  The chore division problem simulates the fair division of a heterogeneous,
undesirable resource among several agents. In the fair division of chores, each
agent only gets the disutility from its own piece. Agents may, however, also be
concerned with the pieces given to other agents; these externalities naturally
appear in fair division situations. We first demonstrate the generalization of
the classical concepts of proportionality and envy-freeness while extending the
classical model by taking externalities into account.
