scholarly journals Afriat's Theorem for Indivisible Goods

2013 ◽  
Author(s):  
Francoise Forges ◽  
Vincent Iehlé
Keyword(s):  
Indivisible Goods ◽  
Afriat’S Theorem

scholarly journals Afriat’s theorem for indivisible goods

2014 ◽  
Vol 54 ◽  
pp. 1-6 ◽  
Author(s):  
Françoise Forges ◽  
Vincent Iehlé
Keyword(s):  
Indivisible Goods ◽  
Afriat’S Theorem

Fair Allocation of Indivisible Goods: Beyond Additive Valuations

2021 ◽  
pp. 103633
Author(s):  
Mohammad Ghodsi ◽  
MohammadTaghi HajiAghayi ◽  
Masoud Seddighin ◽  
Saeed Seddighin ◽  
Hadi Yami
Keyword(s):  
Fair Allocation ◽  
Indivisible Goods

scholarly journals The Complexity of Computing Maximin Share Allocations on Graphs

2020 ◽  
Vol 34 (02) ◽  
pp. 2006-2013
Author(s):  
Gianluigi Greco ◽  
Francesco Scarcello
Keyword(s):  
A Priori ◽  
Utility Functions ◽  
Indivisible Goods ◽  
Bounded Treewidth ◽  
Underlying Graph ◽  
Low Degree

Maximin share is a compelling notion of fairness proposed by Buddish as a relaxation of more traditional concepts for fair allocations of indivisible goods. In this paper we consider this notion within a setting where bundles of goods must induce connected subsets over an underlying graph. This setting received much attention in earlier literature, and our study answers a number of questions that were left open. First, we show that computing maximin share allocations is FΔ2P-complete, even when focusing on consistent scenarios, that is, where such allocations are a-priori guaranteed to exist. Moreover, the problem remains intractable if all agents have the same type, i.e., have the same utility functions, and if either the values returned by the utility functions are polynomially bounded, or the underlying graphs have a low degree of cyclicity (more precisely, have bounded treewidth). However, if these conditions hold all together, then computing maximin share allocations (or checking that none exists) becomes tractable. The result is established via machineries based on logspace alternating machines that use partial representations of connected bundles, which are interesting in their own.

scholarly journals Full substitutability

2019 ◽  
Vol 14 (4) ◽  
pp. 1535-1590 ◽  
Author(s):  
John William Hatfield ◽  
Scott Duke Kominers ◽  
Alexandru Nichifor ◽  
Michael Ostrovsky ◽  
Alexander Westkamp
Keyword(s):  
Production Capacity ◽  
Limited Liability ◽  
Indivisible Goods ◽  
Exchange Economies ◽  
New Class ◽  
Existence Of Equilibria

Various forms of substitutability are essential for establishing the existence of equilibria and other useful properties in diverse settings such as matching, auctions, and exchange economies with indivisible goods. We extend earlier models' definitions of substitutability to settings in which each agent can be both a buyer in some transactions and a seller in others, and show that all these definitions are equivalent. We then introduce a new class of substitutable preferences that allows us to model intermediaries with production capacity. We also prove that substitutability is preserved under economically important transformations such as trade endowments, mergers, and limited liability.

scholarly journals Distributed fair allocation of indivisible goods

2017 ◽  
Vol 242 ◽  
pp. 1-22 ◽  
Author(s):  
Yann Chevaleyre ◽  
Ulle Endriss ◽  
Nicolas Maudet
Keyword(s):  
Fair Allocation ◽  
Indivisible Goods

scholarly journals Strategic Manipulation in a Society with Indivisible Goods

1990 ◽  
Vol 33 (3) ◽  
pp. 228-241
Author(s):  
Takeshi Kimura ◽  
Shinji Mizuno ◽  
Masao Mori
Keyword(s):  
Indivisible Goods ◽  
Strategic Manipulation
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