Lars Ehlers

Coalitional Strategy-Proof House Allocation

Abstract We consider house allocation without endowments. We show that there is a unique maximal domain including all strict preferences on which efficiency and coalitional strategy-proofness are compatible. A preference relation belongs to the unique maximal domain if it is a strict descending ranking of houses to a certain house and indifference holds over it and the remaining houses. We also show that on this domain mixed dictator-pairwise-exchange rules are the only rules satisfying efficiency and coalitional strategy-proofness. Journal of Economic Literature Classification Numbers: C78, D63, D71.

Coalitional strategy-proof and resource-monotonic solutions for multiple assignment problems

We consider the problem of allocating indivisible objects when agents may desire to consume more than one object and monetary transfers are not possible. Each agent receives a set of objects and free disposal is allowed. We are interested in allocation rules that satisfy “appealing” properties from an economic and social point of view. Our main result shows that sequential dictatorships are the only efficient and coalitional strategy-proof solutions to the multiple assignment problem. Adding resource-monotonicity narrows this class down to serial dictatorships.

Truncation Strategies in Matching Markets

Roth and Rothblum [Roth, A. E., U. G. Rothblum. 1999. Truncation strategies in matching markets---In search of advice for participants. Econometrica67 21--43] showed that for matching markets using the deferred acceptance algorithm a physician with symmetric (incomplete) information possibly gains only by truncating her true ranking. We show that in symmetric information environments this result is identical for all priority mechanisms and all linear programming mechanisms introduced in British entry-level medical markets and in public school choice in some American cities.

Strategy-proofness and population-monotonicity for house allocation problems

Abstract We study a simple model of assigning indivisible objects to agents, such as dorm rooms to students, or offices to professors, where each agent receives at most one object and monetary compensations are not possible. For these problems population-monotonicity, which requires that agents are affected by population changes in the same way, is a compelling property because tentative assignments are made in many typical situations, which may have to be revised later to take into account the changing population. We completely describe the allocation rules satisfying population-monotonicity, strategy-proofness, and efficiency. The characterized rules assign the objects by an iterative procedure in which at each step no more than two agents “trade” objects from their hierarchically specified “endowments.”

Strategy-Proof Probabilistic Decision Schemes for One-Dimensional Single-Peaked Preferences

Abstract Collective decision problems are considered with a finite number of agents who have single-peaked preferences on the real line. A probabilistic decision scheme assigns a probability distribution over the real line to every profile of reported preferences. The main result of the paper is a characterization of the class of unanimous and strategy-proof probabilistic schemes with the aid of fixed probability distributions that play a role similar to that of the phantom voters in H. Moulin ( Public Choice 35 (1980), 437–455). Thereby, the work of Moulin (1980) is extended to the probabilistic framework. Journal of Economic Literature Classification Numbers: D71, D81.

Von Neumann-Morgenstern stable sets in matching problems

The following properties of the core of a one well-known: (i) the core is non-empty; (ii) the core is a lattice; and (iii) the set of unmatched agents is identical for any two matchings belonging to the core. The literature on two-sided matching focuses almost exclusively on the core and studies extensively its properties. Our main result is the following characterization of (von Neumann-Morgenstern) stable sets in one-to-one matching problem only if it is a maximal set satisfying the following properties : (a) the core is a subset of the set; (b) the set is a lattice; (c) the set of unmatched agents is identical for any two matchings belonging to the set. Furthermore, a set is a stable set if it is the unique maximal set satisfying properties (a), (b) and (c). We also show that our main result does not extend from one-to-one matching problems to many-to-one matching problems.

Incomplete information and singleton cores in matching markets

We study ordinal Bayesian Nash equilibria of stable mechanisms in centralized matching markets under incomplete information. We show that truth-telling is an ordinal Bayesian Nash equilibrium of the revelation game induced by a common belief and a stable mechanism if and only if all the profiles in the support of the common belief have singleton cores. Our result matches the observations of Roth and Peranson [The redesign of the matching market for American physicians: some engineering aspects of economic design, Amer. Econ. Rev. 89 (1999) 748–780] in the National Resident Matching Program (NRMP) in the United States: (i) the cores of the profiles submitted to the clearinghouse are small and (ii) while truth-telling is not a dominant strategy most participants in the NRMP truthfully reveal their preferences.

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.

In search of advice for participants in matching markets which use the deferred-acceptance algorithm

Many centralized entry-level labor markets use the firm-proposing deferred-acceptance (DA) algorithm to compute the matching that is implemented among workers and firms. We propose a definition of the strategic options a worker faces in the DA-algorithm. Then we develop a theory to advise workers who distinguish between the firms from which they believe not to receive a proposal, the firms from which they might receive a proposal, and the firms from which they certainly receive a proposal. If a worker is not able to deduce which new proposals she receives after having rejected others, then it is not profitable for her to submit a list that reverses the true ranking of any two acceptable firms. Furthermore, it is not beneficial for her to include a firm in her submitted list that is unacceptable to her.

Efficient priority rules

We study the assignment of indivisible objects with quotas (universities, jobs, or offices) to a set of agents (students, job applicants, or professors). Each agent receives at most one object and monetary compensations are not possible. We characterize efficient priority rules by efficiency, strategy-proofness, and reallocation-consistency. Such a rule respects an acyclic priority structure and the allocations are determined using the deferred acceptance algorithm.