Compensation rules for multi-stage sequencing games

This paper focuses on compensation rules for multi-stage sequencing games. These rules distribute the implicit losses and gains when the players move from one stage of a multi-stage sequencing game to a subsequent stage. They are necessary because allocation rules that yield core elements for the games in each stage are not guaranteed to yield core elements for the multi-stage game. Three approaches to find compensation rules that yield core elements are studied. Two compensation rules that lead to stable division rules for multi-stage sequencing games are found as a result of these approaches. Axiomatic characterizations of these division rules are discussed.