Cambridge University Press The Geometry of Efficient Fair Division - Cambridge University Press

Explore the mathematical complexities of resource allocation with The Geometry of Efficient Fair Division from Cambridge University Press. This academic text addresses a fundamental question: what is the most effective way to divide a cake and allocate pieces among a finite collection of players? Moving beyond simple division, this book treats the cake as a measure space. It examines scenarios where each player uses a countably additive, non-atomic probability measure to evaluate the size of their pieces. Because different players generally use different measures, the book provides a rigorous look at how subjective value impacts division. Readers will gain a deep understanding of efficiency properties, investigating whether alternative partitions exist that could make one player happier without making others less happy. The text also analyzes fairness properties to determine if all players perceive their piece as being at least as large as others. This work is a vital resource for those studying the theory and philosophy of economics and mathematical division.