NEW YORK — Broadway saw a slight uptick in Week 37 (Feb. 2-8) in a frame still plagued by winter doldrums and subject to the added sales drain of Kids Night, the two-day initiative that offered free ducats for youths at Rialto offerings.Still, most productions saw week-over-week box office numbers climb, though none to a remarkable degree. Two new productions joined the Main Stem lineup, with “Guys and Dolls” ($373,631) posting middling numbers for its first five previews but drawing promising crowds as attendance hit 96%. On the other hand, largely unknown new tuner “The Story of My Life,” lacking the benefit of a familiar title, brought in just $73,812 for its first full week of eight perfs. “Shrek the Musical” ($636,329), the talk of the town last week due to its box office slide, recovered somewhat (and logged a bump of $133,000, the largest of the sesh) — although the show still has not climbed up to the higher numbers most legiters anticipated from a big-budget, brand-name musical offering. Also notable: Lincoln Center Theater hit “South Pacific” ($798,900), while still going strong, had an unusually soft week compared with recent frames during which the tuner had proved largely unaffected by sales fluctuations. Meanwhile, last year’s Tony-winning play, “August: Osage County” ($252,765), has not yet seen biz pick up, with the show playing to houses that averaged about 50% full. In general, though, the majority of productions on the boards saw their tallies increase. Rialto cume rose about $450,000 to around $12.4 million for a total of 23 shows. That total is lower than the ones logged during the same frame the past few years, when there were more productions playing. Still, the upward movement fits the trends logged in prior seasons, when upticks were also recorded at about this time. The 17 musicals grossed $9,963,923 for 80.5% of the Broadway total, with an attendance of 133,437 at 81.4% capacity and average paid admission of $74.67. The six plays grossed $2,416,757 for 19.5% of the Broadway total, with an attendance of 35,397 at 68.9% capacity and average paid admission of $68.28. Average paid admission was $73.33 for all shows.