distressed, but they also block debt release for debtors who have over-borrowed or failed to balance their budget. Third, we also consider, from the perspective of behavioral law and economics, how bankruptcy judges are influenced by labor market conditions. More precisely, we report evidence that judges' decisions are significantly influenced by the level of unemployment rate in their locality.

The rest of this paper is organized as follows. In section 2 we report the basic features of French bankruptcy law; section 3 presents our data and regression results; section 4 concludes.

FRENCH PERSONAL BANKRUPTCY LAW: AN OVERVIEW

Before benefiting (or otherwise) from a debt discharge, financially distressed debtors generally have to file for bankruptcy before an administrative authority, the "commission de surendettement" (CSUR). This initial bankruptcy filing is automatically associated with the debtor's record in a national file of debtors who fail to reimburse their debts. The CSUR will either accept or reject the debtor's bankruptcy filing: more precisely, the CSUR authorizes debtors to continue the bankruptcy process only if they appear (1) to have significant difficulties in repaying their debts from their current incomes and assets; and (2) are bona fide. All creditors' pursuits (for example, assets seizing) are put on hold during this bargaining process. After examining the debtor's situation (i.e., debts, resources, charges, and the structure of claims), the CSUR (rather than the debtor) has the right to choose between two different bankruptcy procedures, the "plan de redressement" and the PRP. However, debtors can stop both these procedures whenever they have financial incentive to do so.

The "plan de redressement." This procedure aims at elaborating a restructuring debt schedule through debt renegotiation with debtors and their main creditors. The crucial point is that the CSUR calculates a standard level of charges for each debtor, based on a scale that takes into account family size, living expenses, medical and school bills. Debts will be reimbursed from the difference between the debtor's resources or assets and this standard level of charges over a fixed period. When this renegotiation fails, a judge may enforce a debt restructuring schedule by ruling that debtors do not have to reimburse their debts for a maximum of two years. The judge can also partly reduce the debts or elaborate a schedule of repayment for creditors (on condition that debts will be totally reimbursed during a period of ten years at most).

The "procedure de rétablissement personnel" (PRP). When, in a first step, the CSUR estimates that there is no (or very little) chance of debts being reimbursed from future income and assets, a judge (with the debtor's authorization) has to decide in a second step whether debts (except for specific debts such as secured loans, fines, or child support fees) will be discharged or not. In exchange, all the debtor's non-exempt3 assets are liquidated, and the liquidation proceeds are divided among creditors according to a strict priority rule. However, liquidation values are generally very low because debtors who have non-exempt assets will oppose this procedure whenever the value of debt discharged is less than the value of those assets (plus some direct and indirect bankruptcy costs). To order a debt to be discharged, judges have to verify that debtors are unable to repay their debts with their future income and assets, and are bona fide. The first of these criteria means that the debtor's capacity to reimburse the debts should be negatively and significantly related to the probability of a discharge of debt in the PRP. The second excludes debtors who use the bankruptcy procedure strategically to discharge their debts when they have accumulated too many debts in the past.

EMPIRICAL FINDINGS

In this section, we test how judges handle the discharge of debts in exchange for the liquidation of non-exempt assets within the PRP, beginning with our data on PRP.

DATA DESCRIPTION

Our research project studied the practices of courts ruling on personal bankruptcy law. Even though this subject is attractive, due to the steady rise of over-indebtedness in European countries, only limited information is available on the subject of the legal treatment of financial distress. In order to improve the quality of the work delivered by the courts, or at least to understand judicial practices better, the French Ministry of Justice ordered a large data collection on PRP for the period 2004-5.

Information was gathered manually from documents in 158 French courts, including bankruptcy declarations, court decisions and motivations, lists of claims, and characteristics of bankrupts. Using this information, we obtained a database of 4098 judgments delivered in the period 2004-5 in 20 regions (out of a global set of 22 regions), representing nearly 11% of the entire population of debtors filing for a PRP during this period. For each bankruptcy case, we gathered data about the debtor's financial situation at the triggering time: total amount of claims due; total income (including wages, unemployment benefit, family income support, housing benefit, rent allowance, sickness benefit, and old-age pension); total amount of expenses (debt service, dependents, tax, rent, plus additional expenses calculated by the judge on the basis of family size); asset list (exempt or not); and the total number of claims. We regrouped creditors in two sets: financial claimants (banks and firms specializing in consumer credit), and other (rent, taxes, energy or communication bills, private debts, commercial debts, unpaid alimony, tuition fees, fines). We controlled our results according to length of procedure (i.e., the time between the date of PRP filing and the date of judgment) as judicial delay can be considered a proxy for court congestion. After controlling for lack of responses on some of the variables described here, the sample size falls into 1120 observations on a set of 20 French regions.

In this paper, we focus only on bona fide debtors, excluding from the sample 36 debtors who were judged mala fide for the following reasons: falsification of information, voluntary overindebtedness in order to file for bankruptcy, and checks without funds. As a consequence, we analyzed data only for individuals who do not voluntarily become bankrupts in order to benefit from full debt discharge by a judge (or, at least those who have not been identified by the judge). Finally, in designing our analysis, we only retained data for individuals who reported no real estate assets at the triggering time. Of our sample of 1105 debtors, 15 are owners (occupier or not). So, a very large majority of bankrupts have no assets to liquidate in order to benefit from debt release in exchange.

Overall, this figure indicates either that debtors with some real estate assets refuse to file for this bankruptcy procedure, or that such debtors have restricted access to this procedure, meaning that some CSUR impose a debt reschedule plan on these debtors. However, this does not mean that individuals have no assets at all. Of the 1069 individuals, 917 clearly have no assets but 152 own a car and/or furniture. More precisely, 106 bankrupts own a car and no furniture, 11 bankrupts own both a car and furniture, and 35 bankrupts own furniture but no car. However, these assets (cars and furniture) are generally exempt from liquidation because people need cars to get to work, and furniture has a very low liquidation value. As a consequence, we do not take account of debtors' assets in our analysis because debtors are either exempted or have none.4 Note: in first part of Table 1, we report summary statistics on the sample. In second part, we make a distinction between the group of debtors that benefits from a debt discharge and the group that does not. For each group, we compute both the mean and the standard deviation for the following set of variables: size of the debt, resources, current expenses, number of creditors, number of financial creditors, number of ordinary creditors, and duration of the legal process. We also report the results of t-tests to evaluate the difference in means between the two groups of debtors. The equality of variances is verified with the F test. Finally, the p-level reported for both tests represents the probability of error involved in accepting the hypothesis about existence of a difference (in mean or variance).

Table 1 shows that the mean amount of debtors' monthly resources is €904.17, the mean amount of debts is €20775.07 and the mean amount of monthly expenses €1006.58. As a result, debtors have a mean negative capacity to reimburse their debts (here, the difference between resources and expenses). More precisely, 758 debtors have a strictly negative capacity to reimburse, and 311

debtors have a positive one. Further, debtors are indebted to 7.63 creditors at mean, with a minimum of one creditor and a maximum of 35 (median value = 7). The mean number of financial (other) creditors is 2.69 (4.94). Finally, the mean length of the procedure is 34.52 days with a maximum duration of 147 days. Now, if we compare debtors whose debts are discharged by the judge to other bankrupts, we find that 25.35% of debtors in our sample who filed for PRP did not benefit from a debt discharge (note that this ratio is equivalent to 33.2% for the entire population, BANQUE DE FRANCE [2008]). In Table 1, we stress several differences between the two sets of debtors. First, bankrupts whose debt discharge is refused by the judge present the highest values for resources, number of creditors, number of financial creditors, and duration (see t test in Table 1). Second, there is no significant difference between the means (in terms of in debt size, current expenses and number of ordinary creditors) of debtors who benefit from a debt release and those who do not. We explore these differences in the following section and take a closer look at the way judges deal with personal bankruptcy.

DO JUDGES "PUNISH" DEFAULT?

Table 1 indicates that decision making in courts is largely influenced by the financial situation of bankrupts. In this section we examine the possibility that judges "punish" debtors for overindebtedness-that is, they could penalize some debtors by denying them debt discharge if they have too many debts. We note also that, from an economic point of view, debt discharge may be interpreted as a punishment for creditors, for example, because they offered too many credit.

To study these effects, we first control for the debtor's capacity to reimburse debt from (future) income, computing the ratio Reimbursment capacity in the following way. First, for each debtor we calculate the difference between annual resources and annual expenses, divided by the total amount of debts. Second, we multiply each of these values by the median duration of the debt reschedule plans elaborated by the CSURs (approximately five years, BANQUE DE FRANCE [2008]). Recall that when judges decline debt discharge, debtors generally benefit from a reorganization plan under the supervision of a CSUR. Notice also that calculated values are either positive or negative because, for some debtors, expenses are higher than resources. Third, for each debtor we keep the maximum value between zero and the value calculated above. As explanatory variables, we use the structure of claims (number of creditors, number of financial creditors, and number of ordinary creditors) to explore first whether a larger number of claims may significantly influence the bankruptcy court's decision and, second, to what extent judges might consider the case of debtors who seem to have over-borrowed in terms of the number (rather than the amounts) of their claims. We showed in Table 1 that there is no significant difference between the mean amount of debt of debtors who benefit from a debt release and those who do not.

