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Optimal EnvyFree Cake Cutting
 PROCEEDINGS OF THE TWENTYFIFTH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2011
"... We consider the problem of fairly dividing a heterogeneous divisible good among agents with different preferences. Previous work has shown that envyfree allocations, i.e., where each agent prefers its own allocation to any other, may not be efficient, in the sense of maximizing the total value of t ..."
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Cited by 23 (11 self)
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We consider the problem of fairly dividing a heterogeneous divisible good among agents with different preferences. Previous work has shown that envyfree allocations, i.e., where each agent prefers its own allocation to any other, may not be efficient, in the sense of maximizing the total value
On the Complexity of EnvyFree Cake Cutting
, 2009
"... We study the envyfree cakecutting problem for d+1 players with d cuts, for both the oracle function model and the polynomial time function model. For the former, we derive a θ( ( 1 ǫ)d−1) time matching bound for the query complexity of d + 1 player cake cutting with Lipschitz utilities for any d& ..."
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Cited by 1 (0 self)
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We study the envyfree cakecutting problem for d+1 players with d cuts, for both the oracle function model and the polynomial time function model. For the former, we derive a θ( ( 1 ǫ)d−1) time matching bound for the query complexity of d + 1 player cake cutting with Lipschitz utilities for any d
Optimal EnvyFree . . .
, 2011
"... We consider the problem of fairly dividing a heterogeneous divisible good among agents with different preferences. Previous work has shown that envyfree allocations, i.e., where each agent prefers its own allocation to any other, may not be efficient, in the sense of maximizing the total value of t ..."
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We consider the problem of fairly dividing a heterogeneous divisible good among agents with different preferences. Previous work has shown that envyfree allocations, i.e., where each agent prefers its own allocation to any other, may not be efficient, in the sense of maximizing the total value
Twoplayer envyfree multicake division
 Mathematical Social Sciences, 59(1):26 – 37
, 2010
"... Abstract. We introduce a generalized cakecutting problem in which we seek to divide multiple cakes so that two players may get their mostpreferred piece selections: a choice of one piece from each cake, allowing for the possibility of linked preferences over the cakes. For two players, we show tha ..."
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Cited by 4 (0 self)
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that disjoint envyfree piece selections may not exist for two cakes cut into two pieces each, and they may not exist for three cakes cut into three pieces each. However, there do exist such divisions for two cakes cut into three pieces each, and for three cakes cut into four pieces each. The resulting
More than envyfree
 In the Working Papers of the AAAI99 Workshop on Negotiation: Settling Conflicts and Identifying Opportunities, 4449. Menlo Park
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
On EnvyFree Cake Division
"... The old problem introduced by Gamov and Stern to divide a cake between m people so that each person thinks that he has at least as much cake as anybody else (envyfree division), has been solved by Brams and Taylor. This discovery attracted further interst to the area and, a few years later, Roberts ..."
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Cited by 5 (0 self)
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The old problem introduced by Gamov and Stern to divide a cake between m people so that each person thinks that he has at least as much cake as anybody else (envyfree division), has been solved by Brams and Taylor. This discovery attracted further interst to the area and, a few years later
EnvyFree Division of Sellable Goods
"... We study the envyfree allocation of indivisible goods between two players. Our novel setting includes an option to sell each good for a fraction of the minimum value any player has for the good. To rigorously quantify the efficiency gain from selling, we reason about the price of envyfreeness of ..."
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We study the envyfree allocation of indivisible goods between two players. Our novel setting includes an option to sell each good for a fraction of the minimum value any player has for the good. To rigorously quantify the efficiency gain from selling, we reason about the price of envyfreeness
EnvyFree Discrete Protocols
"... Whenever we say something like Alice has a piece worth α we mean it’s worth α TO HER. The term biggest piece means most valuable to the person looking at it. This is not necessarily related to geometric size. We assume the entire cake is worth 1 to everyone. ..."
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Whenever we say something like Alice has a piece worth α we mean it’s worth α TO HER. The term biggest piece means most valuable to the person looking at it. This is not necessarily related to geometric size. We assume the entire cake is worth 1 to everyone.
EnvyFree Makespan Approximation
, 2009
"... We study envyfree mechanisms for scheduling tasks on unrelated machines (agents) that approximately minimize the makespan. For indivisible tasks, we put forward an envyfree polytime mechanism that approximates the minimal makespan to within a factor of O(log m), where m is the number of machines. ..."
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. We also show a lower bound of Ω(log m / log log m). This improves the recent result of Hartline et al. [15] who give an upper bound of (m+1)/2, and a lower bound of 2−1/m. For divisible tasks, we show that there always exists an envyfree polytime mechanism with optimal makespan.
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