The Equal Surplus Division Value for Cooperative Games with a Level Structure

Abstract

In this paper, we investigate the equal surplus division value for cooperative games with a level structure, which is a sequence of coalition structures becoming coarser and coarser. We propose three axiomatizations of the value. Among them, the first two use different variations of the recent population solidarity axiom, and the third one invokes a special reduced game consistency axiom. Due to the existence of a level structure, our axioms impose special restrictions on the players we focus. We show that our value can be characterized with these axioms and other variations of well-known axioms, such as efficiency, standardness, and quotient game property. Besides characterizing the value, we also connect it to the recent field of ordered tree cooperative games, wherein we find that the iterative value can be viewed as a special case of our value.