In order to monitor judicial practice, we run a Logit regression analysis where the dependent variable equals 1 if the judge discharges all the debt and zero otherwise. In a first set of models, shown in Table 2, we control the judgment with the debtor's reimbursement capacity, the duration of the legal procedure, and some indications about debt structure. More precisely, we run two models. Model 1 includes reimbursement capacity, the log of duration of the procedure and the log of the number of creditors. Model 2 distinguishes between the log of financial creditors and the log of ordinary creditors (see our earlier definition of these groups). In Table 3, we report a second set of regressions in which we analyze the robustness of our results, repeating our analysis after introducing the variable Ind(Unemployed), which equals 1 when the debtor is unemployed and zero otherwise. Note: Table 2 reports the results of Logit regression analysis of the determinants of judicial decisions to discharge debts on the decision to (implicitly) order the borrower to repay debts from future income and assets. We report the reimbursement capacity, which is the maximum between zero and the following ratio: at the numerator, we have the product between the difference (annual resources -annual expenses) and the median duration of the debt reschedule plans elaborated by the CSUR. The denominator equals the total amount of debts. The other variables are the log of the length of the judicial procedure, the log of the number of creditors, the log of the number of financial creditors, and the log of the number of ordinary creditors. Collinearity diagnostic: if condition index > 30 then there is strong collinearity. The sample is described in subsection 3.1. Coefficients significant at the 1%, 5%, and 10% levels are indicated by ***, **, and *, respectively.

Note:

In comparison to the regressions depicted in Table 2, we add Ind(Unemployment), a dummy variable that equals 1 if the debtor is unemployed and zero if not (i.e., employed or retired). All other explanatory variables are the same as in Table 2. Collinearity diagnostic: if condition index > 30 then there is strong collinearity. The sample is described in subsection 3.1. Coefficients significant at the 1%, 5%, and 10% levels are indicated by ***, **, and *, respectively.

Obviously, reimbursement capacity is the most important and significant factor to explain the probability of debt discharge. It suggests that those debtors who are least able to repay their debts (or those who are more financially distressed) have a greater probability of benefiting from a fresh start. In addition, we have controlled for the amount of resources, expenses, and debt separately but did not include these variables in the same regression model because of the high degree of correlation between resources and expenses. In this way, we did not find any significant relation between the likelihood of debt discharge and the total amount claimed whatever the set of regressions (regression results are not reported in the paper-note that this result appears in Table 1). Our explanation is as follows. Before filing for this bankruptcy procedure, debtors would have attempted to renegotiate their debts privately, or under the supervision of a CSUR, and have failed. So, these debtors are significantly financially distressed, meaning that the outstanding amount owed does not constitute a way for judges to discriminate between them.

The main finding in Tables 2 and3 is that the coefficient of the log of number of creditors is negative and statistically significant. This means that having a large number of creditors reveals more than the debtors' level of financial distress. Judges might consider that having multiple creditors indicates that debtors have failed to balance their budget, or over-borrowed. In Model 2 we show that it is the number of financial creditors, rather than the number of ordinary creditors (controlling with the reimbursement capacity and the log of duration of the procedure), that tends to disqualify debtors from debt discharge. This result gives some insight into the intuition that it is the number of financial debts (mainly debt consumption or credit cards) that may motivate bankruptcy courts to refuse debt discharge due to over-borrowing. 5 In other words, our data illuminate the extent to which specialized judges are influenced by their sense that debtors are responsible for their financial situation.

In addition, we show in Table 3 that this last result is not robust to the inclusion of a dummy variable-Ind(Unemployed)-indicating whether or not the debtor is unemployed. In Model 4 adjusted for the variables Ind(Unemployed), Reimbursement capacity, Log duration, Log number of financial creditors, and Log number of ordinary creditors, it appears that the log of financial creditors

is not yet significantly associated with the likelihood of debt discharge. We also note in Model 3 that the number of creditors always plays a significant role in the judge's decision, suggesting that a large number of debts may prevent some debtors from a fresh start. As a consequence, our model suggests that the effect of capital structure is not so trivial. Unemployed debtors are more likely to benefit from debt clearing than employed debtors, controlling with debt structure. This result undermines the intuition that the number of financial debts (mainly debt consumption or credit cards) may motivate bankruptcy courts to refuse debt discharge. More simply, it is less clear how the difference between financial and ordinary debts affects the judge's decision. However, this last finding is more in line with the objective to offer financially distressed debtors a fresh start.

Finally, Table 3 contains another interesting result that has to be interpreted with care. It appears that the log of the duration of the procedure plays a role in the court's decision making. Here, we consider that the duration of the legal procedure is closely correlated with the overwhelming number of personal bankruptcy filings with which the courts have to deal. In effect, we are testing whether debtors can throw themselves on the mercy of the judge if their case takes a long time. As a consequence, we do not consider any strategic behavior by lenders or borrowers within the procedure, such as voluntary delays in furnishing information or documents, or claimants' requests to set out the judge's decision. Table 3 shows clearly that the longer the length of the procedure, the smaller the likelihood of debt discharge. So, contrary to the hypothesis described above, debtors do not benefit from judges' leniency when judicial delays increase due to the rise in personal bankruptcy filings.

JUDGES' DECISIONS AND MACROECONOMIC/SOCIAL CONTEXT

To complete our analysis, we explore whether judges' decisions to discharge debts are influenced by the external environment of the bankruptcy case. More precisely, we test a judge's sensibility to the unemployment rate in the court's locality. To do this, we first report the difference between the unemployment rate in the court's locality (one of 20 French regions) and the mean national unemployment rate (the variable (Unemployment rate -Av)). Second, we construct a dummy variable that equals 1 if the unemployment rate in the court's locality is superior to the mean unemployment rate (the variable Ind(Unemployment rate > Av)). This variable allows us to test whether there is a judicial bias in favour of bankrupts when unemployment is relatively high. Table 4 shows this new set of regressions. It appears in Table 4 that the macroeconomic context proxied by the unemployment rate (in comparison to the mean rate) plays a significant role in judicial decision making. The regression estimates indicate that the higher the regional unemployment rate (in comparison to the mean rate), the higher the likelihood of debt discharge. In other words, judges are more likely to enforce debt discharge when there is a clear shortage of employment, or when debtors face increased risk of an adverse event (job loss) in the future (by controlling for the current debtor's employment status).

Again, we use Table 4 to confirm that judges also tend to disqualify debtors with multiple debts from full debt discharge. Our findings complete empirical results showing that economic conditions influence judges' decisions. For instance, ICHINO, POLO AND RETTORE [2003] demonstrate that judges acting in Italian labor courts are more likely to decide in favor of workers when and where unemployment is higher. Further, MARINESCU [2008] gives empirical evidence from British employment courts that judges are more pro-firm when the unemployment rate is raised. All these results support the idea that judges do not only enforce debt or employment contracts, but that they maximize either the welfare of the trial parties or social welfare.

CONCLUSION

Our observations in the French legal system show that even if all countries appear to be acting similarly in their treatment of personal bankruptcy law (reorganization versus liquidation), we need to run more realistic studies to assess better the work of courts in each country. Indeed, cross-country comparisons generally suffer from a gap between bankruptcy rules and judicial practice. For instance, a first reading of the French personal bankruptcy rules indicates that this system has been more prodebtor since 2003, in the sense that it allows for debt discharge (in exchange for liquidation of nonexempt assets) under the supervision of a specialized judge. In this paper, we show that this conclusion may be wrong for two reasons. First, in the period 2004-5, we note that more than one-third of borrowers who filed for such a procedure were denied debt discharge. More surprising, all these debtors were previously identified as financially distressed by an administrative authority or CSUR (meaning that there was no chance of elaborating a rescheduled debt payment, on the assumption that CSUR makes no filtering errors). Second, we find in our sample that a great majority of debtors who filed for PRP had no assets to liquidate.

To better assess the impact of the French bankruptcy procedure on debtors and creditors, we also explore judicial criteria. After eliminating mala fide debtors, we show that a debtor's reimbursement capacity is the judge's dominant consideration in the decision to discharge debts. More interestingly, we find that judges refuse debt discharge when debtors are indebted to multiple creditors, especially financial ones. As a consequence, judges consider that some borrowers are responsible for their financial distress or over-borrowing. In that case, the lower the probability of discharging the debt, the more creditors (financial or not) are protected from default. This could give financial creditors some incentive to increase access to credit with the risk of increasing the probability of over-borrowing when an adverse event occurs. Finally, we show that it is necessary to control our estimate of the probability of debt discharge with some indicators on the macroeconomic context in which judges view the case. In particular, we find great statistical support for the hypothesis that French judges are influenced by local and regional labor market conditions. This analysis is somewhat incomplete. There is still quite a large set of questions to address.

To our knowledge, there is no cross-country analysis that relates the various national personal bankruptcy systems with specific forms of bank debt contracts (size of loan, level and type of collateral, interest rate, duration). As in corporate bankruptcy law, the differences in lenders' legal protection across these countries should correlate with significant differences in lenders' strategies and outcomes. More simply, the design of personal bankruptcy law might help us to understand lenders' recovery rates or the success of informal renegotiations (preceding a bankruptcy filing). Future research efforts are needed to clarify these questions.

