Absence-proofness: A new cooperative stability concept

 (Job Market Paper)

We introduce a new cooperative stability concept, absence-proofness (AP). Given an allocation problem in a society N, and a solution well defined for all subsocieties, a group of people S in N may benefit by leaving a subgroup T in S “out” of the allocation process. After the allocation takes place in the society N\T, agents in S\T may reallocate what they received, plus the endowments of T (if they have any) among all of S. This reallocation is profitable if it is Pareto superior to what S would get in the society N had T not been left aside. We call the solutions that are immune to this kind of manipulations absence-proof. Absence-proofness implies core stability by definition. In fair division problems, where core has no bite, AP imposes core-like participation constraints on solutions. In both fair division problems and TU games, well-known population-monotonicity (PM) property implies AP. Although solutions that are AP but not PM exist for very specific problems, our work suggests that these properties have very close formal implications. In exchange economies with private endowments we provide many negative results. Particularly, the Walrasian allocation rule is manipulable.

Strongly stable and responsive cost sharing solutions for minimum cost spanning tree problems

On the cost sharing solutions to a minimum cost sharing problem, we define a strong stability property absence-proofness that implies stand alone core stability. We show that the famous Bird and Dutta-Kar solutions as well as all non-separable solutions fail this property while all population monotonic solutions are strongly stable. We also propose a family of strongly stable solutions that are easy to compute and more responsive than the well-known folk solution to the asymmetries in the cost data.

Population monotonicity in fair division of multiple indivisible goods

We consider the fair division of a set of indivisible items where each agent can get more than one good and monetary transfers are allowed. For the problems with three or more goods, population monotonicity is incompatible with efficiency except for very specific Cartesian product preference domains. For the 2-goods case, Shapley solution and the constrained egalitarian solution is PM on the subadditive preference domain. We also define hybrid solutions that are PM on the full domain. Among them, the hybrid Shapley solution is PM.

“Arrovian impossibilities in aggregating preferences over non-resolute outcomes”

(with Remzi Sanver), Social Choice and Welfare, 2008, 30 (3), 495-506.

Let A be the set of alternatives whose power set is A. Elements of A are interpreted as non-resolute outcomes.We consider the aggregation of preference profiles over A into a (social) preference over A. In case we allow individuals to have any complete and transitive preference over A, Arrow’s impossibility theorem naturally applies. However, the Arrovian impossibility prevails, even when the set of admissible preferences over A is severely restricted. In fact, we identify a mild “regularity” condition which ensures the dictatoriality of a domain. Regularity is compatible with almost all standard extension axioms of the literature. Thus, we interpret our results as the strong prevalence of Arrow’s impossibility theorem in aggregating preferences over non-resolute outcomes.

“On the alternating use of “unanimity and “surjectivity” in the Gibbard-Satterthwaite Theorem”

(with Remzi Sanver), Economics Letters, 2007, 96 (1), 140-143.

Surjectivity and unanimity can be equivalently used to state the Gibbard-Satterhwaite Theorem. On the other hand, over restricted domains, replacing surjectivity with unanimity makes a stronger statement.

An egalitarian solution for minimum cost spanning tree problems

(with Barış Esmerok)

We ask for equitable allocations in cost sharing of a spanning tree with minimal cost based on two criteria: Lorenz domination and leximin domination. We give an easy algorithm to calculate the unique allocation that both Lorenz dominates and leximin dominates every other allocation in the irreducible core of the associated cost sharing game.  There is still a lot of work to do here. First one is to characterize this solution. Then, the next move is to find an algorithm that calculates the leximin dominant vector in the stand alone core, not in the irreducible core, and axiomatically compare these two solutions.