You will need to log into the Shared mailbox containing the shared calendar and then within Outlook do the following:
1) Choose Tools/Options/Preferences tab/Calendar Options Button/Resource Scheduling Button
2) Select ‘Automatically accept meeting requests and process cancellations’
3) You may also want to select ‘Automatically decline conflicting meeting requests’
You also have to make sure this resource is being invited as a resource, not an attendee. If it is invited as an attendee it will send an invite to the inbox that has to be accepted regardless of the settings mentioned by Aquacer0. When invited as a resource it should get auto-processed instead.