In the first part we find that a number of results carry over from static to dynamic environments. We also find that the work on static models is quite homogeneous, in the sense that most papers employ the same basic consumer demand specification and address the same situations of vertical integration and noncooperative games with simultaneous or sequential actions. The work on dynamic problems of cooperative advertising also shows some similarities.
The second part shows that models incorporating horizontal interaction on either or both layers of the supply chain are much less numerous than those supposing its absence. Participation rates in co-op advertising programs depend on inter- and intra-brand competition, and participation may not always be in the best interest of the firms in the marketing channel.