Formal insurance and altruism networks

We study how altruism networks affect the demand for formal insurance. Agents with CARA utilities are connected through a network of altruistic relationships. Incomes are subject to a common shock and to a large individual shock, generating heterogeneous damages. Agents can buy formal insurance to cover the common shock, up to a coverage cap. We find that ex-post altruistic transfers induce interdependence in ex-ante formal insurance decisions. We characterize the Nash equilibria of the insurance game and show that agents act as if they are trying to maximize the expected utility of a representative agent with average damages. Altruism thus tends to increase demand of low-damage agents and to decrease demand of high-damage agents. Its aggregate impact depends on the interplay between demand homogenization, the zero lower bound and the coverage cap. We find that aggregate demand is higher with altruism than without altruism at low prices and lower at high prices. Nash equilibria are constrained Pareto efficient.