A derivation of the money Rawlsian solution

Abstract

We study the set of envy-free allocations for economies with indivisible objects and quasi-linear utility functions. We characterize the minimal amount of money necessary for its nonemptiness when negative distributions of money are not allowed. We also find that, when this is precisely the available amount of money, there is a unique way to combine objects and money such that these bundles may form an envy-free allocation. Based on this property, we describe a solution to the envy-free selection problem following a pseudo-egalitarian criterion. This solution coincides with the "Money Rawlsian Solution" proposed by Alkan et al. (1991).

Bidding for envy-freeness: A procedural approach to n-player fair-division problems

“…This aspect is emphasized by Alkan et al (1991) and Su (1999).2 Because both these approaches assume non-linear utility in money, the algorithms are not finite; instead they converge on an envy-free solution. Exact solutions can be obtained using the algorithms of Aragones (1995) and Klijn (2000) who assume that players' preferences for money are characterized by linear utility functions. This is a strong restriction, but one that seems appropriate for the present context, nevertheless.…”

“…Here we prove that there is always at least one player who is non-envious at the start and then show how our procedure successively eliminates the envy of players who are envious of non-envious players. In contrast to the algorithms of Aragones (1995) and Klijn (2000), our procedure does not need to keep track of all envy relations, since it uses only maximum envy.5 A further feature distinguishing our compensation procedure from Klijn's algorithm is that it requires only minimal financial resources to establish envy-freeness. The necessary amount is automatically determined through the compensations.…”

“…5, we study alternative methods of dividing the surplus that generally remains after envy-freeness is established.6 The simplest way to obtain 3 Brams and Kilgour (2001) use a similar, but stricter constraint, basically for the same purpose. 4 The same starting point is chosen by Steinhaus (1948), Aragones (1995), or Brams and Kilgour (2001). A notable exception is Klijn (2000).…”

Double implementation in a market for indivisible goods with a price constraint

“…One can also think of envy-freeness as a sufficient requirement of stability since each individual prefers his object to any other object given the vector of prices. Therefore envy-freeness is used as a solution concept in most models dealing with indivisible objects, see for example Alkan et al [2], Aragonés [3], Haake et al [8] and Klijn [9].…”

“…If a social planner were to choose an allocation (µ, p), arguably, he would prefer to select one from the set of envy-free allocations (µ, p) ∈ G(A) since these allocations meet the desirable normative criteria of envy-freeness and hence efficiency. The algorithms proposed by Abdulkadiroǧlu et al [1], Aragonés [3], Brams and Kilgour [5], Haake et al [8], and Klijn [9] were designed to select allocations from the set G(A). However, all of them rely on the knowledge of matrix A.…”