Allow only author to edit post

I want to build a simple intranet application using WordPress in which each user of a specific role can add posts of type ‘Customer’. I want only the author of the post to be able to edit it and also specify who else can edit it.

I don’t want a complete solution as I’m doing this mainly for learning, just some helpful links would be nice. I tried looking for filters which could let me hook into editing permissions but couldn’t find any.