National advertising and cooperation in a manufacturer-two-retailers channel

We consider a supply channel composed of one manufacturer and two retailers. Three cases are studied. The non-cooperative one is a leader-follower relationship. The manufacturer determines his spending in national advertising and the whole sale price. Then, the retailers determine non-cooperatively the price for consumers. The second case is a partial-cooperative one where retailers decide jointly for the price. In the third case, all members of the channel cooperate by maximizing a joint profit function. The spending in advertising and the quantity sold are the lowest in the partial-cooperative case, while retailers' price is the highest. Interestingly, when the degree of substituability between the two products proposed by retailers is low, these latter are worse off with partial-cooperation with respect to non-cooperation. Partial-cooperation is always the worst case for the manufacturer, the whole channel, consumers' surplus and social welfare, while cooperation is the best case. Cooperating members can share the extra-profit by a whole sale price.