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36
The efficiency of fair division
 In Proceedings of the 5th International Workshop on Internet and Network Economics (WINE
, 2009
"... Abstract. We study the impact of fairness on the efficiency of allocations. We consider three different notions of fairness, namely proportionality, envyfreeness, and equitability for allocations of divisible and indivisible goods and chores. We present a series of results on the price of fairness ..."
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Cited by 24 (0 self)
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Abstract. We study the impact of fairness on the efficiency of allocations. We consider three different notions of fairness, namely proportionality, envyfreeness, and equitability for allocations of divisible and indivisible goods and chores. We present a series of results on the price of fairness under the three different notions that quantify the efficiency loss in fair allocations compared to optimal ones. Most of our bounds are either exact or tight within constant factors. Our study is of an optimistic nature and aims to identify the potential of fairness in allocations. 1
Optimal EnvyFree Cake Cutting
 PROCEEDINGS OF THE TWENTYFIFTH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2011
"... We consider the problem of fairly dividing a heterogeneous divisible good among agents with different preferences. Previous work has shown that envyfree allocations, i.e., where each agent prefers its own allocation to any other, may not be efficient, in the sense of maximizing the total value of t ..."
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Cited by 23 (11 self)
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We consider the problem of fairly dividing a heterogeneous divisible good among agents with different preferences. Previous work has shown that envyfree allocations, i.e., where each agent prefers its own allocation to any other, may not be efficient, in the sense of maximizing the total value of the agents. Our goal is to pinpoint the most efficient allocations among all envyfree allocations. We provide tractable algorithms for doing so under different assumptions regarding the preferences of the agents.
No Agent Left Behind: Dynamic Fair Division of Multiple Resources
"... Recently fair division theory has emerged as a promising approach for the allocation of multiple computational resources among agents. While in reality agents are not all present in the system simultaneously, previous work has studied static settings where all relevant information is known upfront. ..."
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Cited by 20 (4 self)
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Recently fair division theory has emerged as a promising approach for the allocation of multiple computational resources among agents. While in reality agents are not all present in the system simultaneously, previous work has studied static settings where all relevant information is known upfront. Our goal is to better understand the dynamic setting. On the conceptual level, we develop a dynamic model of fair division, and propose desirable axiomatic properties for dynamic resource allocation mechanisms. On the technical level, we construct two novel mechanisms that provably satisfy some of these properties, and analyze their performance using real data. We believe that our work informs the design of superior multiagent systems, and at the same time expands the scope of fair division theory by initiating the study of dynamic and fair resource allocation mechanisms. Categories and Subject Descriptors Theory of Computation [Theory and algorithms for application domains]: Algorithmic game theory and mechanism design—Algorithmic mechanism design
Towards More Expressive Cake Cutting
"... Cake cutting is a playful name for the problem of fairly dividing a heterogeneous divisible good among a set of agents. The agent valuations for different pieces of cake are typically assumed to be additive. However, in certain practical settings this assumption is invalid because agents may not hav ..."
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Cited by 17 (10 self)
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Cake cutting is a playful name for the problem of fairly dividing a heterogeneous divisible good among a set of agents. The agent valuations for different pieces of cake are typically assumed to be additive. However, in certain practical settings this assumption is invalid because agents may not have positive value for arbitrarily small “crumbs” of cake. In this paper, we propose a new, more expressive model of agent valuations that captures this feature. We present an approximately proportional algorithm for any number of agents that have such expressive valuations. The algorithm is optimal in the sense that no other algorithm can guarantee a greater worstcase degree of proportionality. We also design an optimal approximately proportional and fully envyfree algorithm for two agents. 1
On maxsum fair cake divisions
 In AAAI
, 2012
"... We consider the problem of selecting fair divisions of a heterogeneous divisible good among a set of agents. Recent work (Cohler et al., AAAI 2011) focused on designing algorithms for computing maxsum—social welfare maximizing—allocations under the fairness notion of envyfreeness. Maxsum allocations ..."
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Cited by 12 (7 self)
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We consider the problem of selecting fair divisions of a heterogeneous divisible good among a set of agents. Recent work (Cohler et al., AAAI 2011) focused on designing algorithms for computing maxsum—social welfare maximizing—allocations under the fairness notion of envyfreeness. Maxsum allocations can also be found under alternative notions such as equitability. In this paper, we examine the properties of these allocations. In particular, we provide conditions for when maxsum envyfree or equitable allocations are Pareto optimal and give examples where fairness with Pareto optimality is not possible. We also prove that maxsum envyfree allocations have weakly greater welfare than maxsum equitable allocations when agents have structured valuations, and we derive an approximate version of this inequality for general valuations. 1
Fair enough: guaranteeing approximate maximin shares
, 2014
"... We consider the problem of fairly allocating indivisible goods, focusing on a recentlyintroduced notion of fairness called maximin share guarantee: Each player’s value for his allocation should be at least as high as what he can guarantee by dividing the items into as many bundles as there are play ..."
