TOKYO, Dec 11 (Reuters) - Japan's Nikkei share average is set to trade in a tight range on Tuesday amid investor caution over signs that the market is overbought, while volume may be subdued ahead of major economic events overseas. A 10 percent rally in the Nikkei over the past month is showing signs that the market is overbought, and profit-taking on exporters could continue this week, market observers said. The Nikkei ended 0.1 percent higher at 9,533.75 on Monday. Its 14-day relative strength index stands at 69.33. A level of 70 or above is deemed overbought, and can often signal a pullback in the near term. Market players said the Nikkei was likely to trade between 9,450 to 9,600 on Tuesday. Nikkei futures in Chicago closed at 9,535, down 5 points from the close in Osaka of 9,540. Exporters have led gains in the market over the past month on the back of the weaker yen, after Shinzo Abe, the leader of the main opposition which is expected to win a Dec. 16 general election, called for the Bank of Japan to embark on "unlimited easing" and set an inflation target of 2 percent. The market was unlikely to rally sharply over the next few days, said Hiroichi Nishi, general manager at SMBC Nikko Securities. "Large exporters may not move much, or even see profit-taking. Instead, investors may see buying opportunities in individual stocks like Renesas based on its new developments." Struggling Japanese chipmaker Renesas Electronics Corp said on Monday it will receive 150 billion yen ($1.8 billion) in aid from a government-backed fund and manufacturers, including key client automakers, to help it stay afloat. Analysts added that investors are keeping an eye on the negotiations over the U.S. "fiscal cliff", a series of automatic tax hikes and spending cuts that could hurt economic growth next year. "It would be difficult to take large positions before more details are out," Nishi said, adding that such events as a two-day meeting of the U.S. Federal Open Market Committee on interest rate policy starting Tuesday may also keep investors on the sidelines. The broader Topix index slipped 0.2 percent to 788.48 on Monday. > Wall St gets small lift from technology and McDonald's > Euro gains vs dollar, Monti seeks to allay concern > Prices edge higher on Washington budget worries > Gold rises on US budget talks, Fed stimulus hopes > Brent oil gains after Chinese oil imports grow STOCKS TO WATCH --Mitsubishi Chemical Holdings Corp Mitsubishi Chemical has decided to freeze plans to spend an additional 30 billion yen or so by 2015 to increase production of lithium ion battery materials, the Nikkei said. --Renesas Electronics Corp Japanese chipmaker Renesas Electronics, hit by slumping orders and competition from rivals like Samsung Electronics Co Ltd, secured a 150 billion yen ($1.8 billion) lifeline from a government-led bailout on Monday.