COMARATIVE VERSUS CONTRIBUTOR NEGLIGENCE: A COMARISON O THE LITIGATION EENDITURES Jef De Mot ost-octoral Researcher WO University of Ghent Center for Avance Stuies in Law an Economics Visiting scholar at the Erasmus University Rotteram Abstract The revious literature on comarative an contributory negligence oints out that aministrative costs are higher uner comarative negligence because the courts must ecie on the egree of negligence by both arties an not just whether the arties were negligent. In this article, I show that this fining is not necessarily correct. I use a rent seeking moel to show that the litigation exenitures may be smaller uner comarative negligence. The revious literature has focuse on only one effect, while there may be three effects at lay. JEL coes: K, K E-mail: Jef.DeMotθUgent.be. I woul like to thank Gerrit De Geest, Ben Deoorter, Michael aure, Steven Shavell an two anonymous referees for helful comments an suggestions. Of course, all remaining errors are my own.
. Introuction In the Unite States as well as in Euroe, comarative negligence rather than contributory negligence is the general rule in tort law see Artigot i Golobares an Gomez omar, 009. Comarative negligence ivies the cost of harm between the arties in roortion to the contribution of their negligence to the accient. Uner a rule of negligence with a efense of contributory negligence, the negligent injurer can escae liability by roving that the victim s recaution fell short of the legal stanar of care see Cooter an Ulen 00. Although these negligence rules have been examine quite extensively in the law an economics literature, it is still ebate whether comarative negligence creates better incentives for arties to aot efficient care than contributory negligence see e.g. Artigot i Golobares an Gómez omar 009; Bar-Gill an Ben-Shahar 00. The early literature conclue that contributory negligence is more efficient e.g. Brown 97; Diamon 97; osner 977. Later it was shown that both rules are equivalent from an efficiency ersective when information is erfect an ecision-makers are error-free e.g. Haock an Curran 985; Shavell 987, but that the equivalence oes not hol when these assumtions are relaxe e.g. Haock an Curran 985; Cooter an Ulen 986. At first, relaxing the assumtions seeme to favor comarative negligence, but more recent literature is rather scetical concerning any general sueriority of one of these liability regimes e.g. Bar-Gill an Ben- Shahar 00. 5 6 In the US, negligence with contributory negligence was the ominant tort-liability rule in common law countries for most of the last 00 years. This change however within the last 0 years. The revailing liability stanar in all but a few of US states is one of comarative negligence. Most civil law jurisictions in Euroe aote the rincile of comarative negligence long before the US mae this change. or examle, Brown 97 states that with comarative negligence, the costs of accients are share between injurer an victim, so neither of them bears the full costs of failing to take otimal care. Consequently, both arties may be inuce to take less care than is otimal. The reason is that uner both rules, if arties of one tye take ue care, then arties of the other tye will reason that they alone will be foun negligent if they o not take ue care see Shavell 00. Note that it is assume that ue care is set at the otimal level. Cooter an Ulen 986 show that uner conitions of evientiary uncertainty, comarative negligence gives moerate incentives to eviate from the stanar of care to both arties. Contributory negligence gives the strongest incentives to one arty an the weakest incentives to the other. Comarative negligence is then the most efficient rule because it minimizes the total amount of eviation from ue care when arties are symmetrically situate. 5 Note that some articles show that comarative negligence rovies better incentives to take efficient care levels than negligence or contributory negligence when injurers as well as victims are heterogeneous see Emons an Sobel 99 an eess an Hege 998 or when arties make recaution ecisions sequentially see Rea 987 an Gray 990. 6 Bar-Gill an Ben-Shahar 00 challenge the assumtion that arties are symmetrically situate: one arty coul be better situate to take care. Also, they show that small intermeiate eviations are not necessarily referre to large eviations which may result from other liability rules they use comuter simulations to show this. Note that some emirical stuies oint out that comarative negligence weaken incentives to take
This ongoing ebate stans in contrast to the lack of conflicting oinions with resect to the relative size of the aministrative costs uner both negligence rules. Comarative negligence is generally consiere to generate higher costs er case. Lanes an osner 987 observe that comarative negligence costs more to aminister than contributory negligence. Shavell 987 states that the efense of contributory negligence may lea to less comlicate roceeings comare to comarative negligence. White 989 argues that comarative negligence seems to generate higher litigation an aministrative costs than the traitional negligence rules because the courts must ecie on the egree of negligence by both arties an not just whether the arties were negligent. Bar-Gill an Ben-Shahar 00 state that contributory negligence might be cheaer to aminister than comarative negligence. 