Abstract:
A new and relatively elementary approach is proposed for solving the problem of
fair division of a continuous resource (measurable space, pie, etc.) between several participants,
the selection criteria of which are described by charges (signed measures). The setting of the
problem with charges is considered for the first time. The problem comes down to analyzing
properties of trajectories of a specially constructed dynamical system acting in the space of
finite measurable partitions. Exponentially fast convergence to a limit solution is proved for
both the case of true measures and the case of charges.
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