• Corpus ID: 246824065

1-convex extensions of incomplete cooperative games and the average value

@inproceedings{Bok20211convexEO,
  title={1-convex extensions of incomplete cooperative games and the average value},
  author={Jan Bok and Martin vCern'y},
  year={2021}
}
The model of incomplete cooperative games incorporates uncertainty into the classical model of cooperative games by considering a partial characteristic function. Thus the values for some of the coalitions are not known. The main focus of this paper is the class of 1-convex cooperative games under this framework. We are interested in two heavily intertwined questions. First, given an incomplete game, in which ways can we fill in the missing values to obtain a classical 1-convex game? Such… 

Positivity and convexity in incomplete cooperative games

A systematic study of incomplete games, focusing on two important classes of cooperative games: positive and convex games, and provides a characterisation of extendability and a full description of the set of symmetric convex extensions.

References

SHOWING 1-10 OF 45 REFERENCES

Convexity and positivity in partially defined cooperative games

A systematic study of partially defined games, focusing on two important classes of cooperative games: convex games and positive games, and characterises the non-extendability to a positive game by existence of a certificate and provides a characterisation for the extreme games of the set of positive extensions.

Introduction to the Theory of Cooperative Games

"Introduction to the Theory of Cooperative Games" systematically studies the main solutions of cooperative games: the core, bargaining set, kernel, nucleolus, and the Shapley value of TU games, and

A fundamental study for partially defined cooperative games

Through the investigations of solutions of complete games associated with the given incomplete game, a focal point solution suggested commonly from different viewpoints is shown.

1-concave basis for TU games and the library game

It is concluded that the classes of 1-convex/1-concave games constitute rather considerable subsets in the entire game space and the so-called library game turns out to be decomposable into suitably chosen 1- Conc Cave games of the basis mentioned above.

Selection-based Approach to Cooperative Interval Games

The definition of strong imputation and strong core as a universal solution concept of interval games is introduced and a new results regarding the core and imputations are shown.

Properties of 1-convex n-person games

SummaryThe subclass of 1-convexn-person games is central in this paper. It turns out that an 1-convexn-person game can be characterized by the structure of the core and that its nucleolus lies in the

Cooperative games under bubbly uncertainty

A new class of cooperative games, namely, the cooperative bubbly games, where the worth of each coalition is a bubble instead of a real number, is presented and a new solution concept, the bubbly core, is defined.

Models in Cooperative Game Theory

Cooperative Games with Crisp Coalitions.- Preliminaries.- Cores and Related Solution Concepts.- The Shapley Value, the ?-value, and the Average Lexicographic Value.- Egalitarianism-based Solution

A new axiomatization of the shapley value