  We use the theory of cooperative games for the design of fair insurance
contracts. An insurance contract needs to specify the premium to be paid and a
possible participation in the benefit (or surplus) of the company. It results
from the analysis that when a contract is exposed to the default risk of the
insurance company, ex-ante equilibrium considerations require a certain
participation in the benefit of the company to be specified in the contracts.
The fair benefit participation of agents appears as an outcome of a game
involving the residual risks induced by the default possibility and using fuzzy
coalitions.