7 The oint of view that comarative negligence entails higher costs er case is obviously true in a setting with exogenous litigation costs. The aitional element of weighing the arties egree of negligence inee generates extra costs. However, the revious literature has overlooke the fact that ifferent effects more recisely, three are at lay in a more realistic setting in which litigation costs are enogenous. 8 We show that in such a setting, comarative negligence can be less costly than contributory negligence. The kernel of the argument can be exlaine with a simle numerical examle. Suose for simlicity that the efenant s negligence is certain an that the arties share the loss J equally when also the laintiff is hel liable. The laintiff can make an aitional investment 9 to increase his chances of not being hel liable from 0% to 50%. 0 Uner a rule of contributory negligence, the marginal benefit from this extra investment equals 0.5.J 0..J = 0..J. Uner a rule of comarative negligence, the marginal benefit of the extra investment is smaller: 0.5.J + 0.5.J/ 0..J + recaution see White 989, is associate with higher automobile liability insurance remiums see lanigan, Johnson, Winkler an erguson 989, an increases binge rinking see Sloan, Reilly an Schenzler 995. Accoring to Dari-Mattiacci an De Geest 005, the current emirical literature oes not allow us to make any statements on whether comarative negligence worsens the arties incentives. Although there can be more accients uner comarative negligence, injurers who exercise care have, on average, lower care costs. In other wors, uner comarative negligence, there are more accients, an less is sent on recaution, but what is sent on recaution is relatively well sent. Some of the emirical stuies nee to be interrete with care for other reasons as well. or examle, lanigan et al. 989 fin that comarative negligence is associate with higher automobile liability insurance remiums, but they i not investigate whether this increase was ue to more accients or to more claims towar injurers. 7 Note further that the allege risk-sreaing virtue of comarative negligence is questionable. Given the availability of thir-arty insurance, there are better alternatives available to srea the risk of acciental harm see White 989. 8 Many relatively recent accounts of litigation stress the imortance of treating litigation exenitures as enogenously etermine. See for examle Sanchirico 006. 9 This is an investment in more or better lawyering services once a trial is imminent or has begun. 0 These numbers are merely illustrative.
0.8.J/ = 0.5.J. Clearly, the benefit is smaller uner a rule of comarative negligence. Intuitively, the stakes are higher uner contributory negligence: if the laintiff is hel liable, he ays everything. Uner comarative negligence, he only bears half of the harm. While the exenitures of the arties concerning the liability of the laintiff are larger uner contributory negligence, we can easily show that the exenitures concerning the liability of the efenant are larger uner comarative negligence. Another numerical examle can easily emonstrate this. Suose that this time the laintiff s negligence is certain an that once again the arties share the loss equally when also the efenant is hel liable. The laintiff can make an extra investment to increase the robability that the efenant will be hel liable from 0 % to 50%. Uner a rule of contributory negligence, the marginal benefit from this extra investment equals 0 since the laintiff will bear the full loss, no matter whether the efenant is foun negligent or not. Uner a rule of comarative negligence, the marginal benefit of the extra investment is larger: 0..J/. Intuitively, when it comes to the negligence of the efenant, the stakes are higher uner comarative negligence. Note that things are more comlex than this. Uner comarative negligence the exenitures may also influence the court s ercetion of the egree of negligence an this may etermine the ivision of the loss uner this negligence rule. We incororate this in the general moel. We fin a relatively simle conition for the case in which the total exenitures are smaller uner comarative negligence than uner contributory negligence. We will see that esecially for high-quality claims, comarative negligence may lea to lower litigation costs than contributory negligence. I stress that this article eals with one articular asect of the relative efficiency of contributory an comarative negligence, namely their relative costs at trial. It oes not aress the overall efficiency of the two negligence stanars. We will rocee as follows. The following section rovies a general moel which incororates contributory negligence an comarative negligence. Section comares the litigation exenitures for contributory an comarative negligence. Section conclues. By this we mean that the inherent egree of fault of the efenant is large an the inherent egree of fault of the laintiff is low. The moel oes not irectly suggest how otential injurers an victims might react in their recautionary ecisions. Note that we will focus on the ure comarative negligence rule, an not on moifie forms e.g. the 50 ercent rule. A moifie rule bars a negligent laintiff s recovery when the laintiff s fault excees a certain level in comarison to the efenant s fault. Otherwise the rule allocates amages base on the relative negligence exhibite by each like ure comarative negligence.
