A Merge Agent for Jira installation requires the following scopes:
Read is required to get information about the original issues, e.g. project configuration. Merge Agent uses that information to prepare the merge dialog and prevent errors.
Write enables Merge Agent to add information from one ticket to another.
Admin is required to get information about workflows. It also enables Merge Agent to edit tickets that cannot be edited by a normal Jira user (e.g. closed tickets).
Act as user is required to merge comments, making them appear as if they were added by their original author.
You can read more about scopes in the Atlassian Developer documentation.