Warranty Contracts and Equilibrium Probabilities

Abstract

This article pertains to warranty contracts associated with the exchange of items that are selected from a large collection of similar items. Warranty contracts for item reliability and quality are, by their very nature, adversarial. They are crafted by lawyers representing one adversary, generally a seller, and are ratified by lawyers representing the other adversary, generally a buyer. The contractual requirements are stated in lay terms and involve only observables. These requirements may or may not be based on a consideration of the underlying failure propensity.

The purpose of this article is to point out that inherent to any meaningful warranty contract there exist values of the propensity that make the contract “fair” to each adversary. We call these values “equilibrium probabilities” they can be viewed as logical probabilities in the sense of Carnap. A warranty contract is said to be “in equilibrium” if the equilibrium probabilities coincide, and a contract that is in equilibrium is said to be“just” if the common equilibrium probabilities coincide with propensity. The ratification of any warranty contract is based on an adversary’s personal probability of the propensity. Thus the scenario of warranty contracts brings into perspective the three predominant notions of probability: objective, logical, and subjective.

The thrust of our message is that the existence of equilibrium probabilities be recognized in warranty contracts. Current practice does not do so. This message should be of particular relevance to those involved in industrial and government contracting wherein the exchange of large monies is at stake.