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

Abstract

Abstract. We develop a procedure for implementing an e‰cient and envy-free allocation of m objects among n individuals with the possibility of monetary side-payments, assuming that players have quasi-linear utility functions. The procedure eliminates envy by compensating envious players. It is fully descriptive and says explicitly which compensations should be made, and in what order. Moreover, it is simple enough to be carried out without computer support. We formally characterize the properties of the procedure, show how it establishes envy-freeness with minimal resources, and demonstrate its application to a wide class of fair-division problems.

Distributed fair allocation of indivisible goods

“…The work of Haake et al [18] is particularly interesting. These authors propose two variants of the same procedure, the first of which assumes that an efficient allocation is given to begin with.…”

“…There has been some work on procedures for finding EEF states in the social choice literature [1,20,18], albeit with little or no attention to computational issues. The work of Haake et al [18] is particularly interesting.…”

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.…”

“…Each contribution usually provides an algorithm designed to select a particular allocation with some desirable properties. For example, algorithms by Abdulkadiroǧlu et al [1] and Haake et al [8] select envy-free allocations while Brams and Kilgour [5] and Chin Sung and Vlach [6] impose nonnegative prices. This paper adopts envy-freeness as a solution concept while ignoring individual rationality and signs of prices.…”