. Moel As mentione in the introuction, comarative negligence ivies the cost of harm between the arties in roortion to the contribution of their negligence to the accient. Uner a rule of contributory negligence, the negligent injurer can escae liability by roving that the victim s recaution fell short of the legal stanar of care. More formally, we can escribe the jugment uner comarative negligence as follows: Lx,y = 0 if x x if x<x an y y σ if x<x an y<y with 0< σ < with x the level of care of the efenant, x the otimal level of care of the efenant, y the level of care of the laintiff, y the otimal level of care of the laintiff an σ the laintiff s share if both arties are consiere liable. By assumtion, the laintiff has suffere harm of. Likewise, we can escribe contributory negligence formally as follows: Lx,y = 0 if x x 0 if x<x an y<y otherwise At trial, both arties choose their level of sening on legal assistance. 5 There are two choice variables on each sie: the litigation effort regaring the negligence of the efenant an the litigation effort regaring the negligence of the laintiff. Both arties are assume to be riskneutral. Each contener aims to maximize his execte income. Each arty is assume resonsible for her own legal costs regarless of the outcome the American rule thus alies. The Litigation Success unctions 6 incororate the insight that in lawsuits, relative Note that for examle x<x nees to be rea as: the court consiers the efenant s amount of care to be lower than the otimal amount of care. In the moel of this aer, the execte awar oes not only een on the levels of care of the arties which lay their role in the moel through, the inherent merit of the case, see further, but also on the exenitures of the arties. 5 or the sake of comleteness, the aenix rovies the articiation constraints of the arties. As we focus in this article on the exeniures once a trial has begun, we o not elaborate on these constraints. 6 One for the efenant s negligence an one for the laintiff s negligence see further. 5
success eens on the true egree of fault or the exogenous merits an on the efforts investe on each sie. If the efenant took an amount of care that is much smaller than the level of ue care, the true egree of fault of the efenant will be high. 7 The true egree of fault is assume to be a value between 0 an. Regaring the efenant s negligence, a true egree of fault of 0 means that the efenant will never lose that issue, no matter how much the other sie sens. A true egree of fault of means that the laintiff will always win the issue, no matter how much the efenant sens. or any other true egree of fault, either arty always has a ositive robability of winning the issue. Regaring the laintiff s negligence, a true egree of fault of 0 means that the laintiff will always win that issue, no matter how much the other sie sens. A true egree of fault of means that the efenant will never lose that issue. The true egree of fault of each issue the efenant s an laintiff s negligence is known by both litigants but is not known by the court. The laintiff an the efenant choose their strategies simultaneously an we look for the Nash equilibrium of this game. The arties have equal stakes an have common knowlege of all the unerlying functions an arameters the actual level of fault, the amount at stake etc.. or the sake of simlicity, the amount at stake is set equal to. Using a stanar contest function 8, the robability that the efenant will be hel negligent by the court equals: where equals the exenitures of the laintiff for the liability of the efenant, equals the exenitures of the efenant for the liability of the efenant an is the true egree of fault of the efenant 0. 9 7 Or hrase alternatively, the exogenous merits of the laintiff s claim regaring the efenant s negligence will be high. 8 Ientical or similar functions are use by Katz 988; armer an ecorino 999 an Hirshleifer an Osborne 00. Konra 009 iscusses this tye of contest function the Tullock contest function in etail. The author thoroughly exlains why this function has been use in so many ifferent areas of alie theory. The function can be erive from axiomatic reasoning an has micro-economic unerinnings as well. 9 Note that 0; 0; 0; 0. 6
