The preceding model may plausibly account for accidents in which potential injurers alone can minimise social costs through precautions and without changing activity levels. A good example may be airline crashes, as there is little that people on the ground can do to reduce the expected cost of such accidents. Furthermore, given the value inherent in fl ying, activity- level reductions among airlines that exercise all cost- justifi ed precautions are unlikely to be effi cient. In such cases, the economic goal of tort law should be to induce airline companies to undertake optimal precau-tions. In practice, society accomplishes this goal through a combination of ex ante regulation, ex post liability in tort, and potential criminal-law enforcement.
In most cases, however, minimising the social cost of accidents necessitates precautions on the part of both prospective injurers and victims. For instance, to reduce the cost of injuries on the road, not only must drivers take appropriate care – pedestrians and cyclists must do so, as well. Such cases are known as bilateral- care scenarios. The relevant question is how courts can employ liability rules to induce both tortfeasors and victims to undertake optimal precautions.
As before, prospective tortfeasors can engage in no, low, moderate, or high levels of care. Each successive increment in precautions by potential injurers reduces the expected cost of accidents by
diminishing the likelihood of their occurrence. Each such increase in care, however, imposes a further cost on tortfeasors. In this model, however, the expected accident cost also depends on victims’ precautions. We shall assume that they, too, can exercise four degrees of care, which like-wise reduces the probability of accidents, though such precautions impose private costs that increase with the degree of care undertaken. Activity levels are fi xed, and so we are unconcerned with spurring the injurers or the victims to substitute their current conduct for alternative forms of behaviour. This table demonstrates the relevant payoffs:
These possible outcomes depend on the respective care levels of the injurers and the victims.
Consistent with its being a bilateral- care model, the social-welfare optimum is for both injurers and victims to undertake a moderate level of precautions. Notice once more that the effi cient result (moderate–moderate) differs from the care combination that minimises the expected accident cost
Injurer Precautions
Cost of Care to Injurers
Victim Precautions
Cost of Care to Victims
Expected Accident Cost
Total Social Cost
None 0 None 0 500 500
Low 20 None 0 470 490
Moderate 50 None 0 430 480
High 80 None 0 415 495
None 0 Low 10 485 495
Low 20 Low 10 450 480
Moderate 50 Low 10 415 475
High 80 Low 10 400 490
None 0 Moderate 20 470 490
Low 20 Moderate 20 435 475
Moderate 50 Moderate 20 400 470
High 80 Moderate 20 380 480
None 0 High 40 455 495
Low 20 High 40 430 490
Moderate 50 High 40 390 480
High 80 High 40 375 495
Figure 2.3
(high–high). Minimising that cost is not necessarily the same as minimising the combined costs of accidents and precautions .
The question, then, is how to induce effi cient behaviour through liability rules in tort. We shall consider the following liability regimes: no liability, strict liability, negligence, strict liability with contributory negligence, and strict liability with comparative negligence. To determine the rational choices of the injurers and victims in the strategic environment in which those actors fi nd them-selves, we shall use game theory. This branch of economic analysis is particularly useful when analysing strategic interrelationships and equilibrium. To determine whether a liability rule induces the right form of behaviour, one must ask of each party: given the other actors’ anticipated deci-sions, what is her rational choice?
BILATERAL- CARE SCENARIOS WITH FIXED ACTIVITY LEVELS | 73
1. No liability
Given the absence of activity- level changes, actors’ private interests are to minimise their expected costs. As each party is non- altruistic, third- party harm will not factor into any person’s decision making. In a setting of no liability, the injurers’ costs are limited to their precautions, if any. Victims’
costs comprised both their own costs of taking care and the expected accident cost.
To determine rational behaviour in the presence of no liability, consider the normal form representation of the choices of injurers and victims. The left- hand fi gure in every cell is the injurers’
payout; the right- hand one is the victims’:
The effi cient outcome is for both the injurers and the victims to take care, which minimises total social costs at 470. To determine what the players will rationally do, however, begin by iden-tifying the injurers’ dominant strategy. As the reader can readily affi rm, regardless of whether victims take no, low, moderate, or high care, the best choice for the injurers is to take no care, which entails a cost of zero. This is the injurers’ dominant strategy.