Table 1 -

 1 Variable means and standard deviations for the bankruptcy sample according to the judgment (debt discharge or not)

	Statistics on the sample	(N=1069)
	Variables	mean	stand.dev.	Variables	mean	stand.dev.
	Total debts (euros)	20775.07	37086.46	Nb. creditors	7.63	4.78
	Resources (euros)	904.16	361.39	Nb. financial creditors	2.69	2.16
	Current expenses (euros)	1006.58	358.16	Nb. ordinary creditors	4.94	4.44
	Duration (days)	34.52	16.66
				Total debts (euros)	No debt discharge	Debt discharge
	Analysis of judgment:			mean	21873.74	20401.97
	Debt discharge (N=798)			t	0.6700
	versus no debt discharge (N=271)		p value	0.5030
				stand. dev.	27758.80	39767.93
				F	0.4872
				p value	<.0001
	Resources (euros)	No debt discharge	Debt discharge Current expenses (euros)	No debt discharge	Debt discharge
	mean	1033.69	860.17	mean	1003.81	1007.52
	t	6.2001		t	-0.1365
	p value	<.0001		p value	0.8914
	stand. dev.	419.06	328.46	stand. dev.	400.00	343.06
	F	1.6277		F	1.3595
	p value	<.0001		p value	0.00075
	Nb. creditors	No debt discharge	Debt discharge Duration (days)	No debt discharge	Debt discharge
	mean	8.15	7.45	mean	37.46	33.51
	t	2.0773		t	3.1251
	p value	0.0380		p value	0.0019
	stand. dev.	4.94	4.72	stand. dev.	18.78	15.78
	F	1.0966		F	1.4161
	p value	0.1713		p value	0.00016
	Nb. financial creditors	No debt discharge	Debt discharge Nb. ordinary creditors	No debt discharge	Debt discharge
	mean	2.9077	2.6215	mean	5.4235	4.8320
	t	1.7116		t	1.3179
	p value	0.0877		p value	0.1878
	stand. dev.	2.4830	2.0384	stand. dev.	4.5712	4.3953
	F	1.4838		F	1.0816
	p value	<.0001		p value	0.2093

Table 2 -

 2 Explanation of debt discharge

		Model 1: 1069 obs.	Model 2: 1069 obs.
	Variables	Debt discharge vs.	Debt discharge vs.
		no debt discharge	no debt discharge
		Estimation	Prob. >khi2	Estimation	Prob. >khi2
	Constant	3.3133 ***	<.0001	3.0718 ***	<.0001
	Reimb. Cap.	-1.6314 ***	<.0001	-1.6347 ***	<.0001
	Log duration	-0.3475 **	0.0108	-0.3513 **	0.0107
	Log Nb. Creditors	-0.3411 **	0.0150
	Log Nb. Fin Creditors			-0.2173 *	0.1000
	Log Nb. Ordin. Creditors			-0.1224	0.2072
	Logit Regression	Nb. debt disch:	798	Nb. debt disch:	798
		Nb. debt resch:	271	Nb. debt resch:	271
		% concordant:	73.4	% concordant:	73.3
		Condition index:	13.85 (<30)	Condition index:	14.89 (<30)
	Estimation method:	Test	khi2 Pr > Khi2	Test	khi2 Pr > Khi2
	maximum likelihood	Likelihood	132.96 <.0001	Likelihood	130.76 <.0001
		Score	30.17 <.0001	Score	27.62 <.0001
		Wald	76.42 <.0001	Wald	74.98 <.0001

Table 3 -

 3 Explanation of debt discharge including debtor's employment status

		Model 3: 1069 obs.	Model 4: 1069 obs.
	Variables	Debt discharge vs.	Debt discharge vs.
		no debt discharge	no debt discharge
		Estimation	Prob. >khi2	Estimation	Prob. >khi2
	Constant	3.1612 ***	<.0001	2.8867 ***	<.0001
	Ind(Unemployed)	0.3363 **	0.0279	0.3205 **	0.0411
	Reimb. Cap.	-1.5721 ***	<.0001	-1.782 ***	<.0001
	Log duration	-0.3561 ***	0.0091	-0.3594 ***	0.0084
	Log Nb. Creditors	-0.3462 **	0.0138
	Log Nb. Fin Creditors			-0.1646	0.2279
	Log Nb. Ordin. Creditors			-0.1434	0.1424
	Logit Regression	Nb. debt disch:	798	Nb. debt disch:	798
		Nb. debt resch:	271	Nb. debt resch:	271
		% concordant:	72.8	% concordant:	72.7
		Condition index:	15.09 (<30)	Condition index:	16.55 (<30)
	Estimation method:	Test	khi2 Pr > Khi2	Test	khi2 Pr > Khi2
	maximum likelihood	Likelihood	137.78 <.0001	Likelihood	134.92 <.0001
		Score	41.62 <.0001	Score	38.92 <.0001
		Wald	81.99 <.0001	Wald	79.67 <.0001

Table 4 -

 4 Explanation of debt discharge related to external environment

		Model 5: 1069 obs.	Model 6: 1069 obs.
	Variables	Debt discharge vs.	Debt discharge vs.
		no debt discharge	no debt discharge
		Estimation	Prob. >khi2	Estimation	Prob. >khi2
	Constant	2.9530***	<.0001	2.7658***	<.0001
	Ind(Unemployed)	0.3587**	0.0203	0.3368**	0.0295
	Reimb. Capacity	-1.5417***	<.0001	-1.6002***	<.0001
	Log duration	-0.2799**	0.0381	-0.3021**	0.0245
	Log Nb. Creditors	-0.3284**	0.0198	-0.3599**	0.0107
	(Unemp. Rate -Av)	29.6725***	<.0001
	Ind(Unemp. Rate > Av)			0.8388***	<.0001
	Logit Regression	Nb. debt disch:	798	Nb. debt disch:	798
		Nb. debt resch:	271	Nb. debt resch:	271
		% concordant:	75.8	% concordant:	75.2
		Condition index:	15.32 (<30)	Condition index:	16.10 (<30)
	Estimation method:	Test	khi2 Pr > Khi2	Test	khi2 Pr > Khi2
	maximum likelihood	Likelihood	155.93 <.0001	Likelihood	161.35 <.0001
		Score	59.08 <.0001	Score	60.88 <.0001
		Wald	95.99 <.0001	Wald	96.93 <.0001

Note:

In comparison to regressions depicted in Table

3

, we introduce in Model 5 the variable (Unemployment rate -Av). Model 6 includes the variable Ind(Unemployment rate > Av). See subsection 3.3 for a description of these variables. Collinearity diagnostic: if condition index > 30 then there is strong collinearity. The sample is described in subsection 3.1. Coefficients significant at the 1%, 5%, and 10% levels are indicated by ***, **, and *, respectively.

We could add other characteristics. For example, we could test whether or not consumers choose freely between the various existing bankruptcy procedures. We could also analyze the conditions under which secured creditors can collect their claims even after the bankruptcy filing, especially their order in the absolute priority rule in the case of liquidation.

Exempt assets are mainly vehicles and other goods essential to life.

In the regression analysis we verified that there was no significant interaction between a judge's decision to cancel debts and a dummy variable that equals 1 if the bankrupt has some assets (car and/or furniture) and zero if none. We do not report this result in this paper.

We have also included the number of creditors squared as regressors in our models in order to test for nonlinearities in the effect of the structure of claims on the judgment (results are not reported in this paper). We found a U-shaped relation between the probability of debt discharge and the number of creditors.


Bruno Deffains
email: bruno.de¤ains@u-paris2.fr.y

Eric Langlais
email: eric.langlais@u-paris10.fr.

Economix

Informational Externalities and Settlements in Mass Tort Litigations

Keywords: Mass Tort Class Action, information sharing, repeated litigation, contingent fees

This paper elaborates on a basic model of mass tort litigation, highlighting the existence of positive informational externalities a¤orded by the discovery process (as a general technology of production of evidences) in order to study when a class action is formed, or when a sequence of individual trials is more likely. We illustrate the argument that when several plainti¤s …le individually a lawsuit against the same tortfeasor, the resolution of the various cases through repeated trials produces positive informational externalities. When class actions are forbidden, these externalities only bene…t to the later plainti¤s (through precedents, jurisprudence...). When they are allowed, the …rst …ler may have an incentive to initiate a class action as far as it enables him to bene…t from these externalities, through the sharing of information with later …lers. We provide su¢ cient conditions under which a class action is formed, assuming a perfect discovery process. We also show that when contingent fees are used to reward attorneys'services, plainti¤s become neutral to the arrival of new information on their case.

Introduction

Informational asymmetries are considered as an important factor to explain the strategies of litigants to solve legal con ‡icts. However, when parties enter into the litigation process, they collect evidences, testimonies, expertises and share many informations during the pretrial negotiation period. Moreover, when there is a collective concern, plainti¤s do not enter simultaneously into the litigation process but rather sequentially, at di¤erent dates. This is the case, for instance, when victims are injured by the same tortfeasor in a quite long period of time (e.g. asbestos or tobacco litigation, medical malpractice or product liability). It follows that some informations of the "…rst movers" bene…t to the other, since as time is passing, new evidences arrive and the "state of the art" changes. As a result, some uncertainty is resolved from the time the …rst claims are solved to the period the later plainti¤s …le. This implies positive informational externalities between plainti¤s because later …llers bene…t from the experience of the …rst plainti¤s. These externalities also allow later plainti¤s to update their beliefs on the likelihood to win at trial. According to this view, class actions may be understood as a device which allows plainti¤s to internalize informational externalities. Speci…cally, class actions allow the earlier victims to retain part of the bene…ts of these externalities, that they would otherwise never recover. As a consequence, when they participate to a class actions, plainti¤s perceive in a better way the existence of the correlation between the individual losses. In other words, plainti¤s would become more con…dent with their chances of success at trial against the same defendant. An additional argument is that the class action's lawyers certainly contribute to the transmission of information between the members.

