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Expand the shares together: envy-free mechanisms with a small number of cuts
, Article Algorithmica ; Volume 81, Issue 4 , 2019 , Pages 1728-1755 ; 01784617 (ISSN) ; Farhadi, M ; Ghodsi, M ; Alijani, R ; Tajik, A. S ; Sharif University of Technology
Springer New York LLC
2019
Abstract
We study the problem of fair division of a heterogeneous resource among strategic players. Given a divisible heterogeneous cake, we wish to divide the cake among n players to meet these conditions: (I) every player (weakly) prefers his allocated cake to any other player’s share (such notion is known as envy-freeness), (II) the allocation is dominant strategy-proof (truthful) (III) the number of cuts made on the cake is small. We provide methods for dividing the cake under different assumptions on the valuation functions of the players. First, we suppose that the valuation function of every player is a single interval with a special property, namely ordering property. For this case, we...
Expand the shares together: envy-free mechanisms with a small number of cuts
, Article Algorithmica ; 2018 ; 01784617 (ISSN) ; Farhadi, M ; Ghodsi, M ; Alijani, R ; Tajik, A. S ; Sharif University of Technology
Springer New York LLC
2018
Abstract
We study the problem of fair division of a heterogeneous resource among strategic players. Given a divisible heterogeneous cake, we wish to divide the cake among n players to meet these conditions: (I) every player (weakly) prefers his allocated cake to any other player’s share (such notion is known as envy-freeness), (II) the allocation is dominant strategy-proof (truthful) (III) the number of cuts made on the cake is small. We provide methods for dividing the cake under different assumptions on the valuation functions of the players. First, we suppose that the valuation function of every player is a single interval with a special property, namely ordering property. For this case, we...
Fair and Efficient Cake Cutting
, M.Sc. Thesis Sharif University of Technology ; Ghodsi, Mohammad (Supervisor)
Abstract
Cake Cutting is an old problem that studies how to allocate a resource among a number of agents to achieve fairness or maximize the revenue by selling the chunks fairly. The primary assumption in the conventional methods of studying Cake Cutting was that the allocator knows everything about the agents and their valuation functions for the different cuts of the cake, which could be impossible in real life. Here we addressed a new setting for an online Cake Cutting problem with unconnected pieces and studied four different objectives upon the setting. There we studied fair and efficient Online Cake Cutting by means of linear fairness and envy freeness. We also added a payment rule to study the...