# Application: The bilateral care model when there is no distinction between injurers and victims

In most bilateral activity situations, there is no clear distinction between injurers and victims because both parties involved in the accident suffer losses. This section illustrates the usefulness of the rule of strict liability with a defence of contributory negligence by considering the analysis of Arlen (1990), who examines the efficiency of various legal rules in a "double harm" setting.

Consider the bilateral model of accident law, but now assume that both injurers *and* victims suffer damage when an accident occurs (in other words, there is no real distinction between injurers and victims). Specifically, suppose that if an accident occurs, the 'injurer' suffers harm of *h,* and the 'victim' suffers harm of *h _{v} >* 0. Let

*x*and

_{t}*x*be the levels of care taken by the injurer and the victim. The probability of an accident given these levels of care is

_{v}*p (x*

_{i},

*x*

_{v}), which has the same properties that we have previously assumed. Let the marginal costs of care be

*w*and

_{t}*w*Assume both parties are risk neutral.

_{v}.Aggregate expected social costs are now:

And the two first-order conditions which characterise the efficient levels of care are:

Consider a rule of no liability, where damaged parties are never compensated for any losses. This rule does not induce efficient behaviour. To see this, note that under a no liability rule, for any combination of care levels, the injurer's marginal benefit of care is:

where the right-hand side of (5.10) is the social marginal benefit of the injurer's care. So, for any level of care taken by the victim, the injurer will choose an inefficiently low level of care, since he fails to fully internalise the social benefits of care. The same reasoning applies to the victim. As a result, the Nash equilibrium under this legal rule results in *both* parties taking an inefficiently low level of care.

A rule of strict liability - where damaged parties are always compensated for all losses that occur as a result of an accident - produces a similar outcome. To see this, note that under a strict liability rule, for any combination of care levels, the injurer's marginal benefit of care is:

where once again the right-hand side is the social marginal benefit of the injurer's care. So, once again, for any level of care taken by the victim, the injurer will choose an inefficiently low level of care, since he again fails to fully internalise the social benefits of care. The same reasoning applies to the victim and the Nash equilibrium results in both parties taking an inefficiently low level of care.

Which legal rules are efficient in this situation? Consider a rule of *strict liability with a defence of contributory negligence,* which states that each party must compensate the other for harm incurred, *unless* the party meets some due standard of care. This requires the court to set a due standard of care *(**z*_{{}, *z*_{v}) for each party. Suppose that these due standards are set at the efficient levels, so (z_{;}, *z** _{v}*) = (x*, x*). Let's check if the efficient outcome is a Nash equilibrium. Suppose that the victim meets his due standard of care, so

*x*

*x*. Since he has met his due standard, he does not have to compensate the injurer. Hence the injurer's expected costs are:*

_{v}=

The legal rule creates an upward 'jump' of p(*x** _{t}*,

*x*

**)*

*h*

*in the injurer's expected cost function at the point x*. To avoid these additional costs the injurer chooses*

_{v}*x*

*x*. In other words, if the victim is expected to behave efficiently, the best response of the injurer is to also behave efficiently. And since the parties are essentially symmetric under this legal rule, a similar line of reasoning applies to the victim: if the injurer is expected to behave efficiently, the best response of the victim is to also behave efficiently. Hence the efficient outcome (x*, x*) is a Nash equilibrium (it is also the only equilibrium). When both parties can take care and both can be harmed as a result of an accident, then the rule of strict liability with a defence of contributory negligence produces efficient outcomes.*

_{{}=