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Books > Science & Mathematics > Mathematics > Geometry
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The Geometry of Efficient Fair Division (Hardcover, New)
Loot Price: R4,243
Discovery Miles 42 430
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The Geometry of Efficient Fair Division (Hardcover, New)
Expected to ship within 12 - 19 working days
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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.
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