When a user does not have the sufficient rights to perform a merge and click on the 'Merge' button, the user is navigated to a new page with containing information message and a 'Set For Merge' button. After clicking on the 'Set For Merge' button, the duplicate set will be added to the DC Job page where a user with rights will be able to proceed the merge.
The 'Set for merge' button appears when a user does not have the rights to perform a merge.
The job will appear on an administrators DC Job page as well, where he can decide to merge or discard the flagged records. The job details will contain the username of the user who requested the merge.
If you want to grant your users permissions to perform a merge, please take into account the following points:
If "Override CRUD when performing merge" settings is set to disable, enabling it may allow the user to perform a merge.
If "Override sharing rules when merging records. The user needs at least Read access to be able to merge records" enabling this setting may allow the user to perform a merge. *These settings can be found in the Object Settings.