As mentione before, the Litigation Success unction incororates the insight that the outcome of a lawsuit eens on the true egree of fault an on the efforts of the arties. An examle may illustrate this. Suose the efenant took an amount of care that is substantially lower than the ue level of care. Then his true egree of fault will be high e.g. =0.8. However, this oes not automatically imly that the robability that he will be hel negligent is high. If the efenant sens much more than the laintiff >> ; e.g. the efenant invests heavily in looking for legal arguments why he shouln t take ue care; or he invests in misreresenting facts so that it looks like he may have taken ue care etc., then the ultimate robability of victory for the laintiff may be relatively low. Similarly, the robability that the laintiff will be hel negligent by the court equals: where equals the exenitures of the laintiff for the liability of the laintiff, equals the exenitures of the efenant for the liability of the laintiff an is the true egree of fault of the laintiff 0. 0 Note that both an can take on any value between 0 an. I stress that both arties have the same estimate of an the same estimate of there are no ivergent exectations; more l ef l formally: = an = ef. Note also that there s no systematic relationshi between an e.g. their sum is not equal to one. The reason is that an are ifferently efine as is tyical in the economic analysis of civil roceure. In the moel of this article, an concern the estimates of two ifferent issues the robability that resectively the laintiff an the efenant will be hel negligent, not the overall estimates that the laintiff will win at trial. Uner contributory negligence, the laintiff s execte value equals: 0 Note that 0; 0; 0; 0. Traitionally, an reresent the subjective robabilities of the laintiff an the efenant that the laintiff will win at trial. In our moel, reresents the estimate of both arties that the laintiff will be hel negligent, an reresents the estimate of both arties that the efenant will be hel negligent. 7
EV l = The first term,, reresents the situation in which the efenant is hel negligent robability but the laintiff is not robability -. Inee, uner contributory negligence, the laintiff will only be aware the amount at stake uner these circumstances. The latter terms reresent the laintiff s exenitures regaring resectively the efenant s an the laintiff s negligence. Similarly, the efenant s execte loss uner contributory negligence equals: EL ef = + + Uner comarative negligence, the execte value of the laintiff s claim equals: EV l = + σ The first term,, reresents the situation in which the efenant is hel negligent an the laintiff is not. In that case, the laintiff is aware the amount at stake. The secon term, σ, reresents the situation in which both arties are hel negligent. In that case, the laintiff only receives artial comensation 0 < σ <. The last two terms reresent the exenitures of the laintiff regaring the efenant s negligence an the laintiff s negligence. Obviously, the laintiff s share σ in case both arties are hel negligent will een on the true egrees of fault an on the exenitures of the arties. or examle, even though the true egree of fault of the efenant may be large is large an the true egree of fault of the laintiff may be small is small, the laintiff s share in case both arties are hel negligent may still be relatively small if the efenant sens a lot on convincing the court that his egree of fault was not so high, an/or that the egree of the laintiff s fault was relatively or the sake of simlicity, we assume the amount at stake to be fixe. The exenitures only influence the robability of winning, not the amount at stake. 8
high. We will assume that the anticiate ivision of the loss among the arties is a function of the relative robabilities of victory which themselves een on the exogenous merits an the exenitures of the arties: σ = The intuition behin this is as follows. The robabilities of victory incororate information about the arties estimates of the court s ultimate view on the laintiff s an the efenant s egree of fault. or examle, if the laintiff thinks there s an 80 ercent chance that the court will hol him negligent, he will exect that in the actual case that the court consiers him to have acte negligently - the court will consier his egree of negligence to be larger than when he thinks that there s only a 0 ercent chance of being hel negligent by the court. We can illustrate the ifference between contributory an comarative negligence with a simle examle. Suose for simlicity that the efenant coul have riven at three ossible sees: 0 km/h ue care, 0 km/h or 0 km/h. The laintiff has alreay hire one exert who will argue that the efenant rove 0 km/h. Now he faces the choice of hiring an extra exert, who will argue that the efenant rove 0 km/h. Uner contributory negligence, hiring the extra exert influences the laintiff s execte value by increasing his robability of winning. 