Bettina Klaus

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.

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.”

Stochastic stability for roommate markets

We show that for any roommate market the set of stochastically stable matchings coincides with the set of absorbing matchings. This implies that whenever the core is non-empty (e.g., for marriage markets), a matching is in the core if and only if it is stochastically stable, i.e., stochastic stability is a characteristic of the core. Several solution concepts have been proposed to extend the core to all roommate markets (including those with an empty core). An important implication of our results is that the set of absorbing matchings is the only solution concept that is core consistent and shares the stochastic stability characteristic with the core.

Median Stable Matching for College Admissions

We give a simple and concise proof that so-called generalized median stable matchings are well-defined for college admissions problems. Furthermore, we discuss the fairness properties of median stable matchings and conclude with two illustrative examples of college admissions markets, the lattices of stable matchings, and the corresponding generalized median stable matchings.

Strategy-proofness, solidarity, and consistency for multiple assignment problems

Abstract. We consider a problem of allocating indivisible objects when agents may desire to consume more than one object and no monetary transfers are allowed. We are interested in allocation rules that satisfy desirable properties from an economic and social point of view. In addition to strategy-proofness and Pareto efficiency, we consider consistency and two solidarity properties (replacement-domination and population-monotonicity). In most of the cases, these properties are satisfied only by serially dictatorial rules.

Strategy-proof division of a private good when preferences are single-dipped

Abstract Pareto-optimal and strategy-proof distributions of a perfectly divisible good among agents with single-dipped preferences are studied. In order to satisfy these two properties and, in addition, either a so-called replacement property or a property of consistency, the whole amount should be assigned to one of the agents. Characterizations of the two classes of division rules satisfying the above conditions are provided.

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.

Manipulation via Endowments in Exchange Markets with Indivisible Goods

We consider exchange markets with heterogeneous indivisible goods. We are interested in exchange rules that are efficient and immune to manipulations via endowments (either with respect to hiding or destroying part of the endowment or transferring part of the endowment to another trader). We consider three manipulability axioms: hiding-proofness, destruction-proofness, and transfer-proofness. We prove that no rule satisfying efficiency and hiding-proofness (which together imply individual rationality) exists. For two agents with separable and responsive preferences, we show that efficient, individually rational, and destruction-proof rules exist. However, for some profiles of separable preferences, no rule is efficient, individually rational, and destruction-proof. In the case of transfer-proofness the compatibility with efficiency and individual rationality for the two-agent case extends to the unrestricted domain. If there are more than two agents, for some profiles of separable preferences, no rule is efficient, individually rational, and transfer-proof.

Coalitional Strategy-Proofness in Economies with Single-Dipped Preferences and the Assignment of an Indivisible Object

We study two allocation models. In the first model, we consider the problem of allocating an infinitely divisible commodity among agents with single-dipped preferences. In the second model, a degenerate case of the first one, we study the allocation of an indivisible object to a group of agents. Our main result is the characterization of the class of Pareto optimal and coalitionally strategy-proof allocation rules. Alternatively, this class of rules, which largely consists of serially dictatorial components, can be characterized by Pareto optimality, strategy-proofness, and weak non-bossiness (in terms of welfare). Furthermore, we study properties of fairness such as anonymity and no-envy. Journal of Economic Literature Classification Numbers: D63, D71.

Solidarity and Probabilistic Target Rules

A metal detector comprising a sensor coil positioned relative to an excited field coil for minimum mutual inductive coupling therebetween to provide a null output from the sensor coil in the absence of objects to be detected. The coils are rigidly secured in a lightweight epoxy casting to preclude deformation of the coils and relative displacement therebetween under varying environmental conditions to preclude drift of the null output. Low frequency excitation on the order of a few hundred up to a few thousand hertz is applied to the field coil to obtain a high degree of insensitivity to moisture conditions existing in the vicinity of the detector for further maintaining constancy of the null output. An auto-nulling circuit for automatically compensating for any long term drift of the detector output is also optionally included.