Anna Bogomolnaia

The Stability of Hedonic Coalition Structures

We consider the partitioning of a society into coalitions in purely hedonic settings, i.e., where each players payoff is completely determined by the identity of other members of her coalition. We first discuss how hedonic and nonhedonic settings differ and some sufficient conditions for the existence of core stable coalition partitions in hedonic settings. We then focus on a weaker stability condition: individual stability, where no player can benefit from moving to another coalition while not hurting the members of that new coalition. We show that if coalitions can be ordered according to some characteristic over which players have single-peaked preferences, or where players have symmetric and additively separable preferences, then there exists an individually stable coalition partition. Examples show that without these conditions, individually stable coalition partitions may not exist. We also discuss some other stability concepts, and the incompatibility of stability with other normative properties. Journal of Economic Literature Classification Numbers: C71, A14, D20.

A New Solution to the Random Assignment Problem

A random assignment is ordinally efficient if it is not stochastically dominated with respect to individual preferences over sure objects. Ordinal efficiency implies (is implied by) ex post (ex ante) efficiency. A simple algorithm characterizes ordinally efficient assignments: our solution, probabilistic serial (PS), is a central element within their set. Random priority (RP) orders agents from the uniform distribution, then lets them choose successively their best remaining object. RP is ex post, but not always ordinally, efficient. PS is envy-free, RP is not; RP is strategy-proof, PS is not. Ordinal efficiency, Strategyproofness, and equal treatment of equals are incompatible. Journal of Economic Literature Classification Numbers: C78, D61, D63.

Sharing a minimal cost spanning tree: Beyond the Folk solution

Several authors recently proposed an elegant construction to divide the minimal cost of connecting a given set of users to a source. This folk solution applies the Shapley value to the largest reduction of the cost matrix that does not affect the efficient cost. It is also obtained by the linear decomposition of the cost matrix in the canonical basis. Because it relies on the irreducible cost matrix, the folk solution ignores interpersonal differences in relevant connecting costs. We propose alternative solutions, some of them arbitrarily close to the folk solution, to resolve this difficulty.

Probabilistic Assignment of Objects: Characterizing the Serial Rule

We study the problem of assigning a set of objects to a set of agents, when each agent receives one object and has strict preferences over the objects. In the absence of monetary transfers, we focus on the probabilistic rules, which take the ordinal preferences as input. We characterize the serial rule, proposed by Bogomolnaia and Moulin (2001) [2]: it is the only rule satisfying sd efficiency, sd no-envy, and bounded invariance. A special representation of feasible assignment matrices by means of consumption processes is the key to the simple and intuitive proof of our main result.

Strategy-Proof Probabilistic Rules for Expected Utility Maximizers

We consider social choice rules which select a lottery over outcomes for each progile of individual preferences. Agents are assumed to have preferences over lotteries satisfying the axioms of expected utility. We exhibit a large class of rules satisfying strategy- proofness.

Strategy-proof assignment on the full preference domain

We consider the problem of efficiently allocating several indivisible objects between agents who are to receive at most one object and whose preferences are private information. We examine this standard “assignment” problem from the perspective of mechanism design giving up the usual assumption of linear preferences and instead using a full preference domain (with indifferences permitted). We characterize two classes of mechanisms: (i) Bi-polar Serially Dictatorial Rules by Essential Single-Valuedness, Pareto Indifference, Strategy-Proofness and Non-Bossiness; and (ii) all selections from Bi-polar Serially Dictatorial Rules by Single-Valuedness, Efficiency, Strategy-Proofness and Weak Non-Bossiness. We compare the outcomes from the (Bi-polar) Serially Dictatorial Rules with the outcomes obtained using a market based approach, namely the “core” of the market. We show that all strongly efficient outcomes in the core can be generated using Serially Dictatorial Rules. Moreover, we argue that Serially Dictatorial Rules have an advantage over the market based approach in that they yield strongly efficient solutions for all preference profiles, making it possible to use randomization to restore equity. When preferences are private information, this type of ex ante equity cannot be implemented using the market based approach.

Random assignment: redefining the serial rule

We provide a new, welfarist, interpretation of the well-known Serial rule in the random assignment problem, strikingly different from previous attempts to define or axiomatically characterize this rule.

Stability Under Unanimous Consent, Free Mobility and Core

In this paper, we consider a population represented by a continuum of individuals uniformly distributed over the unit interval that faces a problem of location and financing of public facilities under the equal share rule. We examine three notions of stability of emerging jurisdiction structures (stability under unanimous consent, free mobility and core) and provide a characterization of stable structures.

Size versus fairness in the assignment problem

When not all objects are acceptable to all agents, maximizing the number of objects actually assigned is an important design concern. We compute the guaranteed size ratio of the Probabilistic Serial mechanism, i.e., the worst ratio of the actual expected size to the maximal feasible size. It converges decreasingly to 1−1e≃63.2% as the maximal size increases. It is the best ratio of any Envy-Free assignment mechanism.

The Egalitarian Sharing Rule in Provision of Public Projects

In this note we consider a society that partitions itself into disjoint jurisdictions, each choosing a location of its public project and a taxation scheme to finance it. The set of public project is multi-dimensional, and their costs could vary from jurisdiction to jurisdiction. We impose two principles, egalitarianism, that requires the equalization of the total cost for all agents in the same jurisdiction, and efficiency, that implies the minimization of the aggregate total cost within jurisdiction. We show that these two principles always yield a core-stable partition but a Nash stable partition may fail to exist.