  We study classic fair-division problems in a partial information setting.
This paper respectively addresses fair division of rent, cake, and indivisible
goods among agents with cardinal preferences. We will show that, for all of
these settings and under appropriate valuations, a fair (or an approximately
fair) division among n agents can be efficiently computed using only the
valuations of n-1 agents. The nth (secretive) agent can make an arbitrary
selection after the division has been proposed and, irrespective of her choice,
the computed division will admit an overall fair allocation.
  For the rent-division setting we prove that the (well-behaved) utilities of
n-1 agents suffice to find a rent division among n rooms such that, for every
possible room selection of the secretive agent, there exists an allocation (of
the remaining n-1 rooms among the n-1 agents) which ensures overall envy
freeness (fairness). We complement this existential result by developing a
polynomial-time algorithm that finds such a fair rent division under
quasilinear utilities.
  In this partial information setting, we also develop efficient algorithms to
compute allocations that are envy-free up to one good (EF1) and
epsilon-approximate envy free. These two notions of fairness are applicable in
the context of indivisible goods and divisible goods (cake cutting),
respectively. This work also addresses fairness in terms of proportionality and
maximin shares. Our key result here is an efficient algorithm that, even with a
secretive agent, finds a 1/19-approximate maximin fair allocation (of
indivisible goods) under submodular valuations of the non-secretive agents.
  One of the main technical contributions of this paper is the development of
novel connections between different fair-division paradigms, e.g., we use our
existential results for envy-free rent-division to develop an efficient EF1
algorithm.

Computer Science and Game Theory