# Selection-based Approach to Cooperative Interval Games

@article{Bok2014SelectionbasedAT, title={Selection-based Approach to Cooperative Interval Games}, author={Jan Bok and Milan Hlad{\'i}k}, journal={ArXiv}, year={2014}, volume={abs/1410.3877} }

Cooperative interval games are a generalized model of cooperative games in which worth of every coalition corresponds to a closed interval representing the possible outcomes of its cooperation. Selections are all possible outcomes of the interval game with no additional uncertainty. We introduce new selection-based classes of interval games and prove their characterization theorems and relations to existing classes based on the interval weakly better operator. We show a new results regarding…

## 7 Citations

### On convexity and solution concepts in cooperative interval games

- Economics, Computer ScienceArXiv
- 2018

Convexity, core and the Shapley value of games with interval uncertainty are studied to capture which properties are preserved when concepts from classical cooperative game theory to interval games.

### Approximations of solution concepts of cooperative games

- Computer Science
- 2022

A method to approximate standard solution concepts based only on partial information given by a so called incomplete game is introduced and derived for diﬀerent solution concepts including the Shapley value, the nucleolus, or the core.

### Positivity and convexity in incomplete cooperative games

- Economics, Computer Science
- 2020

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.

### 1-convex Extensions of Partially Defined Cooperative Games and the Average Value

- Computer ScienceArXiv
- 2021

This paper presents a compact description of the set of 1-convex extensions employing its extreme points and its extreme rays and investigates generalisations of three solution concepts for complete games, namely the τ -value, the Shapley value and the nucleolus.

### N ov 2 01 8 On convexity and solution concepts in cooperative interval games

- Economics, Computer Science
- 2018

In this paper, convexity, core and the Shapley value of games with interval uncertainty are studied to capture which properties are preserved when concepts from classical cooperative game theory to interval games.

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

- Economics, Computer Science
- 2021

This paper introduces generalisations of three solution concepts (values) for complete games, namely the τ -value, the Shapley value and the nucleolus, and shows that all of the generalised values coincide for minimal incomplete games which allows to introduce the average value.

### Convexity and positivity in partially defined cooperative games

- EconomicsArXiv
- 2020

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.

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