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International audienceThis paper examines qualitative properties of efficient insurance contracts in the presence of background risk. In order to get results for all strictly risk-averse expected utility maximizers, the concept of “stochastic increasingness” is used. Different assumptions on the stochastic dependence between the insurable and uninsurable risk lead to different qualitative properties of the efficient contracts. The new results obtained under hypotheses of dependent risks are compared to classical results in the absence of background risk or to the case of independent risks. The theory is further generalized to nonexpected utility maximizers

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We exhibit a general class of interactive decision situations in which all the agents benefit from more information. This class includes as a special case the classical comparison of statistical experimentsà la Blackwell.More specifically, we consider pairs consisting of a game with incomplete information G and an information structure S such that the extended game Γ(G, S) has a unique Pareto payoff profile u. We prove that u is a Nash payoff profile of Γ(G, S), and that for any information structure T that is coarser than S, all Nash payoff profiles of Γ(G, T ) are dominated by u. We then prove that our condition is also necessary in the following sense: Given any convex compact polyhedron of payoff profiles, whose Pareto frontier is not a singleton, there exists an extended game Γ(G, S) with that polyhedron as the convex hull of feasible payoffs, an information structure T coarser than S and a player i