It will depend on which of those pages having both the same content will Google treat as "Authority" than the other page content. If for example, Google treats the copied content as more Authoritative than your original, then Google will penalize you instead - the other page will be penalize too but not that much. What you can do is to either make sure your content is copyright protected (you can use Copyscape.com) or by setting up authorship on your contents (mostly on blog contents - here is the guide - http://googlewebmastercentral.blogspot.com/2011/12/clicks-and-impressions-for-authors.html Thanks
Google will be looking into all the sites/pages. And it knows that who published the article first. And i strongly suggest you to submit the XML feed as a sitemap in google webmaster tools, so that google will know whenever you have a new published page.
Don't worry Google by now may have already cached your content. So stay relaxed and anyone imitating it will come under panda.
Pages are considered as duplicate, as well as websites that are identical to another website on the Internet are also considered to be spam.
I got one of their sites removed, thanks for telling me about how to report a site to google: "Hello, Thanks for reaching out to us. In accordance with the Digital Millennium Copyright Act, we have completed processing your infringement complaint. The following webpages will be removed from Google in a few hours: (Removed URL) Please let us know if we can assist you further. Regards, The Google Team"