Are incentives against justice?

This paper analyzes the manipulability of the Generalized Money Rawlsian Fair (GMRF) solutions in the problem of fairly allocating objects when monetary compensations are possible [Alkan A., Demange G., Gale D., 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 under 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 envy-free and efficient 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 GMRF solutions “naturally implement” the envy-free and efficient solution in Nash and strong Nash equilibria. JEL classification: D63, C72.