In the existing literature on the economics of class actions, it is more usual to …nd arguments regarding the opportunistic/strategic behaviors of one of the three parties involves in mass tort litigation (plainti¤s, defendants or their attorneys) as a result of the existence of informational asymmetries. A speci…c line of research has discussed the existence of, and solution to, agency problems between attorneys and their clients. The main issue is how to monitor the e¤ort undertaken by attorney for the time they spend to their clients'case, and give them e¢ cient incentives to maximize their client's recovery. In particular, the rational for the use of contingent fees [START_REF] Klement | Incentive structures for Class Action lawyers[END_REF], [START_REF] Lynk | The courts and the market: an economic analysis of contingent fees in class-action litigation[END_REF][START_REF] Lynk | The courts and the plainti¤s'bar: awarding the attorney's fees in class-action litigation[END_REF]), or conditional fees [START_REF] Emons | Playing it safe with low conditional fees versus being insured by high contingent fees[END_REF][START_REF] Emons | Conditional versus contingent fees[END_REF], [START_REF] Emons | The economics of US-style contingent fees and UK-style conditional fees: agency problems and the supply of legal services[END_REF]), has been assessed. Some authors have been more concerned with the relationships between plainti¤s as members of a class action. [START_REF] Che | Equilibrium formation of Class Action suits[END_REF] for example analyzes the role of asymmetries of information on the one hand between plainti¤s and the defendant, and on the other hand between the members of the class action. Che assumes that two kinds of plainti¤s (small claim, and large claim) sue against the same tortfeasor, and have the opportunity to join a class action or to …le individually. He …nds a multiplicity of equilibria: either no class action is formed, while there exists a potentially viable class action, or not all the plainti¤s are allowed to join the class action (and speci…cally, not all the smallest or weakest victims), but many opt out. [START_REF] Marceau | Damage averaging and the formation of Class Action suits[END_REF] for their own develop the idea that a class action has the characteristics of a public good, although it is privately produced -since a class action is usually provided by only a subset of plainti¤s. Once the class action is created against a tortfeasor, all the victims have the opportunity to join it, and thus bene…t from the provision of the good without having to incur the initial cost associated to the formation of the class action. For the representative member, this cost is a sunk cost, and it is borne only by the initiator of the class action. Hence, there is a problem of "free-riding", which is formalized by Marceau and Mongrain as a war of attrition: on the one hand, each plainti¤ has an incentive to wait that someone else initiates the class action (because of the sunk cost) but on the second, he bears a penalty in waiting (time is also costly). The authors mainly demonstrate that the identity of the class action initiator depends on the rule of compensation awarded by courts to the class action members: small levels of damage averaging tend to give incentives to the holder of the smallest claim to be the initiator of the class action.

A more recent line of research addresses the issue of the deterrent e¤ects of group versus individual litigation on the injurer's misconduct. [START_REF] Saraceno | Group Litigation, Access to Justice and Deterrence[END_REF] illustrates that group litigation does not always improve deterrence. Despite the fact that group litigation facilitates access to justice for victims (through the bene…ts of scale economies and/or the improvement of their con…dence in a trial), it creates additional transaction costs borne by victims. Moreover, the aggregation of individual cases thanks to a group litigation enables the injurer to reduce its liability costs, since it both facilitates settlement and reduces litigation costs. The combined result of these various e¤ects might be a reduction, rather than an increase, in the deterrent e¤ect of tort law. [START_REF] De¤ains | Class Actions, Compliance and Moral Cost[END_REF] …ndings are more favorable to the deterrence e¤ect of group litigation, relying on a di¤erent argument. They assume that …rms have intrinsic motivations (such as feelings of remorse, guilt, regret and/or shame). They show that the standard aggregation argument in favor of class action holds, increasing e¢ ciency due to lower litigation costs. In the short run intrinsically motivated …rms bene…t from the introduction of a class action procedure. In the long run, new intrinsically motivated entrants are attracted in the market thereby increasing consumer surplus. Overall, the average care level increases.

In the present paper, no asymmetric information exist between litigants, and parties are unable to anticipate ex-ante the behavior of the court during the trial. We rather focus on the impact of information sharing between plainti¤s and we compare the case where class actions are forbidden to the case where they are allowed. In many countries, procedural rules hold such that parties have a free access to the evidences and the various documents that the other party has gathered and will produce at trial. However, uncertainty remains as to the outcome at trial given the existence of an heterogeneity in the decisions of courts, concerning similar cases. A related problem is the emergence of new legal doctrines. For example in the United States, the problem with the asbestos litigation in the eighty's comes partly from the fact that the legal doctrines to apply was not yet developed. So in our work, the main source of uncertainty is coming from the behavior of the courts.

We consider a situation where a given agent, for example through the occurrence of several successive individual accidents, injures a group of victims. If class actions are forbidden, victims will individually enter into the litigation process …ling against the same tortfeasor according to a sequence of moves which is supposed exogenously given1 . It follows that repeated trials entail positive informational externalities which are bene…cial only to the later plainti¤s. The earlier ones who are less informed may undertake strategies that otherwise they would not choose to adopt with a better information. In contrast, the plainti¤s who enter later on in the litigation process may bene…t from the experience of the earlier ones and are allowed to undertake more accurate decisions regarding the various legal options that are available (…le or exit, go to trial, settle or give up). This is a passive transmission of information coming from the earlier plain-ti¤s, but a problem arises because the …rst plainti¤s have no means to bene…t of the information collected by their successors or to retain privately part of the bene…ts associated to the positive informational externality they create. From this perspective, the formation of a class action may be understood as a tool to internalize these externalities. More generally, the formation of a class action makes easier the transmission of information between the plainti¤s. As a consequence, apart of economies of scales coming from the pooling of lawyer's services, we identify a new rationale to the formation of class actions which result from information sharing between plainti¤s. Speci…cally, the pooling of individual information allows all of them to improve their individual assessment of the expected gain at trial. We focus on these incentives to share information between plainti¤s suing the same tortfeasor and we investigate their consequences for the existence of a class actions.

The paper develops as follows. Section 2 presents the model. Section 3 derives the market equilibrium under di¤erent institutional frameworks (sequential trial, information sharing). Section 4 discusses the speci…c issue with contingent fees, and section 5 concludes. Proofs of propositions are in the appendix unless statements are obvious from the text.

The model 2.1 The sequence of individual decisions

We consider a three-stage game, where plainti¤s enter sequentially in the litigation process against the defendant, such that P i is the …rst …ler. In stage 1, P i may choose between two options: either he …les or he exits. In this last case, everything is over for him, and then, P j has only to decide for himself whether he enters and …les individually, or if he exits. If P i opts for …ling, two options are available to him: either he can sue individually, or he can decide to initiate a class action, to which every individuals that have su¤ered a damage may join.

In stage 2 beginning after P i 's move, P j chooses either to sue individually or to register to become a member of the class action.

We assume that the membership is voluntary and open, such that the presence of a class action does not legally compel other plainti¤s to join it, and no individual plainti¤ is denied membership against his wishes. In practice, Courts decide to maintain a class action or not, and prescribe deadlines for claimants' participation or opt out decisions. This framework re ‡ects the equilibrium behaviors of plainti¤s, in such a way that after a limited period of time during which any individual has the opportunity to opt out, the membership becomes binding: no class action member can opt out, and no new plainti¤ can opt in. Moreover, once a class action is formed, which is requiring that more than one plainti¤ register, it sues on behalf of all its members. Here, no di¤erence is made between the case where the representative plainti¤ who has initiated the class action litigates for all members, or the case where the active role is played by the class action's lawyer. We assume that the delegation of the collective negotiation power to one of the member or to a third party leads to no agency problem and does not require any incentive scheme to monitor the e¤orts of the class action representative agent, who is supposed always to act in the best interest of all its members.

In stage 3, pretrial negotiations may also take place, leading to an amicable settlement of claims rather than their litigation at trial. That is, after that a suit (individual or collective) is brought against the defendant, this one has the opportunity to make a take-it-or-leave-it o¤er to the other party (individual plainti¤ or class action). Thus, either the defendant's o¤er is accepted (by a plainti¤ or the class action), and thus the claim is settled, or it is rejected. In this event, we consider that either the claim goes to trial, or the plainti¤ gives up.

As for the court's behavior, it is assumed that the judge awards a compensatory damage equal to the claim of the defendant in case of an individual suit, while he sets the damage obtained by each member of a class action equal to an index of the aggregate merit of the class, which is de…ned as = i +( 1) j , with 2]0; 1[ being either the proportion of plainti¤s i in the population of …lers, or an parameter of the discretion power of judges. The role of this rule of damage averaging is part of the present paper, and the distinction between those possible explanations will be discussed in the last part of the paper.

