The EasyChair system has a special plugin for conflict management. It is especially useful when submissions are anonymous.
To enable this plugin chairs should
(1) Access the configuration page by selecting menu tabs "Administration" -> "Configure".
(2) Find the entry "Conflict management" in the table of plugins
(3) Click on "enable"
This plugin enables features for the advance management of conflicts such as author declarations of conflicts and automatic conflict registration. Chairs can configure these features by using the configuration table.

To read more details about the plugin, click on the table entry. A pop up explanation window will appear to give more information about chosen setting.