5 or examle, if =0.7, hiring one exert costs 0, hiring two exerts 0, an the efenant has chosen to hire one exert at a cost of 0 who will argue that the efenant rove 0 km/h, then hiring two exerts instea of one increases the laintiff s robability of Of course in reality, not all exenitures will have an imact on the way the court erceives the egree of fault of a arty e.g. whether a statute of limitations alies. On average however, larger exenitures of a arty will increase the robability that the court will consier that arty s negligence as less serious. Note however that also with a more general function σ, with σ/ > 0 an σ/ < 0 - it woul be ossible to rove that the exenitures regaring the laintiff s negligence may be smaller uner comarative negligence than uner contributory negligence, an that the exenitures regaring the efenant s negligence are always larger uner comarative negligence. Note also that more comlicate formulas coul be use, e.g. f z. 5 or examle, the court may be convince more easily that the efenant i not take ue care 0 km/h if another exert argues that the efenant rove 0 km/h. 9
winning from 70 % 7/0 to 8 % /7. Uner comarative negligence, hiring the extra exert also influences the laintiff s execte value by increasing the average laintiff s share in case both arties are foun negligent. Suose =0.5. Then the laintiff s average share increases from 0.58 0.7/. to 0.6 0.8/.. Turning from the laintiff s execte value to the efenant s execte loss uner comarative negligence, we obtain in a similar way: EL ef = + σ + + If we now fill in the formulas contest functions for an in the laintiff s execte value an the efenant s execte loss, we obtain the following Nash equilibria 6 :. Comarison of comarative an contributory negligence.. Exenitures regaring the efenant s negligence Uner contributory negligence, the arties exenitures regaring the efenant s negligence equal 7 6 The interior solutions may not constitute an equilibrium. We nee to check for the ossibility of corner solutions, since each layer has a articiation constraint which ensures that laying the game is at least as rofitable as not laying. or the articiation constraints, see the Aenix. 7 Sening at trial with resect to the efenant s negligence is increasing both in the rouctivity arameter an the size of the jugment an ecreasing with the egree of laintiff fault. urther, for a given value of the rouctivity arameter, the amount at stake an the egree of laintiff fault, the arties sen most when the efenant egree of fault equals ½. 0
Uner comarative negligence, the arties exenitures regaring the efenant s negligence equal We can easily see that the exenitures regaring the efenant s negligence are larger uner comarative negligence than uner contributory negligence, since > 0. The reason is twofol. irst, the execte value of exenitures regaring the efenant s negligence is lower uner contributory negligence, since these have zero value when the laintiff is also hel negligent. Secon, aitional investments can lea the court to conclue that the efenant s negligence is relatively large or small. Uner contributory negligence, the egree of negligence oesn t matter for the ultimate ivision of the loss. Uner comarative negligence, it matters a great eal, because the relative egree of negligence influences the ivision of the loss... Exenitures regaring the laintiff s negligence Uner contributory negligence, the arties exenitures regaring the laintiff s negligence equal 8 Uner comarative negligence, the arties exenitures regaring the laintiff s negligence equal 8 Sening at trial with resect to the laintiff s negligence is increasing in the rouctivity arameter, the size of the jugment an the egree of efenant fault. urther, for a given value of the rouctivity arameter, the amount at stake an the egree of efenant fault, the arties sen most when the laintiff egree of fault equals ½.
We can easily see that the exenitures regaring the laintiff s negligence can be either larger or smaller uner comarative negligence than uner contributory negligence. The exenitures can be smaller uner comarative negligence because the execte value of exenitures regaring the laintiff s negligence is lower uner comarative negligence. If the laintiff is hel liable uner contributory negligence, he bears the entire loss. Uner comarative negligence, he only bears art of the loss. The exenitures can be larger uner comarative negligence because aitional investments can lea the court to conclue that the laintiff s fault is relatively small or large... Total exenitures an case quality The total exenitures are smaller uner comarative negligence when: + > + After rearranging terms, we fin that this conition comes own to: <
