25 research outputs found
Characterizing core stability with fuzzy games
No full textShellshear E. Characterizing core stability with fuzzy games. Working Papers. Institute of Mathematical Economics. Vol 410. Bielefeld: Universität Bielefeld; 2009.This paper investigates core stability of cooperative, TU games via a fuzzy extension of the totally balanced cover of a TU game. The stability of the core of the fuzzy extension of a game, the concave extension, is shown to reflect the core stability of the original game and vice versa. Stability of the core is then shown to be equivalent to the existence of an equilibrium of a certain correspondence
A note on apportionment methods
No full textShellshear E. A note on apportionment methods. Working Papers. Institute of Mathematical Economics. Vol 391. Bielefeld: Universität Bielefeld; 2007.This paper investigates the suitability of apportionment methods based on the idea of preserving the coalition function of the simple game represented by the populations of the states. The results show that an apportionment method which satisfies desirable properties such as population monotonicity, house monotonicity, etc., does not exist. A classification of simple voting games via winning coalitions is also given
On core stability and extendability
No full textShellshear E. On core stability and extendability. Working Papers. Institute of Mathematical Economics. Vol 387. Bielefeld: Universität Bielefeld; 2007.This paper investigates conditions under which the core of a TU cooperative game is stable. In particular the author extends the idea of extendability to find new conditions under which the core is stable. It is also shown that these new conditions are not necessary for core stability
Characterizing core stability with fuzzy games
No full textThis paper investigates core stability of cooperative, TU games via a fuzzy extension of the totally balanced cover of a TU game. The stability of the core of the fuzzy extension of a game, the concave extension, is shown to reflect the core stability of the original game and vice versa. Stability of the core is then shown to be equivalent to the existence of an equilibrium of a certain correspondence.cooperative game, core, stable set, fuzzy coalition, fuzzy game, core stability
Über Corestabilität und Zuteilungsverfahren
No full textShellshear E. On core stability and apportionment methods. Bielefeld (Germany): Bielefeld University; 2008.In the thesis two distinct topics in cooperative game theory are investigated. The first problem analyzed is one of the oldest unsolved problems in cooperative game theory. The question asks, under what conditions does an n-person, cooperative, TU game have a stable core? This problem is fundamental for n-person, cooperative, TU game theory as the solution of this problem would provide vital insights into certain properties of the core as well as revealing certain aspects of von Neumann-Morgernstern stable sets. In the thesis new sufficient conditions for core stability are found that turn out to also be necessary for certain classes of games.
In the second chapter of the dissertation the question of core stability is analyzed from a different perspective using the concept of a fuzzy game. This style of game is used to provide new necessary and sufficient conditions for core stability in terms of properties of two correspondences.
The second topic examined in this PhD, in the third chapter, concerns what is known as the apportionment problem. The problem in question is how one can apportion seats, power, etc., in a parliament, committee, etc., corresponding to the size, power, etc., of certain states or parties within a country, company, etc. One is confronted with this problem as soon as one wishes to represent the interests of certain groups in some sort of committee. Hence, this problem is age old but has only recently received a proper mathematical treatment in the twentieth century. In this thesis, a new apportionment method based on game theoretical concepts is investigated for its suitability as an apportionment method to be applied in reality. It is shown that the new apportionment does not fulfill certain desirable criteria. In addition, variations of the new apportionment methods are considered
On core stability and extendability
No full textThis paper investigates conditions under which the core of a TU cooperative game is stable. In particular the author extends the idea of extendability to find new conditions under which the core is stable. It is also shown that these new conditions are not necessary for core stability.core stability, stable core, extendability
A note on apportionment methods
No full textThis paper investigates the suitability of apportionment methods based on the idea of preserving the coalition function of the simple game represented by the populations of the states. The results show that an apportionment method which satisfies desirable properties such as population monotonicity, house monotonicity, etc., does not exist. A classification of simple voting games via winning coalitions is also given.apportionment methods, simple games, winning coalitions
NEW APPORTIONMENT METHODS USING SIMPLE GAMES
No full text This paper investigates the suitability of new apportionment methods based on the idea of preserving the coalition function of the simple game generated by the populations of the states of some country. The new methods fill a gap in the literature concerning apportionment methods based on winning coalitions. The main results in this paper show that the new apportionment methods do not satisfy desirable properties such as house monotonicity, quota, etc. </jats:p
A NOTE ON CHARACTERIZING CORE STABILITY WITH FUZZY GAMES
No full text This paper investigates core stability of cooperative (TU) games via a fuzzy extension of the totally balanced cover of a cooperative game. The stability of the core of the fuzzy extension of a game, the concave extension, is shown to reflect the core stability of the original game and vice versa. Stability of the core is then shown to be equivalent to the existence of an equilibrium of a certain correspondence. </jats:p
NEW APPORTIONMENT METHODS USING SIMPLE GAMES
No full textThis paper investigates the suitability of new apportionment methods based on the idea of preserving the coalition function of the simple game generated by the populations of the states of some country. The new methods fill a gap in the literature concerning apportionment methods based on winning coalitions. The main results in this paper show that the new apportionment methods do not satisfy desirable properties such as house monotonicity, quota, etc.Apportionment methods, simple games, winning coalitions, C71, D72
