BERLIN—Private equity dealmakers are descending on Berlin for their annual get-together, with their industry thriving and many of them wondering how long the good times will last. Armed with billions of dollars, buyout firms have already taken advantage of what has been a record year for mergers and acquisitions (M&A), selling some of their assets for top dollar. Private equity-backed M&A deals more than doubled to a record $818.4 billion in the first nine months of this year, up from $315.2 billion last year, according to Refinitiv. The S&P private equity index, meanwhile, is up 43 percent so far this year, compared with a 25 percent gain in the benchmark S&P 500. Shares of the biggest private equity firms, including Blackstone Group Inc., KKR & Co. Inc., Apollo Global Management Inc., Carlyle Group Inc, and Ares Management, have surged as the U.S. economy rebounded with the easing of coronavirus restrictions. …