Equilibria under Liability Rules: How the Standard Claims Fall Apart

Abstract

In many accident contexts, the accident harm depends on observable as well as unobservable dimensions of the precaution exercised by the parties involved. The observable dimensions are commonly referred to as the `care' levels and the unobservable aspects as the `activity' levels. In a seminal contribution, Shavell (1980) extended the scope of economic analysis of liability rules by providing a model that allows for the care as well as activity level choices. Subsequent works have used and extended Shavell's model to predict outcomes under various liability rules and also to compare their efficiency properties. These works make several claims about the existence and efficiency of equilibria under different liability rules, without providing any formal proof. In this paper, we re-examine the prevalent claims in the literature using the standard model itself. Contrary to prevalent claims, we show that the standard negligence liability rules do not induce equilibrium for all the accident contexts admissible under the model. Under the standard model, even the `no-fault' rules can fail to induce a Nash equilibrium. In the absence of an equilibrium, it is not plausible to make a claim about efficiency of a rule per-se or vis-a-vis other rules. We show that even with commonly used utility functions that meet all the requirements of the standard model, the social welfare function may not have a maximum. In many other situations fully compatible with the standard models, a maximum of the social welfare function is not discoverable by the first order conditions. Under the standard models, even individually optimum choices might not exist. We analyze the underlying problems with the standard models and offer some insights for future research on this subject.