Before revision:  The equilibrium satisfies Pareto optimality, approximate envy-freeness and incentive compatibility in the large . * A combinatorial polynomial time algorithm for an \epsilon-approximate ADHZ equilibrium for the case of dichotomous, and more generally bi-valued, utilities.
After revision:  The equilibrium satisfies Pareto optimality, approximate envy-freeness , and approximate weak core stability . * A combinatorial polynomial time algorithm for an \epsilon-approximate ADHZ equilibrium for the case of dichotomous, and more generally bi-valued, utilities.