Mathematical Programming

, Volume 83, Issue 1, pp 291–311

On finding an envy-free Pareto-optimal division

  • J. H. Reijnierse
  • J. A. M. Potters

DOI: 10.1007/BF02680564

Cite this article as:
Reijnierse, J.H. & Potters, J.A.M. Mathematical Programming (1998) 83: 291. doi:10.1007/BF02680564


This paper describes an algorithm to find an (α-)envy-free Pareto-optimal division in the case of a finite number of homogeneous infinitely divisible goods and linear utility functions. It is used to find an allocation in the classical cake division problem that is almost Pareto-optimal and α-envy-free.


Envy-freeness Pareto-optimality Walras equilibrium 

Copyright information

© The Mathematical Programing, Society, Inc 1998

Authors and Affiliations

  • J. H. Reijnierse
    • 1
  • J. A. M. Potters
    • 1
  1. 1.Department of MathematicsUniversity of NijmegenNijmegenThe Netherlands

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