Victims
No Care Low Care Moderate Care High Care
No Care 0, 500 0, 495 0, 490 0, 495
Injurers Low Care 20, 470 20, 460 20, 455 20, 470
Moderate Care 50, 430 50, 425 50, 420 50, 430
High Care 80, 415 80, 410 80, 400 80, 415
Figure 2.4
4 Note, however, that regardless of what level of care injurers actually take, victims minimise their expected cost by taking moderate precautions. That level of care is therefore victims’ dominant strategy.
What of the victims’ strategy? Victims know that the injurers’ dominant strategy is to take no care. Their best choice is, therefore, to take a moderate amount of care, which minimises their expected losses at 490. 4 The equilibrium is thus for injurers to take no precautions and for victims to act with moderate care. This is a Nash equilibrium because neither the victims nor the injurers can do better given the other parties’ choices. This outcome, however, is ineffi cient because total social cost is 490 instead of the social optimum of 470 in which everyone takes moderate care.
2. Strict liability
Under a strict-liability regime, injurers must compensate victims for the full costs of their injuries.
By assumption, such compensation perfectly restores victims to their pre- injury state, such that they are indifferent as to whether they were involved in an accident or not. To identify the outcome under strict liability, review the normal- form representation shown in Figure 2.5.
The victims’ dominant strategy is obviously not to take care because doing so would entail a private cost without an offsetting private benefi t.
Given victims’ decision not to take care, drivers will minimise their expected costs. They could elect to take no care, in which case their expected cost will be 500. If they decide to take low care, drivers will experience a cost of 20 in precautions and expected liability of 470, for a total expected cost of 490. A rational, risk- neutral driver would thus prefer to take low care than no care. She could do even better, however, by exercising moderate care, as the increment in precautions costs of 30 (50 minus 20) would reduce the expected accident cost by 40 (470 minus 430), thus yielding an expected private cost of 480. It would be irrational for drivers to take a high amount of precautions,
however, as the marginal cost of increasing care to that level would exceed the marginal reduction in expected accident costs. Given the victims’ election not to take care, the drivers’ rational choice is to undertake a moderate amount of care.
Thus, under strict liability, the equilibrium is for drivers to take a moderate amount of care, but for victims not to take any care. The result is a net social cost of 480, which in this model is superior to a setting of no liability, but still less desirable than the effi cient outcome in which all parties exercise moderate care. That social optimum would entail a total cost of just 470.
3. Negligence
Negligence is the most common liability regime in tort law, and thus an important subject of economic analysis. As people perceive different connotations from the term “negligence”, it is crucial to defi ne the term in economic terms: a failure to undertake the amount of precautions that unilaterally minimises the expected social cost of an accident.
Under a negligence regime, if tortfeasors took care, the full social cost of any accidents that occur would fall on victims, save for those costs that tortfeasors incur in precautions. Conversely, if the injurers fail to take the effi cient level of care, all accident costs would fall on them.
In the present model, optimal precautions for both injurers and victims constitute moderate care. If injurers took moderate or high care, the courts would not deem them negligent and the accident costs would lie with victims. Conversely, if injurers took low or no care, they would be negligent and would thus have to compensate victims for their injuries. With these concerns in mind, turn to the game- theory representation of a negligence regime, as applied to this bilateral- care scenario with fi xed activity levels:
Regardless of victims’ precautions, injurers’ best choice is to take moderate precautions at a cost of 50. They would prefer this course to taking a high degree of care because their net costs under the latter approach would be 80. Conversely, if injurers took no care, the courts would fi nd them negligent. Taking no care, tortfeasors’ expected costs would be 500, 485, 470, or 455, depending on whether victims took no, low, moderate, or high care, respectively. Equivalently,
Victims
No Care Low Care Moderate Care High Care
No Care 500, 0 485, 10 470, 20 455, 40
Injurers Low Care 490, 0 470, 10 455, 20 450, 40
Moderate Care 480, 0 465, 10 450, 20 440, 40
High Care 495, 0 480, 10 460, 20 455, 40
Figure 2.5
Victims
No Care Low Care Moderate Care High Care
No Care 500, 0 485, 10 470, 20 455, 40
Injurers Low Care 490, 0 470, 10 455, 20 450, 40
Moderate Care 50, 430 50, 425 50, 420 50, 430
High Care 80, 415 80, 410 80, 400 80, 415
Figure 2.6
BILATERAL- CARE SCENARIOS WITH FIXED ACTIVITY LEVELS | 75
tortfeasors’ expected costs would be 490, 470, 455, or 450 if injurers took low care (which courts would deem negligent). Given these choices, it is rational for drivers to undertake a moderate amount of precautions and hence pay only 50.
