The Banzhaf value as a design tool in coalitional control

In this paper, the game theory solution concept known as Banzhaf value is applied to games in coalitional control schemes. In these schemes, the network topology is modified to achieve a trade-off between performance and communication burden. In particular, we show how to design a coalitional scheme with constraints regarding the Banzhaf value. Several similarities and differences of this value with respect to the Shapley value are stated, and the concept of amalgamated game is introduced in coalitional control as a means to relieve the computational burden. Finally, an academic simulation example illustrates the results obtained in this work.