Selection-based Approach to Cooperative Interval Games

TL;DR

This paper introduces selection-based classes of cooperative interval games, providing new characterization theorems, analyzing core stability, and defining strong imputation and core as universal solution concepts.

Contribution

It presents novel selection-based classes of interval games, characterizes their properties, and explores new stability concepts like strong imputation and strong core.

Findings

New classes of interval games characterized and related to existing classes.

Results on the properties of the core and imputations in interval games.

Introduction of strong imputation and strong core as universal solutions.

Abstract

Cooperative interval games are a generalized model of cooperative games in which the 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 new results regarding the core and imputations and examine a problem of equivalence for two different versions of the core, the main stability solution of cooperative games. Finally, we introduce the definition of strong imputation and strong core as universal solution concepts of interval games.