In order to have trust, you need cooperation and vice-versa.
Cooperation depends on honesty, accurate information, and delivering good products and services.
As trust is built, so will the level of cooperation grow. You can cooperate and compete at the same time when you have trusting relationships with your colleagues. Trustworthy people can be counted on to share information, workload, success and failure. The hidden benefit of trust is power. Your words carry more weight because people are open to ideas coming from someone they trust.