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Cited by 9 (2 self)
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We consider the problem of fairly allocating indivisible goods, focusing on a recentlyintroduced notion of fairness called maximin share guarantee: Each player’s value for his allocation should be at least as high as what he can guarantee by dividing the items into as many bundles as there are players and receiving his least desirable bundle. Assuming additive valuation functions, we show that such allocations may not exist, but allocations guaranteeing each player 2/3 of the above value always exist, and can be computed in polynomial time when the number of players is constant. These theoretical results have direct practical implications.
How to cut a cake before the party ends
 In Proceedings of the 27 th AAAI Conference on Artificial Intelligence
, 2013
"... For decades researchers have struggled with the problem of envyfree cake cutting: how to divide a divisible good between multiple agents so that each agent likes his own allocation best. Although an envyfree cake cutting protocol was ultimately devised, it is unbounded, in the sense that the numbe ..."
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Cited by 8 (6 self)
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For decades researchers have struggled with the problem of envyfree cake cutting: how to divide a divisible good between multiple agents so that each agent likes his own allocation best. Although an envyfree cake cutting protocol was ultimately devised, it is unbounded, in the sense that the number of operations can be arbitrarily large, depending on the preferences of the agents. We ask whether bounded protocols exist when the agents ’ preferences are restricted. Our main result is an envyfree cake cutting protocol for agents with piecewise linear valuations, which requires a number of operations that is polynomial in natural parameters of the given instance.
The efficiency of fair division with connected pieces
 In Proceedings of the Sixth International Workshop on Internet and Network Economics
, 2010
"... We consider the issue of fair division of goods, using the cake cutting abstraction, and aim to bound the possible degradation in social welfare due to the fairness requirements. Previous work has considered this problem for the setting where the division may allocate each player any number of uncon ..."
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Cited by 4 (0 self)
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We consider the issue of fair division of goods, using the cake cutting abstraction, and aim to bound the possible degradation in social welfare due to the fairness requirements. Previous work has considered this problem for the setting where the division may allocate each player any number of unconnected pieces. Here, we consider the setting where each player must receive a single connected piece. For this setting, we provide tight bounds on the maximum possible degradation to both utilitarian and egalitarian welfare due to three fairness criteria — proportionality, envyfreeness and equitability. 1
Fair Assignment Of Indivisible Objects Under Ordinal Preferences
"... We consider the discrete assignment problem in which agents express ordinal preferences over objects and these objects are allocated to the agents in a fair manner. We use the stochastic dominance relation between fractional or randomized allocations to systematically define varying notions of prop ..."
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Cited by 4 (3 self)
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We consider the discrete assignment problem in which agents express ordinal preferences over objects and these objects are allocated to the agents in a fair manner. We use the stochastic dominance relation between fractional or randomized allocations to systematically define varying notions of proportionality and envyfreeness for discrete assignments. The computational complexity of checking whether a fair assignment exists is studied systematically for the fairness notions. We characterize the conditions under which a fair assignment is guaranteed to exist. For a number of fairness concepts, polynomialtime algorithms are presented to check whether a fair assignment exists or not. Our algorithmic results also extend to the case of variable entitlements of agents. Our NPhardness result, which holds for several variants of envyfreeness, answers an open problem posed by
Externalities in Cake Cutting
"... The cake cutting problem models the fair division of a heterogeneous good between multiple agents. Previous work assumes that each agent derives value only from its own piece. However, agents may also care about the pieces assigned to other agents; such externalities naturally arise in fair division ..."
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Cited by 3 (2 self)
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The cake cutting problem models the fair division of a heterogeneous good between multiple agents. Previous work assumes that each agent derives value only from its own piece. However, agents may also care about the pieces assigned to other agents; such externalities naturally arise in fair division settings. We extend the classical model to capture externalities, and generalize the classical fairness notions of proportionality and envyfreeness. Our technical results characterize the relationship between these generalized properties, establish the existence or nonexistence of fair allocations, and explore the computational feasibility of fairness in the face of externalities. 1