Closedness under reduced games

2003 ◽  
Vol 58 (3) ◽  
pp. 441-448 ◽  
Author(s):  
Yan-An Hwang
Keyword(s):  
Reduced Games

A NOTE ON CLOSEDNESS UNDER MOULIN REDUCTION

2004 ◽  
Vol 06 (04) ◽  
pp. 555-559
Author(s):  
YAN-AN HWANG
Keyword(s):  
Convex Games ◽  
Reduced Games

We will find 3 maximal subclasses with respect to essential, superadditive and convex games, respectively such that a game is in one subclass, so are its reduced games.

CONSISTENCY FOR PROPORTIONAL SOLUTIONS

2002 ◽  
Vol 04 (03) ◽  
pp. 343-356 ◽  
Author(s):  
ELENA YANOVSKAYA
Keyword(s):  
Cooperative Game ◽  
Solution Set ◽  
Original Game ◽  
Payoff Vector ◽  
Tu Games ◽  
Reduced Game ◽  
Reduced Games ◽  
Consistency Property ◽  
Finite Set

One of the properties characterizing cooperative game solutions is consistency connecting solution vectors of a cooperative game with finite set of players and its reduced game defined by removing one or more players and by assigning them the payoffs according to some specific principle (e.g., a proposed payoff vector). Consistency of a solution means that any part (defined by a coalition of the original game) of a solution payoff vector belongs to the solution set of the corresponding reduced game. In the paper the proportional solutions for TU-games are defined as those depending only on the proportional excess vectors in the same manner as translation covariant solutions depend on the usual Davis–Maschler excess vectors. The general form of the reduced games defining consistent proportional solutions is given. The efficient, anonymous, proportional TU cooperative game solutions meeting the consistency property with respect to any reduced game are described.

THE CORE AND CONSISTENCY PROPERTIES: A GENERAL CHARACTERISATION

2001 ◽  
Vol 03 (02n03) ◽  
pp. 175-187 ◽  
Author(s):  
YUKIHIKO FUNAKI ◽  
TAKEHIKO YAMATO
Keyword(s):  
General Theorem ◽  
General Definition ◽  
Tu Games ◽  
The Core ◽  
Special Cases ◽  
Reduced Games ◽  
Definition Of ◽  
Consistency Properties

In this paper, we unify various axiomatisations of the core of TU games by means of consistency with respect to different definitions of reduced games. First, we introduce a general definition of reduced games including the reduced games due to Davis and Maschler (1965), Moulin (1985), and Funaki (1995) as special cases. Then, we provide a general theorem from which the characterisations due to Peleg (1986), Tadenuma (1992), and Funaki (1995) can be obtained. Our general theorem clarifies how the three characterisations of the core differ and are related.

scholarly journals Analysis of the small-sided games in volleyball: an ecological approach

2020 ◽  
Vol 22 ◽  
Author(s):  
Augusto Cézar Rodrigues Rocha ◽  
Henrique de Oliveira Castro ◽  
Auro Barreiros Freire ◽  
Bárbara Costa Faria ◽  
Gustavo Palhares Mitre ◽  
...  
Keyword(s):  
Decision Making ◽  
Performance Analysis ◽  
Technical Efficiency ◽  
Ecological Approach ◽  
Environmental Constraints ◽  
Pedagogical Strategy ◽  
Analysis Instrument ◽  
Reduced Games ◽  
Game Performance

Abstract The aim of the present study was to compare the tactical and technical behavior of beginner players in volleyball side-out between four distinct situations of reduced games with different area/player ratios: 4.5 m2 (3.0 m x 3.0 m), 8.0 m2 (4.0 m x 4.0 m), 10.58 m2 (4.6 m x 4.6 m), and 13.52 m2 (5.2 m x 5.2 m). We analyzed 76 games played by 16 players with a mean age of 12.2 ± 0.5 years and experience of 1.2 ± 0.8 years of practice. Tactical and technical behavior was analyzed using an adaptation of the Game Performance Analysis Instrument (GPAI). The analysis was conducted for passing, setting and attacking according to the components related to technical adjustment, technical efficiency and decision-making. The results showed that players presented higher technical and tactical indexes in the passing and setting skills in 4.6 m x 4.6 m and 5.2 m x 5.2 m situations. Also, in the 3.0 m x 3.0 m situation higher technical indexes were found for the attacking. No differences were found in the tactical behavior of attacking for tested situations. We conclude that the environmental constraints imposed by the small-sided games imply distinct technical and technical behaviors. Thus, the pedagogical strategy of using small-sided games for the teaching of volleyball for beginner players must be associated with the intended objectives for each basic volleyball skills.

scholarly journals Dynamic Approaches for Multichoice Solutions

2011 ◽  
Vol 2011 ◽  
pp. 1-13
Author(s):  
Yu-Hsien Liao
Keyword(s):  
Reduced Games ◽  
Shapley Values ◽  
Multichoice Games

Based on alternative reduced games, several dynamic approaches are proposed to show how the three extended Shapley values can be reached dynamically from arbitrary efficient payoff vectors on multichoice games.

scholarly journals A Solution Concept and Its Axiomatic Results under Non-Transferable-Utility and Multi-Choice Situations

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1559
Author(s):  
Yan-An Hwang ◽  
Yu-Hsien Liao
Keyword(s):  
Energy Levels ◽  
Solution Concept ◽  
The Other ◽  
Transferable Utility ◽  
Other Hand ◽  
Reduced Games ◽  
Operational Processes

In real situations, agents might take different energy levels to participate. On the other hand, agents always face an increasing need to focus on non-transferable-utility situations efficiently in their operational processes. Thus, we introduce the replicated core under non-transferable-utility situations, and analyze non-emptiness of the replicated core by means of a balanced result. In order to express the rationality of the replicated core, we also define different reduced games to axiomatize the replicated core.

Reduced games, consistency, and the core

1992 ◽  
Vol 20 (4) ◽  
pp. 325-334 ◽  
Author(s):  
K. Tadenuma
Keyword(s):  
The Core ◽  
Reduced Games
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