On Interim Envy-Free Allocation Lotteries

by   Ioannis Caragiannis, et al.

With very few exceptions, recent research in fair division has mostly focused on deterministic allocations. Deviating from this trend, we study the fairness notion of interim envy-freeness (iEF) for lotteries over allocations, which serves as a sweet spot between the too stringent notion of ex-post envy-freeness and the very weak notion of ex-ante envy-freeness. iEF is a natural generalization of envy-freeness to random allocations in the sense that a deterministic envy-free allocation is iEF (when viewed as a degenerate lottery). It is also certainly meaningful as it allows for a richer solution space, which includes solutions that are provably better than envy-freeness according to several criteria. Our analysis relates iEF to other fairness notions as well, and reveals tradeoffs between iEF and efficiency. Even though several of our results apply to general fair division problems, we are particularly interested in instances with equal numbers of agents and items where allocations are perfect matchings of the items to the agents. Envy-freeness can be trivially decided and (when it can be achieved, it) implies full efficiency in this setting. Although computing iEF allocations in matching allocation instances is considerably more challenging, we show how to compute them in polynomial time, while also maximizing several efficiency objectives. Our algorithms use the ellipsoid method for linear programming and efficient solutions to a novel variant of the bipartite matching problem as a separation oracle. We also study the extension of interim envy-freeness notion when payments to or from the agents are allowed. We present a series of results on two optimization problems, including a generalization of the classical rent division problem to random allocations using interim envy-freeness as the solution concept.


page 1

page 2

page 3

page 4


Fair Division of Mixed Divisible and Indivisible Goods

We study the problem of fair division when the resources contain both di...

On the complexity of Pareto-optimal and envy-free lotteries

We study the classic problem of dividing a collection of indivisible res...

Average Envy-freeness for Indivisible Items

In fair division applications, agents may have unequal entitlements refl...

Fair and Efficient Allocation of Indivisible Chores with Surplus

We study fair division of indivisible chores among n agents with additiv...

Communication Complexity of Discrete Fair Division

We initiate the study of the communication complexity of fair division w...

Best of Both Worlds: Agents with Entitlements

Fair division of indivisible goods is a central challenge in artificial ...

Picking Sequences and Monotonicity in Weighted Fair Division

We study the problem of fairly allocating indivisible items to agents wi...

Please sign up or login with your details

Forgot password? Click here to reset