On convexity and solution concepts in cooperative interval 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.

Positivity and convexity in incomplete cooperative games

“…We can then ask what are the extensions having some desired property, for example being selection superadditive interval games. Indeed, this aligns with the main motivation behind some of the results in [5] and [4].…”