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22
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 11 (6 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
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 7 (5 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.
Optimal Proportional Cake Cutting with Connected Pieces
"... We consider the classic cake cutting problem where one allocates a divisible cake to n participating agents. Among all valid divisions, fairness and efficiency (a.k.a. social welfare) are the most critical criteria to satisfy and optimize, respectively. We study computational complexity of computing ..."
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Cited by 6 (0 self)
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We consider the classic cake cutting problem where one allocates a divisible cake to n participating agents. Among all valid divisions, fairness and efficiency (a.k.a. social welfare) are the most critical criteria to satisfy and optimize, respectively. We study computational complexity of computing an efficiency optimal division given the conditions that the allocation satisfies proportional fairness and assigns each agent a connected piece. For linear valuation functions, we give a polynomial time approximation scheme to compute an efficiency optimal allocation. On the other hand, we show that the problem is NPhard to approximate within a factor of
Equilibrium Analysis in Cake Cutting
"... Cake cutting is a fundamental model in fair division; it represents the problem of fairly allocating a heterogeneous divisible good among agents with different preferences. The central criteria of fairness are proportionality and envyfreeness, and many of the existing protocols are designed to guar ..."
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Cited by 6 (4 self)
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Cake cutting is a fundamental model in fair division; it represents the problem of fairly allocating a heterogeneous divisible good among agents with different preferences. The central criteria of fairness are proportionality and envyfreeness, and many of the existing protocols are designed to guarantee proportional or envyfree allocations, when the participating agents follow the protocol. However, typically, all agents following the protocol is not guaranteed to result in a Nash equilibrium. In this paper, we initiate the study of equilibria of classical cake cutting protocols. We consider one of the simplest and most elegant continuous algorithms – the DubinsSpanier procedure, which guarantees a proportional allocation of the cake – and study its equilibria when the agents use simple threshold strategies. We show that given a cake cutting instance with strictly positive value density functions, every envyfree allocation of the cake can be mapped to a pure Nash equilibrium of the corresponding moving knife game. Moreover, every pure Nash equilibrium of the moving knife game induces an envyfree allocation of the cake. In addition, the moving knife game has an ɛequilibrium which is εenvyfree, allocates the entire cake, and is independent of the tiebreaking rule.
Computational voting theory: Gametheoretic and combinatorial aspects
, 2011
"... For at least two thousand years, voting has been used as one of the most effective ways to aggregate people’s ordinal preferences. In the last 50 years, the rapid development of Computer Science has revolutionize every aspect of the world, including voting. This motivates us to study (1) conceptuall ..."
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Cited by 5 (0 self)
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For at least two thousand years, voting has been used as one of the most effective ways to aggregate people’s ordinal preferences. In the last 50 years, the rapid development of Computer Science has revolutionize every aspect of the world, including voting. This motivates us to study (1) conceptually, how computational thinking changes the traditional theory of voting, and (2) methodologically, how to better use voting for preference/information aggregation with the help of Computer Science. My Ph.D. work seeks to investigate and foster the interplay between Computer Science and Voting Theory. In this thesis, I will discuss two specific research directions pursued in my Ph.D. work, one for each question asked above. The first focuses on investigating how computational thinking affects the gametheoretic aspects of voting. More precisely, I will discuss the rationale and possibility of using computational complexity to protect voting from a type of strategic behavior of the voters, called manipulation. The second studies a voting setting called Combinatorial Voting, where the set of alternatives is exponentially large and has a combinatorial
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 5 (4 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 (3 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
Computing sociallyefficient cake divisions
 In Proc. 12th AAMAS
, 2013
"... ABSTRACT A frequent task facing a MAS designer is to efficiently divide resources amongst multiple agents. We consider a setting in which a single divisible resource, a.k.a. "cake", needs to be divided amongst n agents, each with a possibly different valuation function over pieces of the ..."
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ABSTRACT A frequent task facing a MAS designer is to efficiently divide resources amongst multiple agents. We consider a setting in which a single divisible resource, a.k.a. "cake", needs to be divided amongst n agents, each with a possibly different valuation function over pieces of the cake. For this setting, we address the problem of finding divisions that maximize the social welfare, focusing on divisions where each agent gets a single contiguous piece of the cake. We provide a constant factor approximation algorithm for the problem, and prove that it is NPhard to find the optimal division, and that the problem admits no FPTAS unless P=NP. These results hold both when the full valuations of all agents are given to the algorithm, and when the algorithm has only oracle access to the valuation functions. In contrast, if agents can get multiple, noncontiguous pieces of the cake, the results vary greatly depending on the input model. If the algorithm is provided with the full valuation functions of all agents, then the problem is easy. However, if the algorithm needs to query the agents for information on their valuations, then no nontrivial approximation (i.e. < n) can be guaranteed.
Mechanism Design for Fair Division
, 2012
"... We revisit the classic problem of fair division from a mechanism design perspective and provide an elegant truthful mechanism that yields surprisingly good approximation guarantees for the widely used solution of Proportional Fairness. This solution, which is closely related to Nash bargaining and t ..."
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We revisit the classic problem of fair division from a mechanism design perspective and provide an elegant truthful mechanism that yields surprisingly good approximation guarantees for the widely used solution of Proportional Fairness. This solution, which is closely related to Nash bargaining and the competitive equilibrium, is known to be not implementable in a truthful fashion, which has been its main drawback. To alleviate this issue, we propose a new mechanism, which we call the Partial Allocation mechanism, that discards a carefully chosen fraction of the allocated resources in order to incentivize the agents to be truthful in reporting their valuations. For a multidimensional domain with an arbitrary number of agents and items, and for the very large class of homogeneous valuation functions, we prove that our mechanism provides every agent with at least a 1/e ≈ 0.368 fraction of her Proportionally Fair valuation. To the best of our knowledge, this is the first result that gives a constant factor approximation to every agent for the Proportionally Fair solution. To complement this result, we show that no truthful mechanism can guarantee more than 0.5 approximation, even for the restricted class of additive linear valuations. We also uncover a connection between the Partial Allocation mechanism and VCGbased mechanism design, which introduces a way to implement interesting truthful mechanisms in settings where monetary payments are not an option. We also ask whether better approximation ratios are possible in more restricted settings. In particular, motivated by the massive privatization auction in the Czech republic in the early 90s we provide another mechanism for additive linear valuations that works really well when all the items are highly demanded.