Contiguous Cake Cutting: Hardness Results and Approximation Algorithms

Goldberg, Paul W.; Hollender, Alexandros; Suksompong, Warut

doi:10.1609/aaai.v34i02.5570

Cited by 8 publications

(11 citation statements)

References 17 publications

(29 reference statements)

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“…Two more recent works, by Arunachaleswaran et al [1] and Goldberg et al [29], guarantee connectivity but they are only approximately envy-free. A recent work by Barman and Rathi [6], guarantee both envy-freeness and connectivity under the restriction that value densities of agents satisfy the monotone likelihood ratio property.…”

Section: Other Cake-cutting Algorithmsmentioning

confidence: 99%

Fair cake-cutting algorithms with real land-value data

Shtechman

Gonen

Segal-Halevi

2021

Auton Agent Multi-Agent Syst

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Fair division of land is an important practical problem that is commonly handled either by hiring assessors or by selling and dividing the proceeds. A third way to divide land fairly is via algorithms for fair cake-cutting. Such un-intermediated methods are not only cheaper than an assessor but also theoretically fairer since they guarantee each agent a fair share according to his/her value function. However, the current theory of fair cake-cutting is not yet ready to optimally share a plot of land, and such algorithms are seldom used in practical land division. We attempt to narrow the gap between theory and practice by presenting several heuristic adaptations of famous algorithms for one-dimensional cake-cutting to two-dimensional land-division. The heuristics are evaluated using extensive simulations on real land-value data maps from three different data sets and a fourth (control) map of random values. The simulations compare the performance of cake-cutting algorithms to sale and assessor division in various performance metrics, such as utilitarian welfare, egalitarian welfare, Nash social welfare, envy, and geometric shape. The cake-cutting algorithms perform better in most metrics. However, their performance is greatly influenced by technical implementation details and heuristics that are often overlooked by theorists. We also propose a new protocol for practical cake-cutting using a dynamic programming approach and discuss its run-time complexity versus performance trade-off. Our new protocol performs better than the examined classic cake-cutting algorithms on most metrics. Experiments to assess the amount that a strategic agent can gain from reporting false preferences are also presented. The results show that the problem of strategic manipulation is much less severe than the worst-case predicted by theory.

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Section: Other Cake-cutting Algorithmsmentioning

confidence: 99%

Fair cake-cutting algorithms with real land-value data

Shtechman

Gonen

Segal-Halevi

2021

Auton Agent Multi-Agent Syst

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“…Fair division problems have been classically studied in the context of divisible resources, most prominently in the cake-cutting literature; see (Brandt et al, 2016, Chapter 13) for an excellent survey. There is also a vast literature on connected (or contiguous) cake-cutting, spanning various notions of fairness and economic efficiency (Stromquist, 1980;Su, 1999;Deng et al, 2012;Bei et al, 2012;Aumann et al, 2013;Aumann and Dombb, 2015;Segal-Halevi and Sziklai, 2018;Brânzei and Nisan, 2019;Goldberg et al, 2020). In particular, for equitability, it is known that for any given ordering of the agents, there exists a connected equitable division of a cake consistent with the ordering (Cechlárová et al, 2013).…”

Section: Related Workmentioning

confidence: 99%

Equitable Division of a Path

Misra,

Sonar,

Vaidyanathan

et al. 2021

Preprint

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We study fair resource allocation under a connectedness constraint wherein a set of indivisible items are arranged on a path and only connected subsets of items may be allocated to the agents. An allocation is deemed fair if it satisfies equitability up to one good (EQ1), which requires that agents' utilities are approximately equal. We show that achieving EQ1 in conjunction with well-studied measures of economic efficiency (such as Pareto optimality, non-wastefulness, maximum egalitarian or utilitarian welfare) is computationally hard even for binary additive valuations. On the algorithmic side, we show that by relaxing the efficiency requirement, a connected EQ1 allocation can be computed in polynomial time for any given ordering of agents, even for general monotone valuations. Interestingly, the allocation computed by our algorithm has the highest egalitarian welfare among all allocations consistent with the given ordering. On the other hand, if efficiency is required, then tractability can still be achieved for binary additive valuations with interval structure. On our way, we strengthen some of the existing results in the literature for other fairness notions such as envy-freeness up to one good (EF1), and also provide novel results for negatively-valued items or chores.

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“…Cake cutting has been a central topic in the area of social choice and economics for decades. While the existence and computation of fair allocations have been extensively studied (Aziz and Mackenzie 2016a, b;Brams and Taylor 1995;Dubins and Spanier 1961;Goldberg et al 2020;Stromquist 1980;Su 1999), the work of Chen et al (2013) that we mentioned earlier was the first to consider incentive issues. As with Chen et al, Maya and Nisan (2012) considered piecewise uniform valuations and gave a characterization of truthful and Pareto optimal mechanisms for two agents.…”

Section: Related Workmentioning

confidence: 99%

Truthful fair division without free disposal

2020

Self Cite

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We study the problem of fairly dividing a heterogeneous resource, commonly known as cake cutting and chore division, in the presence of strategic agents. While a number of results in this setting have been established in previous works, they rely crucially on the free disposal assumption, meaning that the mechanism is allowed to throw away part of the resource at no cost. In the present work, we remove this assumption and focus on mechanisms that always allocate the entire resource. We exhibit a truthful and envy-free mechanism for cake cutting and chore division for two agents with piecewise uniform valuations, and we complement our result by showing that such a mechanism does not exist when certain additional constraints are imposed on the mechanisms. Moreover, we provide bounds on the efficiency of mechanisms satisfying various properties, and give truthful mechanisms for multiple agents with restricted classes of valuations.

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Contiguous Cake Cutting: Hardness Results and Approximation Algorithms

Cited by 8 publications

References 17 publications

Fair cake-cutting algorithms with real land-value data

Fair cake-cutting algorithms with real land-value data

Equitable Division of a Path

Truthful fair division without free disposal

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