Disputed lands
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Cited by (18)
Keep your distance: Land division with separation
2023, Computational Geometry: Theory and ApplicationsSimple fair division of a square
2020, Journal of Mathematical EconomicsA reinterpretation of Coase's land monopoly model: Locational specificity and the betterment potential of land as de jure and de facto property
2019, Progress in PlanningCitation Excerpt :For instance, Lucas and Rossi-Hansberg,3 like Alonso on whose famous land use model sociologist Guest (1978) and transport economists Banister and Berechman (2003) relied, referred to a “location” not in terms of any actual place but distance from a referent point (be it the “centroid” of the CBD or city border). There is a huge volume of literature generated by economists who favour a mathematic, game-theoretic approach to deal with “land,” which is known as “cake-cutting” a two-dimensional good (i.e., dividing land as if cutting a cake) with a view towards obtaining a fair cut for each participant (Chambers, 2005; Dall’Aglio & Maccheroni, 2009; Segal-Halevi, Nitzan, Hassidim, & Aumann, 2017). Land boundaries were specifically mentioned in the literature, but more as concepts in a theoretical or virtual exercise than as actual subdivisions.
Resource-monotonicity and population-monotonicity in connected cake-cutting
2018, Mathematical Social SciencesCitation Excerpt :Since then, game theorists analyzed the strategic issues related to cake-cutting, while computer scientists were focusing mainly on how to implement solutions, i.e. the computational complexity of cake-cutting protocols. Many economists regard land division as an important application of division procedures (e.g. Berliant and Raa, 1988; Berliant et al., 1992; Legut et al., 1994; Chambers, 2005; Dall’Aglio and Maccheroni, 2009; Hüsseinov, 2011; Nicolò et al., 2012). Hence, they note the importance of imposing some geometric constraints on the pieces allotted to the agents.
Fair and square: Cake-cutting in two dimensions
2017, Journal of Mathematical EconomicsCitation Excerpt :Hill (1983), Beck (1987), Webb (1990) and Berliant et al. (1992) study the problem of dividing a disputed territory between several bordering countries, with the constraint that each country should get a piece that is adjacent to its border. Berliant et al. (1992), Ichiishi and Idzik (1999) and Dall’Aglio and Maccheroni (2009) acknowledge the importance of having nicely-shaped pieces in resolving land disputes. They prove that, if the cake is a simplex in any number of dimensions, then there exists an envy-free and proportional partition of the cake into polytopes.
Redividing the cake
2022, Autonomous Agents and Multi-Agent Systems