  In fair division applications, agents may have unequal entitlements
reflecting their different contributions. Moreover, the contributions of agents
may depend on the allocation itself. Previous fairness notions designed for
agents with equal or pre-determined entitlement fail to characterize fairness
in these collaborative allocation scenarios.
  We propose a novel fairness notion of average envy-freeness (AEF), where the
envy of agents is defined on the average value of items in the bundles. Average
envy-freeness provides a reasonable comparison between agents based on the
items they receive and reflects their entitlements. We study the complexity of
finding AEF and its relaxation, average envy-freeness up to one item (AEF-1).
While deciding if an AEF allocation exists is NP-complete, an AEF-1 allocation
is guaranteed to exist and can be computed in polynomial time. We also study
allocation with quotas, i.e. restrictions on the sizes of bundles. We prove
that finding AEF-1 allocation satisfying a quota is NP-hard. Nevertheless, in
the instances with a fixed number of agents, we propose polynomial-time
algorithms to find AEF-1 allocation with a quota for binary valuation and
approximated AEF-1 allocation with a quota for general valuation.
