On core stability and extendability

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.core stability, stable core, extendability

Characterizing core stability with fuzzy games

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.cooperative game, core, stable set, fuzzy coalition, fuzzy game, core stability

A note on apportionment methods

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.apportionment methods, simple games, winning coalitions

Technology shift impacts on the recruitment management triangle

Purpose – This paper investigates the constraints an organisation faces when using recruitment agencies and having to trade-off between the speed of hiring a candidate, the cost of a candidate and the match of the candidate against the job requirements across different job seniorities. We analyse how technology can shift the cost and hiring speed in spite of these constraints. Design/methodology/approach – The research design is exploratory, quantitative and cross-sectional. The study employed a two-factor, unbalanced class Analysis of Variance (ANOVA) including interaction effects to test the difference between the means of the class of interest and a control class. Findings – Our empirical findings confirm that (1) the technological innovation of a recruitment agency marketplace can liberate organisations from their time, cost and quality hiring constraints, accelerating the time to hire by four times and reducing costs by over 12%, and (2) these results hold across varying role seniority levels. Originality/value – This study contributes to the existing literature in three ways: (1) it introduces the recruitment triangle from project management into the recruitment literature; (2) it demonstrates how technological innovations such as recruitment agency marketplaces are able to provide a shift in the constraints posed by the recruitment triangle

On core stability and extendability

Shellshear 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

Über Corestabilität und Zuteilungsverfahren

Shellshear 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

A note on apportionment methods

Shellshear 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

Characterizing core stability with fuzzy games

Shellshear 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 CHARACTERIZING CORE STABILITY WITH FUZZY GAMES

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.Cooperative game, core, stable set, fuzzy coalition, fuzzy game, core stability, JEL Classification: C71

NEW APPORTIONMENT METHODS USING SIMPLE GAMES

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.Apportionment methods, simple games, winning coalitions, C71, D72