This paper proposes a procedure for implementing efficient egalitarian equivalent allocations in an exchange economy, using the perfect equilibrium concept. This procedure is an extension of the "divide and choose" method in two ways: it is defined for more than two agents and the divider's advantage is removed by auctioning the role of divider among the agents (as in Crawford [1]).Thus, in contrast with other equilibrium concepts (Nash, dominant), the perfect one solves the efficiency-justice dilemma.