A.G. Sulzberger won a bake-off among three cousins and is next in line to lead the company that publishes the New York Times. Sulzberger, 36, the son of Publisher Arthur “Pinch’ Sulzberger, Jr., was named deputy publisher by the publisher on Wednesday. The Post reported exclusively on Oct. 9 that Arthur Gregg Sulzberger would beat out Sam Dolnick, 35, an associate editor, and David Perpich, 39, a business-side executive. Pinch Sulzberger turned 65 in September and while there is no formal retirement age at the New York Times Company, his father, nicknamed Punch Sulzberger, stepped down as publisher in 1992 when he was the same age. If, as expected, A.G. Sulzberger becomes publisher in 2017, he will face tough decision almost immediately — including further downsizings in the newsroom early next year and choosing a successor to Executive Editor Dean Baquet, 60. Newsroom leaders typically serve until 65, the Times reported on Wednesday.