Ankara : The Department of Economics, İhsan Doğramacı Bilkent University, 2011.Thesis (Ph. D.) -- Bilkent University, 2011.Includes bibliographical references leaves 161-165.This thesis consists of four main chapters. In the first main part, hedonic coalition
formation games where each player’s preferences rely only upon the members of her
coalition are studied. A new stability notion under free exit-free entry membership
rights, referred to as strong Nash stability, is introduced which is stronger than both
core and Nash stabilities studied earlier in the literature. The weak top-choice property
is introduced and shown to be sufficient for the existence of a strongly Nash stable partition.
It is also shown that descending separable preferences guarantee the existence
of a strongly Nash stable partition. Strong Nash stability under different membership
rights is also studied. In the first main part, hedonic coalition formation games are
also extended to cover formation games, where a player can be a member of several
different coalitions, and these games are studied. In the second main part, Nash implementability
of a social choice rule (via a mechanism) which is implementable via
a Rechtsstaat is studied. A new condition on a Rechtsstaat, referred to as equal treatment
of equivalent alternatives (ET EA), is introduced, and it is shown that if a social
choice rule is implementable via some Rechtsstaat satisfying ET EA then it is Nash
implementable via a mechanism provided that there are at least three agents in the society.
In the third main part, a characterization of the Borda rule on the domain of weak
preferences is studied. A new property, which is referred to as the degree equality,
is introduced, and it is shown that the Borda rule is characterized by weak neutrality,
reinforcement, faithfulness and degree equality. In the fourth main part, the graduate
admissions problem with quota and budget constraints is studied as a two sided many
to one matching market. The students proposing algorithm, which is an extension of
the Gale-Shapley algorithm, is constructed, and it is shown that the students proposing
algorithm ends up with a core stable matching if the algorithm stops. However, there
exist graduate admissions problems for which there exist core stable matchings, while
neither the departments proposing nor the students proposing algorithm stops. It is
proved that the students proposing algorithm stops if and only if no cycle occurs in
the algorithm. It is also shown that no random path to core stability for the graduate
admissions problem exists.Karakaya, MehmetPh.D