Economic Theory of Bilateral Accidents

The first example, shown in table 7.1, concerns a bilateral accident between the railroad and Party A. Each party can choose either to take no care to avoid an accident or to take care. The effort of taking care imposes a cost of five on the party taking care. The probability of an accident occurring varies between 0.06 and 0.16 depending on the level of care taken by either or both parties. The more care 

Level of Care Cost of Care Accident Probability Expected Accident Cost Total Cost 

Here the cost of the railroad taking care is ten, the cost of taking care for Party B is three, and the damages incurred by each party in an accident are fifty. The accident probabilities, conditional on the level of care taken, are the same as in the first example. The preferred societal outcome is where social costs are minimized at fifteen. Hence, due care for Party B is to take care, and due care for the railroad is not to take care. Note that while the probability of an accident would be lower if both parties took care, society s best interests are served when the railroad is not required to undertake the expense of taking care. 

The reader will appreciate that by changing the costs of taking care, the effects of taking care on accident probabilities, and the amounts of accident damage sustained, additional examples could be provided where the optimal societal outcome is for either one, none or both parties to take care. 

Determining due care is only half of the story. It is also necessary to see whether both parties will freely choose this level of care. Game theory is a powerful tool for investigating actual behavior. It uses a payoff matrix which indicates the total care and accident cost borne by each party conditional on the level of care by both parties. The payoff matrix for the first example is shown in table 7.3. Each cell of the matrix is defined by the level of care taken by the two parties. For example the upper-right cell represents the situation where the railroad takes care but Party A does not. Inside the cell in parentheses are shown the costs to the railroad and then, after the comma, to Party A. Because these are costs, they are shown as negative amounts. For example, in the upper-right cell the railroad incurs its expected accident costs of ten plus five which is the cost of taking care, and Party A only bears its expected accident costs of ten. 

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