The individual outcomes depend on the various litigation expenditures incurred by the plainti¤, since …ling a suit is a costly activity. When …lling an individual suit both plainti¤s bear the same litigation costs, which are of two kinds. The …rst one corresponds to the administrative registration of the claim, C > 0; which is supposed to be a sunk cost: whatever his decision, either he maintains his action until it is settled through a negotiation with the defendant or at trial, or he gives up after registration, the plainti¤ never recovers this expenditure. The second one, C p > 0 , corresponds to litigation costs per se such as attorney fees, auditing or expertise costs and so on, that are borne only when the plainti¤ …les, to produce evidences in order to strengthen the court's beliefs that the defendant is liable. In contrast, joining a class action allows plainti¤s to litigate for smaller individual costs, K p > 0: Moreover, members of the class action incur an additional sunk cost K > 0 (corresponding to registration costs and various administrative costs). We assume that:

Assumption 1: j > i > C p
Assumption 2: 0 < K p < C p ; and 0 < K < K p which means that if a plainti¤ were aware of the defendant's liability, he would be prone to sue individually. Notice that the conditions of assumption 2 put on the various transaction costs simply insures that a class action entails scales economies on the various litigation costs: C + C p > K + K p . Scales economies achieved through the pooling of attorney's services and the decrease in the number of plainti¤'s individual appearances in front of the court, are a classical motive to explain the great appeal of class actions.

The de…nition of the nature of both kinds of costs are introduced for ease of exposition. The clue of the story is coming from the distinction between an entry cost which is paid in order that the plainti¤ have an access to the litigation process, on the one hand, and a cost paid only when the plainti¤ continues his suit until the end at trial, on the second. Notice that a more sensible interpretation would consider that C as K correspond both to administrative costs per se coming from the registration of the claim in from of the court plus the various sunk costs associated to the use of attorney's counsels (…xed costs such as …ling costs, including expertise expenditures) during the pretrial period, whereas C p as K p would include more strictly only the expenditures incurred by the plainti¤ when his case goes to trial, for instance those corresponding to the lawyer fees.

Finally, we assume that the rate of impatience is null for all agents.

The technology of information and beliefs updating rules

In our set up, as the plainti¤s enter sequentially in the litigation process, the timing of information arrival is stylized as follows:

Figure 1 We consider circumstances where all the information which may be obtained (the set of all possible messages) by P j is the same as what is available for the former P i . Thus, everything goes as if the messages successively obtained by the litigants were initially drowned in the same set of messages2 . But, basically, although both plainti¤s have access to the same technology of information, they have not the ability to update their initial beliefs using the same information: plainti¤ P i enters …rst and only observes his own message, while plainti¤ P j observe a combination of two messages, consisting in his own message and plainti¤ P 0 i s personal message.

In order to describe the technology of information, we retain a speci…cation in terms of joint probabilities which may appear as poorly intuitive. Nevertheless, this is the more general and straightforward way, since we are more interested with the bene…ts associated with the process of beliefs updating allowed by this technology, than on the distortions coming from di¤erence between pure individual subjective priors. Anyway, any service of messages reveals the existence of such a joint probability distribution (see [START_REF] Hirschleifer | The analytics of uncertainty and information[END_REF], Laffont (2000) for the basic case of an unidimensional technology of information). Formally, let us denote the set of all available messages providing some piece of evidence with respect to the liability or guiltiness of the defendant. When the P i (respectively P j ) pays the litigation costs, he receives a message ! (respectively ! 0 ) randomly picked in ; which will be used to improve his assessment of the likelihood that the defendant will be found liable/not liable at trial. Since we consider the case of an aggregate technology of information, let us take as a primitive the joint probability distribution P : S ! [0; 1]; where S = fL; N Lg is the set of relevant states of the nature regarding the status of the defendant (Liable, Non liable); p(L; !; ! 0 ) 0 is the likelihood that the defendant is liable and the messages obtained respectively by plainti¤s i and j are (!; ! 0 ); while p(N L; !; ! 0 ) 0 is the likelihood that the defendant is non liable and the messages obtained respectively by P i and P j are (!; ! 0 ).

We have to consider the various probabilities which are relevant in order to describe the informational status of plainti¤s, at each stage of the litigation process. Speci…cally, our general assumption implies that individuals have common priors, but that beliefs updating allows them to have di¤erent posteriors.

First, the primitives are connected to the plainti¤s' common priors on the defendant's liability in a simple way:

p L = X (!;! 0 )2 2 p(L; !; ! 0 ) p N L = X (!;! 0 )2 2 p(N L; !; ! 0 )
Using the available technology of information, the plainti¤s are also allowed to assess their chances to obtain additional information. For example:

p i (!) = X ! 0 2 p(L; !; ! 0 ) + X ! 0 2 p(N L; !; ! 0 )
represents P i 's individual priors to obtain an individual message, when the message obtained by the other plainti¤ is not observable. In our set up, where P j …les after P i , we are interested by the case where P j has the opportunity to observe also the message previously obtained by i; hence, the probability of such an event according to the technology of information at hand is:

p j (!; ! 0 ) = p(L; !; ! 0 ) + p(N L; !; ! 0 )
As a consequence, P j will update his beliefs according to the rule:

(R1) : p j (Lj!; ! 0 ) = p(L; !; ! 0 ) p(L; !; ! 0 ) + p(N L; !; ! 0 )
when he observes both his own message and the message of the other plainti¤, but P i can only condition his revision of beliefs on a unique message according to the rule:

(R2) : p i (Lj!) = P ! 0 2 p(L; !; ! 0 ) P ! 0 2 p(L; !; ! 0 ) + P ! 0 2 p(N L; !; ! 0 ) with: p(L; w) = X ! 0 2 p(L; !; ! 0 )
In this context, the possible evidences that may be gathered during the discovery process does not change after that P i eventually …les and before P j decides to enter. Nevertheless, P j may bene…t of the message obtained by P i (he bene…ts of the e¤orts undertaken by the former in the discovery process). Thus, he may update his likelihood of success according to both messages.3

Institutional framework and equilibrium

We …rst introduce as a benchmark model the case of a system allowing only individual suits: thus two repeated trials occur. Then, we introduce the possibility of a class action, plainti¤ having the opportunity either to sue individually of to register a class action.

Precedents, repeated trials and pure individual suits

When repeated trials occur (P 's case is …rst settled), the last …ler may bene…t of the existence of jurisprudence or precedents as a result of a pure informational e¤ect. We investigate how this involuntary sharing of information between plain-ti¤s a¤ects the individual incentives to …le.

Assume that the class action is not allowed as a litigation option: plainti¤s can …le only an individual suit. Players'moves in stage 3 are the following: for the defendant, make an individual o¤er O i (O j ) for plainti¤ i (respectively j); and each individual plainti¤ may choose between: go to trial T ; exit E; settle S). Let us denote s( i ; !) and s( j ; !; ! 0 ) the settlement o¤er made by the defendant respectively to P i and P j .

When a case is litigated, any information which is revealed is always shared between the plainti¤ and the defendant. In the present set up, the defendant always exercise his rights to the discovery process, since it allows him either to settle for an o¤er lesser than when the plainti¤ is silent, and/or to litigate while saving the trial costs. The following lemma …rst solves for the e¢ cient decision of the defender and the response of the plainti¤s when the last stage of the game is seen as a "one-shot" bargaining process, exhibited in …gure 2:

Figure 2 Lemma 1 Consider plainti¤ s and defendant's moves in stage 3: i) For any message ! 2 , corresponding to the information obtained by P i , the best "one shot" individual o¤ er made by the defendant to plainti¤ P i is: s( i ; !) = max 0; p j (Lj!) i C p . P i accepts this o¤ er.

ii) For any combination of messages (!; ! 0 ) 2 , corresponding to the information obtained by P j , the best "one shot" individual o¤ er made by the defendant to plainti¤ P j is s( j ; !; ! 0 ) = max(0; p j (Lj!; ! 0 ) j C p ). P j accepts this o¤ er.

All proofs of the paper are in the appendix. Note that for concreteness, we adopt in the paper the convention that the indi¤erence between trial and settlement amounts to a strict preference for the settlement (see the discussion in [START_REF] Rasmusen | Games and information[END_REF], [START_REF] Shavell | Sharing information prior to settlement or litigation[END_REF]).

Coming back to stage 2, P j evaluates his own opportunity to …le or not. Let us denote his expected utility level given the various possible messages that he may receive as follows:

Eu j ( j ; p j (Lj:;

:)) = X (!;! 0 )2 2 p j (!; ! 0 ) max 0; p j (Lj!; ! 0 ) j C p C
while, conditional on its priors, his expected utility level is:

Eu j ( j ; p L ) = p L j C p C
The following lemma analyses when plainti¤ P j sues or gives up.

