Dynamically consistent bi-level cooperation of a dynamic game with coalitional blocs

Abstract

In many real-life scenarios, groups or nations with common interest form coalition blocs by agreement for mutual support and joint actions. This paper considers two levels of cooperation: cooperation among members within a coalition bloc and cooperation between the coalition blocs. Coalition blocs are formed by players with common interests to enhance their gains through cooperation. To increase their gains coalition blocs would negotiate to form a grand coalition. A grand coalition cooperation of the coalitional blocs is studied. The gains of each coalition are defined as components of the Shapley value. Dynamically consistent payoff distributions between coalitions and among players are derived for this double-level cooperation scheme. For definition of players’ gains inside each coalition the proportional solution is used.