An Algorithmic Version of Kuhn's Lone-Divider Method of Fair Division

Dawson, C. Bryan

doi:10.35834/2001/1303172

Cited by 1 publication

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“…That is why we will give just a rough sketch of the procedure. For a more detailed description, the reader is referred to Kuhn [Kuh67], see also, e.g., [BT96,RW98,Daw01].…”

Section: Lone Dividermentioning

confidence: 99%

Degrees of Guaranteed Envy-Freeness in Finite Bounded Cake-Cutting Protocols

Lindner,

Rothe

2009

Preprint

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Cake-cutting protocols aim at dividing a "cake" (i.e., a divisible resource) and assigning the resulting portions to several players in a way that each of the players feels to have received a "fair" amount of the cake. An important notion of fairness is envy-freeness: No player wishes to switch the portion of the cake received with another player's portion. Despite intense efforts in the past, it is still an open question whether there is a finite bounded envy-free cake-cutting protocol for an arbitrary number of players, and even for four players.We introduce the notion of degree of guaranteed envy-freeness (DGEF) as a measure of how good a cake-cutting protocol can approximate the ideal of envy-freeness while keeping the protocol finite bounded (trading being disregarded). We propose a new finite bounded proportional protocol for any number n ≥ 3 of players, and show that this protocol has a DGEF of 1 + n 2 /2 . This is the currently best DGEF among known finite bounded cake-cutting protocols for an arbitrary number of players. We will make the case that improving the DGEF even further is a tough challenge, and determine, for comparison, the DGEF of selected known finite bounded cake-cutting protocols.

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“…That is why we will give just a rough sketch of the procedure. For a more detailed description, the reader is referred to Kuhn [Kuh67], see also, e.g., [BT96,RW98,Daw01].…”

Section: Lone Dividermentioning

confidence: 99%

Degrees of Guaranteed Envy-Freeness in Finite Bounded Cake-Cutting Protocols

Lindner,

Rothe

2009

Preprint

View full text Add to dashboard Cite

show abstract

An Algorithmic Version of Kuhn's Lone-Divider Method of Fair Division

Cited by 1 publication

References 0 publications

Degrees of Guaranteed Envy-Freeness in Finite Bounded Cake-Cutting Protocols

Degrees of Guaranteed Envy-Freeness in Finite Bounded Cake-Cutting Protocols

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