Lemma 2 i) Assume that only "good news" are expected to arrive; then, information is not worth for P j i.e.:

if min p j (Lj!; ! 0 ); for all (!; ! 0 ) 2 C p j , then:

Eu j ( j ; p j (Lj:;

:)) = p L j C p C
ii) Assume that there exists a unique combination of messages (!; !0 ) 2 such that p(L; !; !0 )

Cp j ; then, information is worth for P j , i.e. : Eu j ( j ; p j (Lj:; :)) Eu j ( j ; p L ) 0:

iii) Assume that there exists at least one combination of messages (!; !0 ) 2 such that p(L; !; !0 ) Cp+C j ; then P j always …les individually, i.e. Eu j ( j ; p j (Lj:; :)) 0.

Part i) implies that if priors are "optimistic" for P j , then P j always …les, i.e. p L Cp+C j =) Eu j ( j ; p j (Lj:; :)) 0, but if p L < Cp+C j then the plainti¤ gives up (Eu j ( j ; p j (Lj:; :)) < 0).

Part ii) means that if priors are "pessimistic" for P j , then P j may nevertheless …le, i.e. we may have Eu j ( j ; p j (Lj:; :)) 0 although p L Cp+C j . Part iii) means that once there exists a very good news, the plainti¤ always prefer to …le an individual suit.

The same qualitative results also apply to P i : in stage 1, he evaluates the opportunity to …le or not without the knowledge of the relevant message that will be available in the future, but only knowing the set of possible messages a¤orded by the available technology of information. Let us de…ne by:

Eu i ( i ; p i (Lj:)) = X !2 p i (!) max 0; p i (Lj!) i C p C
his expected utility level associated to the technology of information, and:

Eu i ( i ; p L ) = p L i C p C
his satisfaction level associated to his priors, which are the same as the other plainti¤. Thus, we have: Lemma 3 i) Assume that only "good news" are expected to arrive; then, information is not worth for P i , i.e.: if min p i (Lj!); for all ! 2 C p i , then:

Eu i ( i ; p i (Lj:)) = p L i C p C
ii) Assume that there exists a unique message ! 2 such that p(L; !)

Cp i ; then, information is worth for P i , i.e.: Eu i ( i ; p i (Lj:)) Eu i ( i ; p L ) 0:

iii) Assume that there exists at least one message ! 2 such that p(L; !)

Cp+C i
; then P i always …les individually, i.e. Eu i ( i ; p i (Lj:)) 0.

Considering together lemma 2 and 3, we obtain the conditions under which entering the discovery process is worth to a plainti¤. Information has a positive value in the present context only when litigants know that bad news sometimes may be obtained. With additional information, a plainti¤ updates his priors, and he is allowed to undertake the best possible decision in every circumstances, given that he can exercise an exit option if the information learned appears to be unfavorable for his case.

In this sense, the updating of beliefs may explain that holders of nuisance suits or pessimistic victims (conditionally on their priors: i.e. p L C p C < 0) have an incentive to …le, in the hope to learn good news in the future and pursue until trial their action. In this last case, it depends on stronger conditions on the technology of information. This is highlighted in parts iii) of the lemmas. Each gives a simple su¢ cient condition required whatever the priors (optimistic or pessimistic) in order to induce a plainti¤ to …le an individual lawsuit, saying that the plainti¤ knows that there exists at least a very favorable message entailing a large probability that the defendant will be seen liable by the court. This last result may be understood as follows: it is not worth that a plainti¤ expect to always receive a favorable message in the future; in contrast, in order to induce him to …le a suit, it is su¢ cient that there a single favorable message exists, given that in others circumstances, he will be induced to give up having only paid the administrative sunk costs.

In contrast, part i) of both lemmas shows interestingly enough that when the available (technology of) information does not allow the possibility of bad events or news, such that the plainti¤s expect to obtain a positive payment from the defendant in any future event, then the discovery process provides no additional value in the sense that whether plainti¤s update their priors depending on the new message collected or use their priors, in both cases they undertake the same e¢ cient decision.

Lemmas 1 to 3 lead to the following proposition:

Proposition 4 Assume that there exists at least one combination of messages (!; !0 ) 2 such that p(L; !; !0 )

Cp+C i
; then there exists a Subgame Perfect Equilibrium where i) each plainti¤ …le individually, and ii) both cases are settled.

The requirement that there exists a p(L; !; !0 ) Cp+C i also implies that p(L; !; !0 ) Cp+C j ; meaning that any information delivered by the technology which appears as favorable for P i is also good for P j . As it is easily seen, this is a weak requirement in the sense that it is su¢ cient that plainti¤s are aware of the fact that there is one chance to obtain at least a good information, to induce them to …le a suit. There is no need to be sure that good news always arrive in the future.

The next corollary is also a straightforward consequence of the previous lemmas:

Corollary 5 If information has a positive value, then: i) Any information favorable to the defendant (respectively, to the plainti¤ s) reduces (increases) the settlement o¤ er, as compared to the case where no additional information arrives.

ii) The probability of settlement is smaller than one.

For the sake of proof, consider the …rst plainti¤'s decision -the argument is the same for the second one. An information favorable to the defendant corresponds to a message satisfying: p L > p i (Lj!), which implies p L i C p > p i (Lj!) i C p ; the reverse inequalities apply in case of an information favorable to the plainti¤. Now, in the case where information is worth, there is only a subset i of possible messages for the …rst plainti¤ such that p i (Lj!) i C p > 0, 8! 2 i : then, the probability of settlement corresponds to the cumulative probability that the plainti¤ obtains these favorable messages P !2 i p(!) < 1:

Information sharing in Class Action

We now assume that class actions are available.

To begin with, let us focus more speci…cally on the proper subgame beginning after P j decides to adhere to the class actions. In stage 3, the defender makes an o¤er to the members, such that when the information pooled by the members of the class action corresponds to the messages (!; ! 0 ), the settlement bene…t of each member is s( ; !; ! 0 ). This implies that the defendant makes a positive o¤er to the Class Action soon as p j (Lj!; ! 0 ) > Kp : On the other hand, in any proper subgame in stage 3 beginning after that P i gives up to initiate a class action, or after that P i gives up to join it, the best individual o¤ers of the defendant are those of lemma 1 (see also …gure 3 where these subgames have been replaced by the defendant's best o¤er).

We can now analyze the e¢ cient decisions of P j , considering separately the decision to join or not the class action (decision node following the entry of P j ), and …nally the decision to …le or not (decision node initiating the subgame of …gure 3). P j 's e¢ cient decisions in stage 2 may be as follows:

Lemma 7 Assume that there exists a subset of combinations of messages j 2 such that for any (!; ! 0 ) 2 j : p(L; !; ! 0 ) Cp+C j ; and assume that Cp Kp ( j i) where = max p j (Lj!; ! 0 ); for all (!; ! 0 ) 2 j . Then, i) P j always …les in the second stage, and ii) he prefers to join the class action when it has been initiated by P i rather than to sue individually.

The following lemma focuses on the decision of the …rst plainti¤.

Lemma 8 Assume that there exists a subset of messages i , such that for any ! 2 i : p i (L; !) Cp+C i . Then, P i always …les in the …rst stage, and he prefers to initiate the class action rather than to sue individually.

Using the results of lemmas 6 to 8, we have: Proposition 9 Assume that: (C1) there exists a unique combination of messages (!; ! 0 ) 2 2 such that p(L; !; !0 ) Cp+C i , and (C2):

^ Cp Kp p j (Lj!;! 0 )( j i) :
Then, there exists a SPE where i) the class action is formed, and ii) the aggregate case is settled.

Proposition 9 displays a set of su¢ cient conditions in order that the class action comprising both types of individuals exists in equilibrium.

The result of proposition 9 is a direct consequence of our technology of information, and of our assumption that the discovery process is perfect allowing a perfect mutualization of information between plainti¤s and the defendant. In such a case, the two important issues are 1/ whether the …rst plainti¤ prefers the structure of information de…ned by the set of his own personal messages, or the structure associated to the combination of two messages, his personal one and the information of the other plainti¤; 2/ whether the second one obtains a higher payments when he becomes a member of the class action or not.

In our set up, P j observes his own message and the …rst plainti¤'s one whether or not he joins the class action; thus, he prefers to join the class action as long as the decrease in the litigation costs associated to the collective action (K p < C p ) is not fully compensated by the decrease in the expected payment awarded at trial given that the court uses an index of the aggregate claim in case of a class action ( < j ): (C2) corresponds to the requirement needed to insure the participation of P j : it must be that the proportion of large stakes in population of plainti¤ is high enough.

On the other hand, the basic reason explaining why the …rst plainti¤ initiates the class action, is that when the discovery process is perfect, the posteriors distribution p j (Lj:; :) is more informative in the sense of [START_REF] Blackwell | Equivalent comparison of experiments[END_REF] than the posteriors distribution p i (Lj:): for any message ! 2 ; there always exists at least one message ! 0 2 such that: p j (Lj!; ! 0 ) > p i (Lj!) and one message ! 00 2 such that: p j (Lj!; ! 00 ) < p i (Lj!). Thus, the posterior beliefs p i (Lj:) provides the plainti¤ with some information which has been "garbled" in the transmission as compared to the priors p j (Lj:; :). Anything goes as if the information associated to p j (Lj:; :) were sent, but it has been received by P i with some additional noise, such that …nally P i recognized only the information attached to p i (Lj:):

It is straightforward to verify that when plainti¤s having large stake become the …rst …lers, nothing more is added to the results, since the class action is formed under the same conditions as those in proposition 9. Thus, the order of plainti¤s' entry entails here no strategic aspect in contrast to what occurs in [START_REF] Daughety | A Dynamic Model of Lawsuit Joinder and Settlement[END_REF], [START_REF] Marceau | Damage averaging and the formation of Class Action suits[END_REF], [START_REF] Saraceno | Group Litigation, Access to Justice and Deterrence[END_REF].

