Hi everybody! I have to say I agree with vicente and mariaklec. According to Merriam Webster's Dictionary
http://www.learnersdictionary.com/search/play
play at [phrasal verb] play at (something) 1
: to do (something) in a way that is not serious ▪ They were only playing at trying to fix the problem.
2 chiefly Brit
: to play by pretending to be (someone or something) ▪ (Brit) She liked to play at doctors and nurses as a child. —often used in the phrase play at being (something) ▪ boys playing at being soldiers
3 Brit —used to say in an annoyed way that you do not know the reason for someone's behavior ▪ What is he playing at? ▪ I have no idea what he was playing at.
and the same info in the Longman Dictionary:
http://www.learnersdictionary.com/search/play
Maramaras here you have some examples of phrasal verbs (including play at) you'll find them useful:
http://www.advanced-english-grammar....verb-play.html
Hope it help!
Just in case of doublt:
http://www.answerbag.com/q_view/1096659