Abstract: This paper develops a model of fair allocation of a social endowment of objects and money where agents may experience externalities. An allocation is fair if no agent prefers the allocation obtained by swapping her consumption bundle with any other agent. Under very general assumptions on preferences, we show that: (i) for each common lower bound on agents' individual consumption of money, if there is enough money to distribute, then there are fair allocations meeting the lower bound; (ii) for each amount of money to distribute, there are fair allocations; and (iii) if agents’ preferences satisfy one of two sets of sufficient conditions, then fair allocations are also efficient. We apply our results to the fair allocation of objects and money when agents are inequality averse; to the fair allocation of houses and money in a country populated by altruistic citizens; and to the fair allocation of tasks and salary among workers who experience “pain” from trying to keep up with the “social standards” at work. We present two additional applications to economies without externalities. First, our results applied to economies with egoistic agents are non-trivial generalizations of previous results in the literature. Second, after a suitable transformation, our theorems deliver existence of fair and efficient allocations for the time division problem with negatively-monotone preferences, i.e., the allocation of a non-homogeneous one-dimensional continuum from which agents prefer smaller to larger sets.

Abstract: We consider the problem of fairly allocating a bundle of infinitely divisible commodities among a group of agents with classical references. As a solution, we propose to select the allocations at which the sizes of the sets of feasible bundles that each agent would have preferred are minimal and equal. We then turn to the manipulability of this solution. Then identify the equilibrium allocations of the manipulation game associated with the rule in the domain of preferences for which all commodities are normal. For each preference profile, each equal-division constrained Walrasian allocation is an equilibrium allocation. Conversely, each equilibrium allocation is equal-division constrained Walrasian.

Abstract: How should we allocate a social endowment of objects among a group of agents when monetary compensation is not possible? We follow the axiomatic approach. First, we impose two axioms on rules: efficiency and consistency. Previous research arrived at a “dictatorship” result by imposing another property: neutrality [Ergin, H., 2000. Consistency in house allocation problems. J. Math. Econ. 34, 77-97.] We identify efficient and consistent rules that depart from this dictatorship and recover some fairness. Under the mild assumption that there are at least four objects, we characterize such a family of rules using minimal notions of efficiency and consistency. Second, we investigate the restrictions imposed by incentives properties on this family. We characterize the subfamily of strategy-proof rules and show that it can be described by means of a natural generalization to the variable population setting of the “endowment inheritance rules” [Pápai, S., 2000. Strategy-proof Assignment by Hierarchical Exchange, Econometrica 68, 1403-1433]. A corollary of this characterization is that if there are at least four objects, then efficiency, consistency, and strategy-proofness imply group strategy-proofness and reallocation-proofness.

Last update: August-5-2008