Essays on applied economics



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Chapter 2




Liability Rules and Evolutionary Dynamics11


(Published in



Journal of Institutional and Theoretical Economics, 157 (4) Dec 2001.)


Abstract

We consider the convergence properties of behavior under a comparative negligence rule (CN) and under a rule of negligence with contributory negligence (NCN), assuming bilateral care with three care levels. Using an evolutionary model, we show that CN reduces the proportion of the population using low care more rapidly than does NCN. However NCN increases the proportion of the population using high (efficient) care more rapidly than does CN. As a result, the mean care level increases more rapidly and the mean social cost falls more rapidly under CN than under NCN. (JEL: K 13, C 79)



  1. Introduction


An economic analysis of law considers tort liability as a tool that can induce injurers to internalize the costs they impose on others. An efficient liability rule should provide incentives for a causative contributor to an accident to minimize the sum of accident and avoidance costs by taking cost-justified precautions. Many authors have discussed the equilibrium and efficiency of different liability rules. (BROWN [1973], LANDES AND POSNER [1987], SHAVELL [1987], ARLEN [1992]).

An important issue is how to choose the best liability rule. In recent years the comparative negligence rule (CN hereafter) has spread widely, replacing the rule of negligence with contributory negligence (NCN hereafter). Eight US states had adopted comparative negligence by 1971, but an additional 34 adopted it between 1971 and 1985. CN was argued to be inferior to NCN because the court must decide on the degree of the negligence by both parties (WHITE [1988]). POSNER [1992] stated that “the modern movement to substitute comparative for contributory negligence” is one of the three “most important counter examples to the efficiency theory of law”. WHITE [1989] tested empirically whether the incentive to take care to avoid accidents is stronger under NCN than under CN.
The above literature only considered whether the rules provide an efficient incentive to take care. WITTMAN, FRIEDMAN, CREVIER AND BRASKIN [1997] addressed another consideration in choosing among liability rules: the speed of convergence to equilibrium levels of care. When behavior is not at equilibrium, Nash equilibrium is seldom achieved instantaneously. WITTMAN, FRIEDMAN, CREVIER AND BRASKIN [1997] undertook an experimental test of convergence to equilibrium under different liability rules. In their laboratory experiment, convergence to equilibrium (measured by mean care level) is much more rapid under comparative negligence than under contributory negligence. They gave no theoretical explanation for their result.
From time to time, society is away from the equilibrium level of care for different reasons. Individuals may not be fully rational. In auto accidents, there may be new drivers who do not correctly perceive the risks and costs, such as when a demographic bulge hits driving age, or a wave of immigration produces a stock of new drivers. At any time some individuals may experiment with new strategies. When a court or legislature changes the rules, it will take time before drivers adapt themselves to that change. Changing technology can change the risk and cost of driving significantly12. Any of these factors can require drivers to adjust their behavior to a new optimum, incurring high social costs if the adjustment is slow.
The main contribution of this paper is that we use an evolutionary approach to analyze the speed of convergence under different liability rules, using a simple setting of bilateral care with three care levels. Homogenous drivers decide whether to take a high, medium or low levels of care. The high level of care is the social optimum. In this setting of three care levels, the Nash equilibrium under both CN and NCN is the social optimum.

The evolutionary approach assumes that a strategy that does well is imitated, while a strategy that does badly is rejected. We assume that in every period an individual reflects on the payoff from his strategy and shares strategy and payoff information with others. In every period a fraction of those individuals with a lower payoff change their current strategies to more profitable strategies. This eventually leads to the convergence to the equilibrium strategy. Because of inertia and uncertainty the fraction of individuals that change their strategy in any period is relatively small. The greater is the payoff difference, the greater is the incentive to change the strategy.


We show that CN reduces the proportion of the population using low care more rapidly than does NCN. However NCN increases the proportion of the population using high (efficient) care more rapidly than does CN. As a result, the mean care level increases more rapidly and the mean social cost falls more rapidly under CN than under NCN during the early periods. This is consistent with the result in WITTMAN, FRIEDMAN, CREVIER AND BRASKIN [1997].
The paper is organized as follows: section 2 states the basic assumptions and the Nash equilibrium under different liability rules, section 3 considers evolutionary dynamics and section 4 concludes.

  1. Liability Rules and Nash Equilibrium



W
e consider a framework of bilateral care with three care levels. Suppose the population has infinitely many drivers. There are only three levels of care for each driver, high (), medium () and low (), with the costs of taking care as , , and respectively. For simplicity, we also use to denote the amount of care under three care levels, . Once an accident occurs, a total damage is incurred.

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