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

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.

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

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.

Alternative Reductions and Axiomatizations of the Unit-Level-Core

By simultaneously considering both the players and the participation levels, we introduce two alternative definitions of the reduced games. Further, several axiomatizations of the unit-level-core are also obtained by applying related properties of consistency and its converse.

Dynamic Approaches for Multichoice Solutions

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.

MOULIN REDUCTION, V-N REDUCTION AND AXIOMATIZATIONS OF THE DUPLICATE CORE

In this paper, we extend to the multi-choice games cases the reduced games introduced by Moulin (1985) and Voorneveld and van den Nouweland (1998), respectively. Also, we provide several axiomatizations of the duplicate core on multi-choice games by means of the properties of consistency and its converse.

A NOTE ON CLOSEDNESS UNDER MOULIN REDUCTION

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.