We provide axiomatic characterizations of two natural families of rules for aggregating equivalence relations: the family of join aggregators and the family of meet aggregators. The central conditions in these characterizations are two separability axioms. Disjunctive separability, neutrality,...

For the class of tree games, a new solution called the average tree solution has been proposed recently. We provide a characterization of this solution. This characterization underlines an important difference, in terms of symmetric treatment of the agents, between the average tree solution and...

We consider dominant strategy implementation in private values settings, when agents have multi-dimensional types, the set of alternatives is finite, monetary transfers are allowed, and agents have quasi-linear utilities. We show that any implementable and neutral social choice function must be...

We study mechanism design in a setting where agents know their types but are uncertain about the utility from any alternative. The lnal realized utility of each agent is observed by the principal and can be contracted upon. In such environments, the principal is not restricted to using only...

We study deterministic single object auctions in private values environments. We show that a deterministic allocation rule is implementable (in dominant strategies) if and only if it is a generalized utility maximizer. With a mild continuity condition, we show that a deterministic allocation...

We study mechanism design in quasi-linear environments when there are two alternatives. We show that under a mild range condition, every implementable deterministic allocation rule is a generalized utility function maximizer. In unbounded domains, if we replace our range condition by an...

We consider implementation of a deterministic allocation rule using transfers in quasi-linear private values environments. We show that if the type space is a multidimensional domain satisfying some ordinal restrictions, then an allocation rule is implementable in such a domain if and only if it...

We consider the problem of choosing a partition of a set of objects by a set of agents. The private information of each agent is a strict ordering over the set of partitions of the objects. A social choice function chooses a partition given the reported preferences of the agents. We impose a...

We consider deterministic dominant strategy implementation in multidimensional dichotomous domains in private values and quasi-linear utility setting. In such multidimensional domains, an agent's type is characterized by a single number, the value of the agent, and a non-empty subset of...

We study an economy where a collection of indivisible goods are sold to a set of buyers who want to buy at most one good. We characterize the set of Walrasian equilibrium price vectors in such an economy using sets of overdemanded and underdemanded goods. Further, we give characterizations for...