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- Title
Dominance invariant one-to-one matching problems.
- Authors
Mauleon, Ana; Molis, Elena; Vannetelbosch, Vincent; Vergote, Wouter
- Abstract
Solution concepts in social environments use either a direct or indirect dominance relationship, depending on whether it is assumed that agents are myopic or farsighted. Direct dominance implies indirect dominance, but not the reverse. Hence, the predicted outcomes when assuming myopic (direct) or farsighted (indirect) agents could be very different. In this paper, we characterize dominance invariant one-to-one matching problems when preferences are strict. That is, we obtain the conditions on preference profiles such that indirect dominance implies direct dominance in these problems and give them an intuitive interpretation. Whenever some of the conditions are not satisfied, it is important to understand whether the agents are myopic or farsighted in order to use the appropriate stability concept. Furthermore, we characterize dominance invariant one-to-one matching problems having a non-empty core. Finally, we show that, if the core of a dominance invariant one-to-one matching problem is not empty, it contains a unique matching, the dominance invariant stable matching, in which all agents who mutually top rank each other are matched to one another and all other agents remain unmatched.
- Subjects
INVARIANTS (Mathematics); MATCHING theory; SOCIAL context; SECRETARY problem (Probability theory); ECONOMIC equilibrium
- Publication
International Journal of Game Theory, 2014, Vol 43, Issue 4, p925
- ISSN
0020-7276
- Publication type
Article
- DOI
10.1007/s00182-014-0411-4