The procedural value for cooperative games with non-transferable utility

I adapt Raiffa's discrete bargaining solution in order to take the possibility of partial cooperation into account when there are more than two players. The approach is non-cooperative. I slightly modify the bargaining procedure proposed by Sjöström for supporting the Raiffa solution, exactly as Hart and Mas-Colell introduced the possibility of partial cooperation in (a slight variation of) the Rubinstein procedure. I characterize the unique subgame perfect equilibrium outcome and so justify a new value for cooperative games with non-transferable utility. The so-called procedural value is obtained by applying recursively the Raiffa solution to appropriate bargaining problems. It appears to satisfy nice properties.