In situations when a team member escalates a complaint regarding another employee mostly it is due to miscommunication. The best approach is to understand the problem from both members with an open mind and translate the issue with the context of blind spots and intention to clear out the misunderstanding. From my experience, escalations typically occur due to a lack of well-structured processes. In these cases, it is best to identify gaps in the process that lead to the escalation and then improve the process to reduce repeats of occurrences.
Escalations are infrequent if processes are transparent, communication across teams is frequent and openness and trust exists between team members.
Where conflicts arise due to competition in the team, the desire to do the best for the firm should be used as the pivot to reach a decision. In such cases typically you have focused team members who each want to do their best and be rewarded for their efforts. In such cases, separating out the responsibilities with the intention that each can win while collaborating lays a framework that can be used to advance the team’s collective goals.
Escalations should be given due time for direct discussion with the people involved so as to discourage repeats.