When Prudent Behavior Immobilizes: Asymptotic Stability in Matching Problems With Externalities

Abstract

In matching problems with externalities, prudence measures the importance given to potential reactions when evaluating a deviation; social connectedness, on the other hand, measures the capacity to react to such deviations. Intuitively, a matching problem should be more likely to have a stable solution when these attributes are high. Assuming that externalities are arbitrary and preferences are random, the role of prudence and social connectedness in stability is studied. Among other results, it is shown that asymptotic stability---a property that never holds in the absence of externalities---is achieved even in situations where social connectedness is low and prudence vanishes. However, those who ignore the reactions of other individuals have a destabilizing effect on society: the probability of a matching being stable converges to zero as the number of myopic agents increases, regardless of the percentage of the population they represent.