Add to ORKGWe consider a competitive insurance market in which agents can privately enter into multicontractual insurance relationships and undertake hidden actions. We study the existence of linear equilibria when insurance companies do not have any restriction on their pricing rules. We provide conditions under which a linear equilibrium exists. We show that two different types of linear equilibria could exist: A first one in which insurance companies make zero expected profits, and a second one in which they make strictly positive expected profits. We also analyze the welfare properties of the linear equilibria. We show that they are not always second best Pareto optimal