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0. Preface; 1. Notation and preliminaries; 2. Geometric object #1a: the individual pieces set (IPS) for two players; 3. What the IPS tells us about fairness and efficiency in the two-player context; 4. The general case of n players; 5. What the IPS and the FIPS tell us about fairness and efficiency in the n-player context; 6. Characterizing Pareto optimality: introduction and preliminary ideas; 7. Characterizing Pareto optimality I: the IPS and optimization of convex combinations of measures; 8. Characterizing Pareto optimality II: partition ratios; 9. Geometric object #2: The Radon-Nikodym set (RNS); 10. Characterizing Pareto optimality III: the RNS, Weller's construction, and w-association; 11. The shape of the IPS; 12. The relationship between the IPS and the RNS; 13. Other issues involving Weller's construction, partition ratios, and Pareto optimality; 14. Strong Pareto optimality; 15. Characterizing Pareto optimality using hyperreal numbers; 16. The multi-cake individual pieces set (MIPS): symmetry restored.
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Add The geometry of efficient fair division, 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 , The geometry of efficient fair division to the inventory that you are selling on WonderClubX
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Add The geometry of efficient fair division, 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 , The geometry of efficient fair division to your collection on WonderClub |