Fair cake-cutting
WebCake-cutting may seem like a problem in recreational mathematics, but ideas behind these algorithms have been applied to a number of important real-world problems, including international negotiations and divorce settlements, and there are even com-mercial companies, such as Fair Outcomes, based on cake cutting algorithms. WebOct 13, 2015 · Fair Cake-Cutting among Groups arXiv Authors: Erel Segal-Halevi Bar Ilan University Shmuel Nitzan Bar Ilan University Abstract This paper extends the classic cake-cutting problem from...
Fair cake-cutting
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WebAug 12, 2024 · We study the fair division of a continuous resource, such as a land-estate or a time-interval, among pre-specified groups of agents, such as families. Each family is given a piece of the resource and this piece is used simultaneously by all family members, while different members may have different value functions. Three ways to assess the fairness … WebOct 18, 2024 · Our results support the practical use of the celebrated Selfridge-Conway procedure, and more generally, of envy-free cake-cutting mechanisms. We also find …
Websider the most basic cake cutting algorithm for the case of two agents, the Cut and Choose algorithm.1 Agent 1 cuts the cake into two pieces that are of equal value according to its … Fair cake-cutting is a kind of fair division problem. The problem involves a heterogeneous resource, such as a cake with different toppings, that is assumed to be divisible – it is possible to cut arbitrarily small pieces of it without destroying their value. The resource has to be divided among several partners who … See more There is a cake C, which is usually assumed to be either a finite 1-dimensional segment, a 2-dimensional polygon or a finite subset of the multidimensional Euclidean plane R . There are n people … See more Proportionality The original and most common criterion for justice is proportionality (PR). In a proportional cake-cutting See more In addition to the desired properties of the final partitions, there are also desired properties of the division process. One of these properties is truthfulness (aka incentive compatibility), which comes in two levels. • Weak … See more There is a generalization of the cake-cutting problem in which there are several cakes, and each agent needs to get a piece in each cake. • Cloutier, Nyman and Su study two-player envy-free multi-cake division. For two cakes, they prove … See more In some cases, the pieces allocated to the partners must satisfy some geometric constraints, in addition to being fair. • The … See more In addition to justice, it is also common to consider the economic efficiency of the division; see efficient cake-cutting. There are several levels … See more Reasoning about the run-time complexity of algorithms requires a model of computation. Several such models are common in the literature: • The Robertson–Webb query model - in which the algorithm may ask each agent a query of one of two … See more
WebDivide and choose (also Cut and choose or I cut, you choose) is a procedure for fair division of a continuous resource, such as a cake, between two parties. It involves a … WebApr 22, 2024 · Fair cake-cutting is a kind of fair division problem. The problem involves a heterogeneous resource, such as a cake with different toppings, that is assumed to be …
WebApr 9, 2012 · Yes, there is a very interesting theory on fair division. It all starts with the following example introduced by Steinhaus in 1948. Two questions have to be raised: the definition of fairness and the way we can guarantee a fair division. In this article, we will only …
WebJun 17, 2024 · Since its formalization as the cake-cutting problem (Steinhaus 1948 ), this research question has inspired a large interdisciplinary research for finding mechanisms that produce fair allocations without giving agents incentives to misrepresent their … mame machinesWebApr 15, 2024 · In this paper, we resolve this open problem by proving that there does not exist a deterministic, truthful and proportional cake cutting mechanism, even in the special case where all of the... mame interfaceWebThis is known as the cut-and-choose protocol, because one participantcuts and the other chooses. Theorem. The cut-and-choose protocol forn =2 is a fair cake-cutting protocol. Proof: If Alice follows the protocol, then both pieces are worth the same to her, so each piece must be worth exactly 1/2 by her measure. mame in retroarchWebApr 10, 2024 · Cutting the Cake: A Language for Fair Division. Noah Bertram, Alex Levinson, Justin Hsu. The fair division literature in economics considers how to divide resources between multiple agents such that the allocation is envy-free: each agent receives their favorite piece. Researchers have developed a variety of fair division protocols for … mame motherboardmame macbook dmg sourceforgeWebNov 16, 2024 · Abstract. We investigate cases of preference change in the context of cake-cutting problems. In some circumstances, believing that some other player can be credited with a particular preference structure triggers a preference shift by imitation. As a result of this, players may experience regret. However, in typical examples the extent of the ... mame killer instinct romWeb(1) cut the cake into three pieces of equal value to himself and then took a piece for himself, but this piece may have been more valuable to (2) or (3) than any of the other pieces, so … mame on atom cpu