On Determining the Importance of Attributes with a Stopping Problem

One of the approaches in consumer theory considers each product as a collection of attributes. As opposed to the traditional approach, according to which consumer preferences for products are the underlying features of economic modeling, they are now derived from the composition and strength of products' attributes. In this paper I try to answer the question of how one can determine the relative importance of the different attributes of a product. In order to answer this question a stopping problem model is constructed. An agent faces a sequence of i.i.d. multi-dimensional products of which he can observe only one attribute. At each stage the agent has to decide whether he wants to stop, taking the best product so far, or whether he prefers to continue by observing a specific attribute of the next product. The model is solved for an optimal observing policy. In the finite case, second order stochastic dominance characterizes the optimal strategy in the sense that if it holds between the two random variable induced by the expected utility given an attribute, it is never optimal to observe the "dominating" one. In the infinite horizon case, observing one attribute only is always optimal. However, the infinite horizon optimal strategy may not be myopically optimal. The seeming discrepancy between finite and infinite horizon models vanishes for a sufficiently large horizon, thus making the infinite case optimal attribute the one chosen for a long period in finite horizon cases also. Identifying the infinite case optimal attribute allows us to determine the performance of the model in the in the long run even when second order stochastic dominance does not hold.