What is the rational choice for victims? They know that injurers have an incentive to take a moderate amount of care. Given drivers’ choice to do so, victims understand that they must pay the cost of unavoidable accidents. They will thus decide successively to increase precautions as long as each additional expenditure in care reduces the expected cost of accidents by more than that amount.
Given drivers’ election to take moderate precautions, if victims took no care, they would face an expected cost of 430. If they take low care, they will experience combined costs in precautions and accident costs of 425. If they take moderate or high precautions, victims will face a net expected cost of 420 and 430, respectively. Victims will minimise their expected costs, and will thus take moderate care, given drivers’ decision also to take moderate care. Victims’ taking moderate precautions does not affect drivers’ incentive also to undertake moderate care, and so this is an equilibrium.
In the present model, a negligence standard is effi cient, as it leads both injurers and victims to take optimal precautions.
4. Strict liability with contributory negligence
Strict liability alone is ineffi cient in the present model because it insures victims against all accident costs, thus inducing them not to take socially benefi cial, but privately costly, precautions. Injecting contributory negligence changes this calculus because it insures victims only if they do not act negligently. As “negligence” means not taking the precautions that minimise the expected social cost of accidents, courts will deem victims negligent in this model if they take less than moderate care.
What level of care will potential victims take? The answer depends on the anticipated behaviour of drivers, and vice versa, as the following matrix demonstrates:
Take victims’ strategy fi rst. If injurers took no care, victims would minimise their expected costs by exercising moderate care, which would result in an expense of 20, as opposed to the costs of 500, 495, or 40 in taking no, low, or high care, respectively. The reader can readily verify that, regardless of which level of care injurers take, victims’ rational choice is to take moderate care, which is thus their dominant strategy.
Victims
No Care Low Care Moderate Care High Care
No Care 0, 500 0, 495 470, 20 455, 40
Injurers Low Care 20, 470 20, 460 455, 20 450, 40
Moderate Care 50, 430 50, 425 450, 20 440, 40
High Care 80, 415 80, 410 460, 20 455, 40
Figure 2.7
Injurers do not have a dominant strategy. If victims take no care, injurers do best by also taking no care. If the victims take low care, the injurers again do best by not taking care. If the victims exercise moderate precautions, however, the injurers’ best action is to take moderate care, which is also the rational choice if the victims undertake a high degree of care. Nevertheless, in this game, the injurers know that the victims’ dominant strategy is to take moderate care, which means that the injurers will also take moderate care. This is the effi cient result.
The victims, therefore, have an incentive to exercise a moderate amount of care when subjected to strict liability with contributory negligence. In light of the victims’ decision to act in this way, the drivers also have an incentive to take moderate care if victims take care. Like negligence, strict liability with contributory negligence leads to the effi cient outcome under the assumptions of this model. Notice, however, that strict liability with contributory negligence is more costly for a court to apply than a simple rule of strict liability.
5. Strict liability with comparative negligence
Strict liability with a defence of comparative negligence holds injurers responsible for harm to victims, though it discounts injured parties’ recovery by the percentage to which they were negli-gent. This, too, leads to the effi cient outcome in which both drivers and victims take moderate precautions.
To see why, fi rst consider victims’ incentives. They know that, under this liability regime, drivers must make good the harm caused, save to the extent that victims’ negligent behaviour contributes to the relevant injury. So, if both injurers and victims take no care, the expected accident cost is 500, but the courts will limit victims’ recovery to 470 on account of victims’ failure to take moderate precau-tions at an expense of 20, which expenditure would have reduced the expected accident cost to 470.
Victims would therefore be better off spending 20 on precautions. The reader can confi rm that this result stays the same regardless of whether drivers take low, moderate, or high levels of care.
Given victims’ incentive to take moderate care, it is rational for drivers also to exercise moderate care. The reason is that, absent negligence on victims’ part, drivers must pay all accidents costs. To the extent that drivers can disproportionately reduce expected accident costs by undertaking precautions, they will do so. In this model, drivers’ taking moderate care minimises their expected payout, which consists of the cost of their taking care plus their expected liability costs from the unavoidable accidents that occur.