This conition is more less likely to be fulfille as increases ecreases. In other wors, the stronger weaker the laintiff s case 9, the more likely it is that exenitures are smaller larger uner comarative negligence than uner contributory negligence. Take for the examle the case in which =0.8 an =0.. Then the conition is clearly fulfille 0.<0.6. In the case in which =0. an =0.8, the conition is not fulfille.>0.0. The intuition behin this fining is the following. irst, when the true level of fault of the efenant increases, the imortance of the outcome of the issue of the laintiff's negligence increases uner both rules, but more so uner contributory negligence than uner comarative negligence. We can easily see this by looking at extreme examles. Suose the true level of fault of the efenant is equal to zero. Then the efenant will not be hel negligent by the court. Uner both contributory an comarative negligence, the arties will sen nothing on the issue of the laintiff's negligence, because it oes not matter for the outcome. The laintiff will bear the loss anyway, since the efenant will not be hel negligent. Now suose the true level of the efenant's fault increases to. Then the efenant will be hel negligent by the court with certainty. Uner contributory negligence, the outcome of the issue of the laintiff's negligence is now extremely imortant. Whoever wins this issue, wins the case. Uner comarative negligence, the outcome of the issue of the laintiff's negligence is relatively less imortant, ue to the sharing character of this rule, unlike the all-or-nothing character of contributory negligence. Even if the laintiff loses this issue, he will still be aware a fraction of his loss. Secon, when the true level of fault of the laintiff ecreases, the imortance of the outcome of the issue of the efenant's negligence increases uner both rules, but more so uner contributory negligence than uner comarative negligence. We can again see this by looking at extreme examles. Suose the true level of fault of the laintiff is equal to. Then the laintiff will be hel negligent by the court with certainty. Uner contributory negligence, the arties will not sen anything regaring the issue of the efenant's negligence, since the laintiff will bear the loss ue to his negligent behavior. Uner comarative negligence, the arties will incur exenitures regaring the issue of the efenant s negligence, because the laintiff can still be aware a fraction of the loss of he wins this issue. Now suose the true 9 Taking both the efenant s an the laintiff s behavior into account.
level of the laintiff's fault ecreases to 0. Then the laintiff will not be hel negligent by the court. Uner contributory negligence, the outcome of the issue of the efenant's negligence is now extremely imortant. Whoever wins this issue, wins the case. Uner comarative negligence, the outcome of the issue of the efenant's negligence is also more imortant, but relatively less so. Thir, the greater the ifference between the true levels of fault of the arties, the smaller the value of investing in trying to convince the court that one's level of fault was more moest. The effects of such investments are more heavily iscounte when the ifference between the levels of fault is relatively large. 0 These finings may exlain an emirical result from Low an Smith 995. They fin that on average, the comarative negligence stanar rouces greater incentives to file a lawsuit, but also that as claimant negligence increases, the incentives to litigate on the margin are stronger for claimants in contributory negligence settings. Low an Smith exlain this last result by aealing to the view that litigation is sometimes use as a variance-increasing strategy. Incentives to emloy such a strategy may have been reuce by the tren to aot comarative negligence. The moel in this article shows that rent seeking exenitures may rovie an alternative or comlementary exlanation for this henomenon.. Conclusion Litigation exenitures can be either smaller or larger uner a rule of comarative negligence than uner a rule of contributory negligence. The ifferences between both rules can be summarize as follows. irst, comarative negligence increases the exenitures of the arties because the exenitures may influence the court s view on the relative egree of negligence, 0 A simle examle can illustrate this. Suose we can reresent the level of fault of the laintiff by the number 0., an the efenant's level of fault by the number 0.8, an that the court uses the following formula to etermine the laintiff's share: 0.8/0.8+0. = 0.8. Now suose the efenant can make an investment i that will reuce his level of fault as ultimately erceive by the court with 0. 0.8-0.=0.7. Then the laintiff's share woul equal 0.7/0.7+0. = 0.78. Now we look at a case in which the levels of fault are more close: 0.5 for the laintiff an 0.8 for the efenant. The laintiff's share will be 0.8/0.8+0.5 = 0.6. Clearly, the investment i, which again reuces the level of fault of the efenant with 0., has a greater ay-off for the efenant in such a closer case: 0.7/0.7+0.5= 0.58. So here we get a reuction of 0.0, while in the revious case the reuction was only 0.0. Clearly, there will be more investment in the latter tye of cases.
