A look back at the core of games in characteristic function form: some new axiomatization results

TL;DR

This paper presents three new axiomatizations of the core in characteristic function form games, broadening the understanding of these games without restrictions like balancedness, and focusing on games with bounded individually rational pay-offs.

Contribution

It introduces axiomatizations applicable to the entire class of such games, including those without transferable utility and without common restrictions.

Findings

Provided three new axiomatizations of the core.

Extended axiomatization to all games with bounded individually rational pay-offs.

Did not require restrictions like non-levelness or balancedness.

Abstract

In this paper we provide three new results axiomatizing the core of games in characteristic function form (not necessarily having transferable utility) obeying an innocuous condition (that the set of individually rational pay-off vectors is bounded). One novelty of this exercise is that our domain is the {\em entire} class of such games: i.e., restrictions like "non-levelness" or "balancedness" are not required.