scholarly journals Strategy-Proofness, Envy-Freeness and Pareto Efficiency in Online Fair Division with Additive Utilities

2019 ◽  
pp. 527-541
Author(s):  
Martin Aleksandrov ◽  
Toby Walsh
Keyword(s):  
Fair Division ◽  
Pareto Efficiency ◽  
Additive Utilities ◽  
Strategy Proofness

scholarly journals When Do Envy-Free Allocations Exist?

2019 ◽  
Vol 33 ◽  
pp. 2109-2116 ◽  
Author(s):  
Pasin Manurangsi ◽  
Warut Suksompong
Keyword(s):  
Phase Transition ◽  
High Probability ◽  
Fair Division ◽  
The Other ◽  
Other Hand ◽  
Additive Utilities ◽  
The One

We consider a fair division setting in which m indivisible items are to be allocated among n agents, where the agents have additive utilities and the agents’ utilities for individual items are independently sampled from a distribution. Previous work has shown that an envy-free allocation is likely to exist when m = Ω (n log n) but not when m = n + o (n), and left open the question of determining where the phase transition from non-existence to existence occurs. We show that, surprisingly, there is in fact no universal point of transition— instead, the transition is governed by the divisibility relation between m and n. On the one hand, if m is divisible by n, an envy-free allocation exists with high probability as long as m ≥ 2n. On the other hand, if m is not “almost” divisible by , an envy-free allocation is unlikely to exist even when m = Θ(n log n)/log log n).

scholarly journals Strategy proofness and Pareto efficiency in quasilinear exchange economies

2014 ◽  
Vol 9 (2) ◽  
pp. 361-381 ◽  
Author(s):  
Mridu Prabal Goswami ◽  
Manipushpak Mitra ◽  
Arunava Sen
Keyword(s):  
Pareto Efficiency ◽  
Exchange Economies ◽  
Strategy Proofness

scholarly journals Pure Nash Equilibria in Online Fair Division

2017 ◽  
Author(s):  
Martin Aleksandrov ◽  
Toby Walsh
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Specific Property ◽  
Fair Division ◽  
Pareto Efficiency ◽  
Pure Nash Equilibrium ◽  
Group Strategy ◽  
Is Strategy ◽  
Strategy Proof ◽  
Online Mechanism

We consider a fair division setting in which items arrive one by one and are allocated to agents via two existing mechanisms: LIKE and BALANCED LIKE. The LIKE mechanism is strategy-proof whereas the BALANCED LIKE mechanism is not. Whilst LIKE is strategy-proof, we show that it is not group strategy-proof. Indeed, our first main result is that no online mechanism is group strategy-proof. We then focus on pure Nash equilibria of these two mechanisms. Our second main result is that computing a pure Nash equilibrium is tractable for LIKE and intractable for BALANCED LIKE. Our third main result is that there could be multiple such profiles and counting them is also intractable even when we restrict our attention to equilibria with a specific property (e.g. envy-freeness, Pareto efficiency).

scholarly journals Fair Division of a Graph

2017 ◽  
Author(s):  
Sylvain Bouveret ◽  
Katarína Cechlárová ◽  
Edith Elkind ◽  
Ayumi Igarashi ◽  
Dominik Peters
Keyword(s):  
Simple Structure ◽  
Fair Division ◽  
Fair Allocation ◽  
Connected Subgraph ◽  
Solution Concepts ◽  
Accessibility Relation ◽  
Acyclic Graphs ◽  
Special Cases ◽  
Additive Utilities ◽  
The Relationship

We consider fair allocation of indivisible items under an additional constraint: there is an undirected graph describing the relationship between the items, and each agent's share must form a connected subgraph of this graph. This framework captures, e.g., fair allocation of land plots, where the graph describes the accessibility relation among the plots. We focus on agents that have additive utilities for the items, and consider several common fair division solution concepts, such as proportionality, envy-freeness and maximin share guarantee. While finding good allocations according to these solution concepts is computationally hard in general, we design efficient algorithms for special cases wherethe underlying graph has simple structure, and/or the number of agents---or, less restrictively, the number of agent types---is small. In particular, despite non-existence results in the general case, we prove that for acyclic graphs a maximin share allocation always exists and can be found efficiently.

Fair Division in the Internet Age

2019 ◽  
Vol 11 (1) ◽  
pp. 407-441 ◽  
Author(s):  
Hervé Moulin
Keyword(s):  
Fair Division ◽  
Social Institutions ◽  
The Internet ◽  
Practical Implementation ◽  
Internet Age ◽  
Science Community ◽  
Additive Utilities ◽  
Computational Simplicity ◽  
The One ◽  
User Friendly

Fair division, a key concern in the design of many social institutions, has for 70 years been the subject of interdisciplinary research at the interface of mathematics, economics, and game theory. Motivated by the proliferation of moneyless transactions on the internet, the computer science community has recently taken a deep interest in fairness principles and practical division rules. The resulting literature brings a fresh concern for computational simplicity (scalable rules) and realistic implementation. In this review of the most salient fair division results of the past 30 years, I concentrate on division rules with the best potential for practical implementation. The critical design parameter is the message space that the agents must use to report their individual preferences. A simple preference domain is key both to realistic implementation and to the existence of division rules with strong normative and incentive properties. I discuss successively the one-dimensional single-peaked domain, Leontief utilities, ordinal ranking, dichotomous preferences, and additive utilities. Some of the theoretical results in the latter domain are already implemented in the user-friendly SPLIDDIT platform ( http://spliddit.org ).

The Geometry of Efficient Fair Division

2005 ◽  
Author(s):  
Julius B. Barbanel ◽  
Alan D. Taylor
Keyword(s):  
Fair Division

Fair Division

2000 ◽  
Author(s):  
Michael J. Meurer
Keyword(s):  
Fair Division
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