On convexity and solution concepts in cooperative interval games

TL;DR

This paper explores how classical cooperative game theory concepts like convexity, core, and Shapley value extend to interval games with uncertainty, comparing different generalizations and their properties.

Contribution

It analyzes the preservation of properties in interval games and compares various approaches to generalizing classical concepts under uncertainty.

Findings

Certain properties are preserved under specific generalizations.

Different generalizations of classical concepts relate in predictable ways.

The study clarifies how uncertainty affects solution concepts in cooperative games.

Abstract

Cooperative interval game is a cooperative game in which every coalition gets assigned some closed real interval. This models uncertainty about how much the members of a coalition get for cooperating together. In this paper we study convexity, core and the Shapley value of games with interval uncertainty. Our motivation to do so is twofold. First, we want to capture which properties are preserved when we generalize concepts from classical cooperative game theory to interval games. Second, since these generalizations can be done in different ways, mainly with regard to the resulting level of uncertainty, we try to compare them and show their relation to each other.