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Matching market models ignore prior commitments. Yet many job seekers, for example, are already employed, and the same holds for many other matching markets. I analyze two-sided matching markets with pre-existing binding agreements between…
In two-sided matching markets, the agents are partitioned into two sets. Each agent wishes to be matched to an agent in the other set and has a strict preference over these potential matches. A matching is stable if there are no blocking…
This paper proposes a reformulation of the scenario-based two-stage unit commitment problem under uncertainty that allows finding unit-commitment plans that perform reasonably well both in expectation and for the worst case realization of…
It is well-known that wave-type equations with memory, under appropriate assumptions on the memory kernel, are uniformly exponentially stable. On the other hand, time delay effects may destroy this behavior. Here, we consider the…
While the stable marriage problem and its variants model a vast range of matching markets, they fail to capture complex agent relationships, such as the affiliation of applicants and employers in an interview marketplace. To model this…
The Secretary problem is a classical sequential decision-making question that can be succinctly described as follows: a set of rank-ordered applicants are interviewed sequentially for a single position. Once an applicant is interviewed, an…
I introduce a stability notion, dynamic stability, for two-sided dynamic matching markets where (i) matching opportunities arrive over time, (ii) matching is one-to-one, and (iii) matching is irreversible. The definition addresses two…
The Deferred Acceptance (DA) algorithm is an elegant procedure for finding a stable matching in two-sided matching markets. It ensures that no pair of agents prefers each other to their matched partners. In this work, we initiate the study…
Matching algorithms have demonstrated great success in several practical applications, but they often require centralized coordination and plentiful information. In many modern online marketplaces, agents must independently seek out and…
Increasing aggregate diversity (or catalog coverage) is an important system-level objective in many recommendation domains where it may be desirable to mitigate the popularity bias and to improve the coverage of long-tail items in…
The stable marriage problem is a well-known problem of matching men to women so that no man and woman who are not married to each other both prefer each other. Such a problem has a wide variety of practical applications ranging from…
The Stable Roommates problem involves matching a set of agents into pairs based on the agents' strict ordinal preference lists. The matching must be stable, meaning that no two agents strictly prefer each other to their assigned partners. A…
Assume that $n = 2k$ potential roommates each have an ordered preference of the $n-1$ others. A stable matching is a perfect matching of the $n$ roommates in which no two unmatched people prefer each other to their matched partners. In…
We consider the stability of matchings when individuals strategically submit preference information to a publicly known algorithm. Most pure Nash equilibria of the ensuing game yield a matching that is unstable with respect to the…
Some aspects of the problem of stable marriage are discussed. There are two distinguished marriage plans: the fully transferable case, where money can be transferred between the participants, and the fully non transferable case where each…
The standard two-sided and one-sided matching problems, and the closely related school choice problem, have been widely studied from an axiomatic viewpoint. A small number of algorithms dominate the literature. For two-sided matching, the…
Consider the object allocation (one-sided matching) model of Shapley and Scarf (1974). When final allocations are observed but agents' preferences are unknown, when might the allocation be in the core? This is a one-sided analogue of the…
In this note, we present a simpler algorithm for joint seat allocation problem in case there are two or more merit lists. In case of two lists (the current situation for Engineering seats in India), the running time of the algorithm is…
We consider an occupation market in which preferences of members are treated as non linear general increasing functions. The arrangement of members is separated into two non over-lapping sets, set of workers and set of firms. We consider…
We consider a finite horizon optimal stopping problem related to trade-off strategies between expected profit and cost cash-flows of an investment under uncertainty. The optimal problem is first formulated in terms of a system of Snell…