Are incentives against economic justice?

We consider the problem of fairly allocating a social endowment of indivisible goods and money when the domain of admissible preferences contains, but is not restricted to, quasi-linear preferences. We analyze the manipulability of the Generalized Money Rawlsian Fair (GMRF) solutions [Alkan A., Demange G., Gale D., 1991. Fair allocation of indivisible goods and criteria of justice. Econometrica 59, 1023-1039]. These solutions are envy-free, efficient, and satisfy a strong form of solidarity when budget changes. (i) We show that the Nash and strong Nash equilibrium correspondences of the “preference revelation game form” associated with each GMRF solution coincide with the no-envy solution. Even though each agent has an incentive to lie if the others truthfully report their preferences, in equilibrium, no agent prefers another agent’s allotment to hers according to her true preferences; moreover, in equilibrium, efficiency is preserved according to agents’ true preferences. (ii) As a corollary, we show that the GMRF solutions “naturally implement” the no-envy solution in Nash and strong Nash equilibria. JEL classification: D63, C72.