The Geometry Of Efficient Fair Division 2005 Edition at Meripustak

The Geometry Of Efficient Fair Division 2005 Edition

Books from same Author: Julius B. Barbanel, Alan D. Taylor

Books from same Publisher: CAMBRIDGE

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  • General Information  
    Author(s)Julius B. Barbanel, Alan D. Taylor
    PublisherCAMBRIDGE
    ISBN9780521842488
    Pages472
    BindingHardback
    LanguageEnglish
    Publish YearJanuary 2005

    Description

    CAMBRIDGE The Geometry Of Efficient Fair Division 2005 Edition by Julius B. Barbanel, Alan D. Taylor

    What is the best way to divide a 'cake' and allocate the pieces among some finite collection of players? In this book, the cake is a measure space, and each player uses a countably additive, non-atomic probability measure to evaluate the size of the pieces of cake, with different players generally using different measures. The author investigates efficiency properties (is there another partition that would make everyone at least as happy, and would make at least one player happier, than the present partition?) and fairness properties (do all players think that their piece is at least as large as every other player's piece?). He focuses exclusively on abstract existence results rather than algorithms, and on the geometric objects that arise naturally in this context. By examining the shape of these objects and the relationship between them, he demonstrates results concerning the existence of efficient and fair partitions.