In connection with the American Repertory Theatre’s world premiere production of Christine Evans’ play “Trojan Barbie,” The Weekly Dig is sponsoring a Barbie Doll competition and exhibition at the Space 242 Gallery in the South End, Boston. Artists are invited to create artwork inspired by or made with Barbie dolls. Twelve works will be chosen by Tak Toyoshima, art director for the Dig, and featured in a special exhibition from March 27 through April 17. The grand prize includes publication in the Dig, four tickets to “Trojan Barbie” and the Harvard Art Museum; and two $100 gift cards to Zipcar and Blick Art Supplies. For entry details and information, visit http://www.weeklydig.com/trojan-barbie. “Trojan Barbie,” which is directed by Carmel O’Reilly, opens at Zero Arrow Theatre on March 28. For ticket information, visit http://www.amrep.org.