The case with conditional fees

One way to understand the results of the previous section is the following: for plainti¤s, the opportunity to obtain additional information may work as a credible threat in order to obtain recovery from the defendant, although they have pessimistic beliefs before trial. In this section, we introduce contingent fees as an alternative for attorney'earnings. An argument in favor of contingent or conditional fees is that they induce the absence of risk of …lling a lawsuit for plainti¤s, since the risk is borne by the attorney: plainti¤s owe their attorney a fee only when there is recovery, i.e. when they win at trial. 4 In the present set up, the rational for conditional fees is assessed in terms of information acquisition.

When conditional fees are introduced, a plainti¤ pays the amount corresponding to his attorney's services only in the case where he wins at trial. Hence, the expected payment at trial is equal to the probability to win (given the relevant information.) times his damage award minus attorney's fees:

p i (Lj!)( i C p ) : for P i p j (Lj!; ! 0 )( j C p ) : for P j p j (Lj!; ! 0 ) ( K p ) : for a Class Action
The following proposition shows that as compared to the decisions based on that, whatever the available information, plainti¤s are not con…dent with respect to their chances of success at trial, i.e. they can not know whether the judge will be favorable to their case; on the one and, it is relatively easy to assess the value of individual damages (which may be considered as a public information), but on the second, the cause of the victims'injury may be quite di¢ cult or costly to establish; thus, the plainti¤s'individual assessment of the likelihood to win at trial are always smaller than unity. Each plainti¤ evaluates ex-ante the opportunity to …le a suit or to give up, knowing that he will bene…t of a new information later on and that the additional informations will generate a new assessment of his chances at trial, such that he will undertake ex-post the best decision conditionally on his information. In this way, we capture two salient points of the litigation process: i) a main relevant source of uncertainty for parties is created by the behavior of the court that is unknown ex-ante. ii) Scienti…c evidences are imperfect, some of them may be strongly controversial, there may exist a large disagreement between experts'opinions, judges may have bias of judgment, mistaken beliefs, and/or unfortunately reject some pieces of evidences. Our main result is that the opportunity to constitute a class action is not always exploited since, apart of scales economies, it depends on whether the discovery process provides good news as well as bad news. Finally, we …nd that the contingent fees system reduces the incentives to organize class actions on an information sharing basis, in the sense that it renders plainti¤s neutral to the arrival of news.

Hence Eu j ( j ; p j (Lj:; :)) Eu j ( j ; p L ), which is by de…nition the value of the information a¤orded by the available technology of messages. Thus, assuming a unique combination (!; ! 0 ) 2 : such that max 0; p j (Lj!; ! 0 ) j C p = p j (Lj!; ! 0 ) j C p , the result is direct.

iii) Let us assume that there exists at least one combination of messages (!; !0 ) 2 such that p(L; !; !0 ) Cp+C j ; remark that this implies:

p j (Lj!; !0 ) = p(L; !; !0 ) p j (!; !0 ) C p p j (!; !0 ) j C p j
As a result, it comes that: Eu j ( j ; p j (Lj:;

:)) = p j (!; !0 ) p j (Lj!; !0 ) j C p + X (!;! 0 )6 =(!;! 0 ) p j (!; ! 0 ) max 0; p j (Lj!; ! 0 ) j C p C p(L; !; !0 ) j p j (!; !0 )C p C p(L; !; !0 ) j C p C
since by construction P (!;! 0 )6 =(!;! 0 ) p j (!; ! 0 ) max 0; p j (Lj!; ! 0 ) j C p 0: Now, given that p(L; !; !0 ) j C p C 0 by assumption, we obtain Eu j ( j ; p j (Lj:; :)) 0. Hence the result.

Proof of lemma 3: omitted (qualitatively the same as in lemma 2).

Proof of proposition 4:

More speci…cally, we prove the following results:

Claim 11 Assume that there exists at least one combination of messages (!; !0 ) 2 such that p(L; !; !0 ) Cp+C i ; then there is a Subgame Perfect Equilibrium which corresponds to the following set of actions:

1/ Each plainti¤ …les individually. 2/ The defendant makes two individual o¤ ers: s( i ; !) = max 0; p i (Lj!) i C p ; 8! 2 for P i , and s( j ; !; ! 0 ) = max 0; p j (Lj!; ! 0 ) j C p ; 8(!; ! 0 ) 2 for P j 3/ Each plainti¤ accepts (at each decision node where he has to play) his speci…c individual o¤ er proposed by the defendant, for every possible information he may receive.

Proof of claim 13. To prove 1/ it is su¢ cient to remark that if there exists at least one combination of messages (!; !0 ) 2 such that p(L; !; !0 ) Cp+C i , then we also have:

p i (Lj!) = X ! 0 2 p(L; !; ! 0 ) P ! 0 2 p(L; !; ! 0 ) + P ! 0 2 p(N L; !; ! 0 ) = X ! 0 2 p(L; !; ! 0 ) + p(N L; !; ! 0 ) P ! 0 2 p(L; !; ! 0 ) + P ! 0 2 p(N L; !; ! 0 ) p(L; !; ! 0 ) p(L; !; ! 0 ) + p(N L; !; ! 0 )
which means that the following relationship linking P 0 i s the two types of posterior beliefs p i (Lj:) and p j (Lj:; :) always applies:

8! 2 : p i (Lj!) = X ! 0 2 (!; ! 0 )p j (Lj!; ! 0 ) (1)
with (!; ! 0 ) = p i (!;! 0 ) p i (!) < 1 and

P ! 0 2
(!; ! 0 ) = 1; meaning that the posteriors p j (Lj:; :) are more spread than the posteriors p j (Lj:); i.e. for any message ! 2 ; there always exists at least one message ! 0 2 such that: p j (Lj!; ! 0 ) > p i (Lj!); and there always exists at least one message ! 00 2 such that: p j (Lj!; ! 00 ) < p i (Lj!): By de…nition, this amounts to say that the posteriors p j (Lj:; :) are more informative than the posteriors p j (Lj:). This is useful in the rest of the proof.

When P i initiates a CA, and when P j joins it, information sharing between plainti¤s leads to an expected utility level for the former which is by de…nition: Eu i ( ; p j (Lj:; :)) = X (!;! 0 )2 2 p i (!; ! 0 ) max 0; p j (Lj!; ! 0 ) K p K with p i (Lj!; ! 0 ) = p j (Lj!; ! 0 ); 8(!; ! 0 ) 2 2 , whereas if P i …les an individual suit, he obtains:

Eu i ( i ; p i (Lj:)) = X !2 p i (!) max 0; p i (Lj!) i C p C
Hence, P i initiates the CA more particularly soon as:

Eu i ( ; p j (Lj:; :)) Eu i ( i ; p i (Lj:)) 0

Let us exhibit simple conditions under which the RHS inequality in (2) is true. For that, assume that there exists a subset of message i such that any ! 2 i satis…es: p i (L; !) Cp+C i ; which implies that p i (Lj!) Cp i ; as a consequence, it is easy to see that:

Eu i ( i ; p i (Lj:)) = X !2 i p i (!) p i (Lj!) i C p C X !2 i p i (L; !) i C p C 0
(!; ! 0 )p j (Lj!; ! 0 ) i C p , for any any ! 2 i ; implying thus:

X ! 0 2 (!; ! 0 )p j (Lj!; ! 0 ) i C p X ! 0 2 (!; ! 0 ) p j (Lj!; ! 0 ) i C p X ! 0 2
(!; ! 0 ) max 0; p j (Lj!; ! 0 ) i C p Pre-multiplying by p i (!); summing over all ! 2 i , and …nally rearranging, we obtain:

X !2 i p i (!) p i (Lj!) i C p X !2 i X ! 0 2 p i (!) (!; ! 0 ) max 0; p j (Lj!; ! 0 ) i C p = X !2 i X ! 0 2
p i (!; ! 0 ) max 0; p j (Lj!; ! 0 ) i C p X (!;! 0 )2 2 p i (!; ! 0 ) max 0; p j (Lj!; ! 0 ) i C p = Eu i ( i ; p j (Lj:; :)) Now, given that > i and using assumption 2, it comes that: Eu i ( ; p j (Lj:; :)) Eu i ( i ; p j (Lj:; :)): Hence (2) holds, and the lemma 8 is proven:

Proof of proposition 9: Once more, we prove the following claim:

Claim 12 Assume that: (C1) there exists a unique combination of messages (!; ! 0 ) 2 2 such that p(L; !; !0 ) Cp+C i , and (C2): ^ Cp Kp p j (Lj!;! 0 )( j i) : Then, there is a SPE associated to the following set of actions:

1/ Each plainti¤ …les. 2/ P i initiates the CA, and P j joins it. 3/ The defendant makes three o¤ ers: s( i ; !) = max 0; p i (Lj!) i C p ; 8! 2 for P i s( j ; !; ! 0 ) = max 0; p j (Lj!; ! 0 ) j C p ; 8(!; ! 0 ) 2 for P j s( ; !; ! 0 ) = max 0; p j (Lj!; ! 0 ) K p ; 8(!; ! 0 ) 2 for a Class Action 4/ At each decision node in stage 3 where he has to choose an action, each plainti¤ accepts the o¤ er (either individually or as a member of the CA) proposed by the defendant, for every possible information they may receive.

