Cooperative solutions in multi-star network games

A model also known as multi-agent systems, namely the multi-star model is considered. In a multi-agent system, a two-level game is played, the first-level is the external game, and the second-level is the internal game. An approach is proposed how to distribute the benefits to players in the first-level game and the second-level game. The characteristic functions are constructed for the multi-star model. Based on the proposed characteristic functions, the combination of the Shapley value and the proportional solution as natural optimal principle to distribute the benefits in the first-level game and in the second-level game is proposed.