which only matters uner comarative negligence. Secon, comarative negligence also increases the exenitures regaring the efenant s negligence for another reason. The value of these exenitures is lower uner contributory negligence, since these are worthless if the laintiff is also hel negligent. Thir, comarative negligence can ecrease the exenitures regaring the laintiff s negligence. If the laintiff is hel liable uner contributory negligence, he ays everything. Uner comarative negligence, he only bears art of the harm. It thus becomes less worthwhile to fight har. Total exenitures are more likely to be smaller uner comarative negligence as the efenant s egree of fault increases relative to the laintiff s egree of fault. Several extensions are ossible. or examle, instea of looking for the Nash equilibrium, we coul look for the Stackelberg equilibrium. Inee, the arties o not necessarily always choose their strategies simultaneously. In some instances, one sie may be able to commit to a level of effort, to which the other sie then makes an otimizing resonse. It woul be natural to assume that it s the laintiff who makes a commitment, since there is no lawsuit unless the laintiff initiates it. Another extension coul examine the exenitures regaring the efenant s an the laintiff s negligence in a sequential trial. This article assume trials are unitary. inally, even in unitary trials, one coul introuce the ossibility that one arty acknowleges his negligence or acknowleges that the other arty in t act negligently, so that only one issue nees to be litigate. One coul then analyze uner which negligence rule the arties are more likely to o this. See Hirshleifer an Osborne 00. or a comarison of exenitures in unitary versus sequential trials, see De Mot, Lui an arisi 0, who buil further on Lanes 99. 5
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8 AENDI I. Interior Nash equilibria A. Contributory negligence The laintiff s execte value equals: EV l =, thus EV l The execte loss of litigation for the efenant equals: EL ef = + +, thus EL ef With resect to the laintiff s execte value, the first orer conitions are: an With resect to the efenant s execte value, the first orer conitions are: an rom combining these first orer conitions, it s easy to see that an. utting this back in the first orer conitions gives us: ; The laintiff s execte value reaches a maximum in, since the secon orer conitions are fulfille: EV l 0 EV l 0 EV l EV l > EV l since EV l EV l, We can show in a similar way that the efenant s execte loss reaches a minimum in,.
9 EV l an >, thus whenever the articiation constraint of the laintiff is fulfille, see further at II. B. Comarative negligence B.. irst an secon orer conitions The laintiff s execte value equals EV l = + σ, thus EV l The execte loss of litigation for the efenant equals: EL ef = + σ + +, thus EL ef With resect to the laintiff s execte value, the first-orer conitions regaring the efenant s negligence an the laintiff s negligence are:, thus, thus With resect to the efenant s execte loss, the resective first-orer conitions are:
0, thus, thus We can easily see that an. If we ut an in, we get: If we ut an in, we get: The laintiff s execte value reaches a maximum in, since the secon orer conitions are fulfille: a 0 EV l : 0 EV l 0 This conition is fulfille whenever the articiation constraint of the laintiff is fulfille - > 0; see further at II. b 0 EV l : 0 EV l 0 c EV l EV l > EV l : 0 6 5 6 5 6 5 5 5 5 6 We can show in a similar way that the efenant s execte loss reaches a minimum in,.
This conition is fulfille whenever the laintiff s articiation constraint is fulfille - ; see further at II. II. articiation constraints II.. Contributory negligence or contributory negligence, the articiation constraint for the for the laintiff requires that 0, thus that When the exogenous merits regaring the laintiff s negligence are larger than the exogenous merits regaring the efenant s negligence, the exenitures of the laintiff are larger than the execte jugment, creating a negative execte value suit. The articiation constraint for the efenant requires that. The articiation constraint of the efenant is always satisfie. This is in line with the literature on ure negligence rules see e.g. armer an ecorino, 999; the reason is that for the given rouction technology the success function, the marginal value of aitional exenitures is not large enough to create a negative execte efense for the efenant. II.. Comarative negligence or comarative negligence, the articiation constraint for the for the laintiff requires that - > 0 A substantial amount of claims are file uner comarative negligence but not uner contributory negligence claims for which the exogenous merits are relatively large for both issues an the exogenous merits regaring the laintiff s negligence are larger than the exogenous merits regaring the efenant s negligence. On the other han, some claims are
file uner contributory negligence, but not uner comarative negligence claims for which the exogenous merits are relatively small for both issues an the exogenous merits regaring the laintiff s negligence are slightly larger than the exogenous merits regaring the efenant s negligence. or these claims, the aitional exenitures that comarative negligence creates can make the suit have negative execte value. Overall, more claims are file uner comarative negligence than uner contributory negligence. The articiation constraint for the efenant requires that + < Once again, just as uner contributory negligence, the articiation constraint of the efenant is always satisfie.