One of my favourite examples of cross-fertilization is in the relationship between Tesco and the Royal Bank of Scotland. Some years ago, they set up a joint venture called Tesco Personal Finance, which basically provides financial services to Tesco's retail customers under the Tesco brand name. I have discussed this elsewhere as an interesting example of the "plug-and-play" component-based business (Tesco plugs a bank into its retail business, RBS plugs a retail channel into its banking business.)
What I want to discuss here is the impact on innovation.
One of the creative strengths of the venture is that each company has a distinct view of customer demand - clear but different. This is very roughly how it works. Tesco takes a retail perspective, and seeks to develop financial services that fitted this perspective. Taking a banking perspective, the Royal Bank does not immediately recognize the validity or viability of what Tesco wants to do. However, the Bank finds a way to implement it for Tesco's customers. Subsequently, the Bank recognizes the value of this, and makes the service available to its own customers as well. The joint venture is therefore a source of innovation for each partner; the clash between the retail perspective and the banking perspective is creatively productive.
Perhaps it's important to put this into context. Both companies are already well-managed and innovative, with strong leadership, and there is undoubtedly a great deal of mutual respect and growing trust, based on similar values. The joint venture merely amplifies and extends existing competence in innovation. This is essentially a symmetric venture, where the partners deal as equals.
Of course, innovation can also come from asymmetric ventures, where one partner is much larger than the other. Perhaps one side has economic strength or market position while the other side has technical strength or innovation competence. If such arrangements are well-managed, they can bring benefits to both sides. But genuine cross-fertilization may not occur, especially when the traffic in ideas is assumed to be one-way.