You are so right to focus on building a spirit of cooperation. Top talent is only as good as the team and the leader, in most cases.
"A" players need strong leadership in order to play as part of the team. Strong leadership means that the leader clearly understands her responsibility to the talent, can engage the team in a common vision, can redirect the talent if they stray too far from the vision, and teaches the talent to build solid relationship up, down and across the organization.
An "A" leader can develop an exceptional team of "B" and "C" players, but a "B" or "C" leader can lose the attention of their "A" players.
This is sometimes in conflict with the metrics aspect of a performance driven culture, as it focuses on getting the right work done through the individual talent. This requires lots of dialogue, great questions and collective thinking. In other words, the solution to building a spirit of cooperation is to help leaders be clear on their responsibilities, continuously learn and build leadership, communication and relationship skills, and have the courage to have open and honest dialogue with their teams.
In today's busy work environment, this is often a challenge because building skills and building relationships take time. But consider it an investment because it will pay off in the long run.