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The stability of the equilibrium outcomes in the admission games induced by stable matching rules
(SPRINGER HEIDELBERG, 2008)
A stable matching rule is used as the outcome function for the Admission game where colleges behave straightforwardly and the students` strategies are given by their preferences over the colleges. We show that the ...
The pareto-stability concept is a natural solution concept for discrete matching markets with indifferences
(SPRINGER HEIDELBERG, 2011)
In a decentralized setting the game-theoretical predictions are that only strong blockings are allowed to rupture the structure of a matching. This paper argues that, under indifferences, also weak blockings should be ...
A characterization of strongly stable fractional matchings
(Springer, 2019-07)
In this paper, we characterize the strongly stable fractional matchings for the marriage model as the union of the convex hull of connected sets of stable matchings. Moreover, we present an algorithm that computes the set ...
The roommate problem with externalities
(Springer, 2020)
This paper extends the roommate problem to include externalities, allowing preferences for a partner to depend on the situation of others. Stability concepts for matchings and partitions of the set of agents are proposed ...
Single agents and the set of many-to-one stable matching
(Academic Press, 2000-03)
Some properties of the set of many-to-one stable matchings for firms that have responsive preferences and quotas are not necessarily true when firms' preferences are substitutable. In particular, we provide examples in ...
A note on the multiple partners assignment game
(ELSEVIER SCIENCE SA, 2010)
In the assignment game of Shapley and Shubik [Shapley, L.S., Shubik, M., 1972. The assignment game. I. The core, International journal of Game Theory 1, 11-130] agents are allowed to form one partnership at most. That paper ...
Binary Operations for the Lattice Structure in a Many-to-Many Matching Model
(Springer, 2019-05)
The lattice structure of the set of stable matchings in many-to-many matching model is well known in literature. If preferences of the agents are substitutable, this result can be obtained by fixed-point methods, for that ...
The Blocking Lemma for a many-to-one matching model
(Elsevier Science, 2010-09)
The Blocking Lemma identifies a particular blocking pair for each non-stable and individually rational matching that is preferred by some agents of one side of the market to their optimal stable matching. Its interest lies ...
Stable Matchings in the Marriage Model with Indifferences
(Operations Research Society of China, 2020-08)
For the marriage model with indifferences, we define an equivalence relation over the stable matching set. We identify a sufficient condition, the closing property, under which we can extend results of the classical model ...