Once more, we do not tackle with the problem of multiplicity of equilibria, only focusing on the equilibrium path where the class action is formed.

Proof of claim 14. To prove 1/ and 2/ it is su¢ cient to remark that if there exists a unique combination of messages (!; !0 ) 2 such that p(L; !; !0 ) Proof of proposition 10: Consider the case of the …rst type of plainti¤s. Equivalent arguments may be obtained in the case of the second plainti¤ and in the case of a CA.

When conditional or contingent fees are introduced, the defendant's best o¤ers to plainti¤ i in stage 3 are the following, under assumption 2: s( i ; !) = max 0; p i (Lj!)( i C p ) = p i (Lj!)( i C p ) : under conditional fees s( i ; !) = max 0; p i (Lj!)(1 t) i = p i (Lj!)(1 t) i : under contingent fees i) Thus, whatever the message, the plainti¤ always obtains a positive payment -thus, he always accepts the defendant's o¤er.

ii) As a result, the plainti¤'individual expected utility level in case of individual suits is equal to:

Eu i ( i ; p i (Lj:)) = p L ( i C p ) C = Eu i ( i ; p L ) (3)
Notice that by assumption 1: Eu j ( j ; p L ) > Eu i ( i ; p L ): It is straightforward to see that individual suits are both bene…cial for the plainti¤s soon as Eu i ( i ; p L ) 0; meaning that their common priors must satisfy: p L C i Cp . iii) Finally, both contingent and conditional fees (for a normalized cost : t i = C p ) allows for higher settlement o¤ers, given that they induce a decrease in the expected payments from plainti¤s to their attorney: p i (Lj!) i C p > p i (Lj!)( i C p ) : under conditional fees p i (Lj!) i C p > p i (Lj!)(1 t) i : under contingent fees as compared to the …xed costs system of the previous section.

Figure 3 Lemma 6

 36 Figure 3

  j always …les and joins the CA initiated by the other plainti¤; -p i (Lj!) p i (L; !) p(L; !; !0 )+ P ! 0 6 =! 0 p(L; !; ! 0 ) > p(L; !; !0 ) Cp+C i; thus, by lemma 8, P i always …les and initiated the CA, Finally, 3/ and 4/ are direct from lemma 5.

We were not aware of the existence of a recent contribution related to ours, i.e.[START_REF] Daughety | A Dynamic Model of Lawsuit Joinder and Settlement[END_REF], until we prepared the …nal draft of the present paper. Two noticeable di¤erences in assumptions exist: in Daughety and Reinganum's paper, each plainti¤ has private information about damages, and the timing of plainti¤s moves is endogenous. Finally, Daughety and Reinganum give a more comprehensive analysis of the possible equilibria, including defendants'use of preemptive settlement strategies.

Thus, under some circumstances, plainti¤ j may receive exactly the same message as plainti¤ i: the weight of evidence or the signi…cance of the message is increased in such a case.

In some circumstances however, P j may gather an additional information, which is whether the evidence that should have been by the previous plainti¤ (even when he only obtained partial information) is or not always available or true. In words, some events previously unbelievable are now available as pieces of evidence, and more speci…cally are seen as acceptable by Courts (unforseen contingencies).

The other advantage is that they enable plainti¤s to monitor the e¤ort undertaken by attorney for the time they spend to their clients' case, and give them e¢ cient incentives to maximize their client's recovery (for references, see the introduction of the paper).

the priors, the arrival of new information during the litigation process does not change plainti¤'s decision .

Proposition 10 Under conditional fees: i) Parties always settle.

ii) The value of information is null for both plainti¤ s.

iii) the settlement o¤ ers are larger than under the …xed costs rule.

Proposition 10 shows that plainti¤s become neutral to the arrival of news when contingent fees are used, such that the decision to …le depends only on their initial belief of the outcome at trial. This suggests that if contingent fees may solve agency problems between plainti¤s and their counsel, on the other hand they may entail pervasive e¤ects such as making victims not enough careful with the arrival of new information.

The intuition is the following. Consider a plainti¤ with an initial belief on his case, who wants to verify the quality of his claim at trial: he may use a simple "test"corresponding to buying the services of a lawyer; this last one will inform the plainti¤ whether he has a high probability to win at trial or a law one, and when alternative litigation strategies may be used at trial, contingent fees monitors attorney's e¤orts to choose the strategy leading to maximal recovery for plainti¤. Proposition 10 tells us that this test is of no value for the plainti¤: his initial decision to enter or not depends only on his prior beliefs on his case, when contingent fees are used, since in case of an individual suit for example we have: Eu i ( i ; p i (Lj:)) = Eu i ( i ; p L ) and Eu j ( j ; p j (Lj:; :)) = Eu j ( j ; p L ).

When contingent fees are used, a plainti¤ pays an amount corresponding to a …xed percentage of the value of the claim only in case of recovery, i.e. the costs corresponding to the payment of attorneys'services is proportional to the expected value of the claim; in such a case, the value of the expected outcome at trial is a given percentage of the claim:.

: for a CA with t (respectively ) 2]0; 1[ being the percentage of the value of the claim in case of an individual action (collective action) charged by the attorney, and t > : It is straightforward to verify that a similar result applies.

Conclusion

The present paper illustrates that the existence of positive informational externalities and the opportunity of information sharing could be a strong motive for the formation of a class action. In our set up, the discovery process is such APPENDIX Proof of lemma 1: Given that the administrative cost C is sunk, it is easy to see that when P j obtains the message ! 0 after that P i has received message !, the defendant chooses a "take-it-or-leave-it"o¤er in order to render the plainti¤ indi¤erent between going to trial (suing) or accepting the o¤er: hence s( j ; !; ! 0 ) = max 0; p j (Lj!; ! 0 ) j C p , where p j (Lj!; ! 0 ) follows R1. Symmetrically, when he faces the message ! with P i , the defendant makes a "take-it-ot-leave-it" o¤er in order to render the plainti¤ indi¤erent between going to trial (suing) or accepting the o¤er: hence s( i ; !) = max 0; p i (Lj!) i C p , where p i (Lj!) follows R2. Hence the result.

Proof of lemma 2:

i) Consider that min p j (Lj!; ! 0 ); 8(!; ! 0 ) 2 Cp j ; thus, 8(!; ! 0 ) 2 , it comes that max 0; p j (Lj!; ! 0 ) j C p = p j (Lj!; ! 0 ) j C p , such that:

given that, by construction of the technology of information, we have both:

Hence the result. ii) More generally, given that 8(!; ! 0 ) 2 : max 0; p j (Lj!; ! 0 ) j C p p j (Lj!; ! 0 ) j C p , we have after multiplying both terms of this inequality by p j (!; ! 0 ) and then summing over all the possible messages:

; thus, by part v) of lemma 2, P j always …les, given that he accepts any o¤er s( j ; !; ! 0 ) = max 0; p j (Lj!; !0 ) j C p ;

-p i (L; !)

; thus, by part v) of lemma 3, P i accepts the o¤er s( i ; !) = max 0; p i (Lj!) i C p ; and he always …les. 2/ and 3/ are direct from lemma 1.

Proof of lemma 6: as lemma 1, it is straightforward since K is sunk.

Proof of lemma 7:

Consider the subgame where the defendant o¤ers s( j ; !; ! 0 ) to P j , which is accepted. Remark …rst that if the subset j 2 exists, for any (!; ! 0 ) 2 j ; P j may obtain a positive payment equal to max 0; p j (Lj!; ! 0 ) j C p = p j (Lj!; ! 0 ) j C p 0. Thus, following the proof of part v) in lemma 2, had he decided to sue individually, P 0 j s expected utility level would be positive since:

Eu j ( j ; p j (Lj:; :))

given that by construction for any (!; ! 0 ) 2 j : p(L; !; ! 0 ) j C p + C: Now for any message (!; ! 0 ) 2 , in order that P j be better o¤ when he joins the CA rather than to have sued individually, it must be that:

which is true as far as

Cp Kp p j (Lj!;! 0 )( j i) . Hence assume that Cp Kp ( j i) where = max p j (Lj!; ! 0 ); for all (!; ! 0 ) 2 j ; then for any (!; ! 0 ) 2 j :

Finally, after multiplying both the LHS and the RHS terms of this inequality by p j (!; ! 0 ) and then summing over all the possible messages, we obtain: Eu j ( ; p j (Lj:; :)) Eu j ( j ; p j (Lj:; :)) 0 Hence the result.

Proof of lemma 8:

The crucial issue is whether the …rst plainti¤ prefers the structure of information de…ned only by the set of his own personal messages, or the structure of information associated to the set of combinations of two messages, his personal ones and the messages of the other plainti¤. We shall show that the second one is more informative in the sense of [START_REF] Blackwell | Equivalent comparison of experiments[END_REF] than the …rst one; as a result, P i obtains a higher expected utility with the second one.

To understand this, remark that by (R2) for any message ! 2 we have: