Troubled game maker Zynga Inc. closed its Cambridge office Tuesday as part of a companywide cost-cutting plan as it continues to struggle with the decline of game playing on Facebook and increasing competition. The local outpost had grown to about 50 employees, formed after the San Francisco company acquired two Boston-area start-ups in 2010 and 2011, Conduit Labs and Floodgate Entertainment. The unit, known as Zynga Boston, launched its first game, Adventure World, in September 2011.
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