When KKR & Co. offered almost $4 billion for a Japanese IT consulting company back in August, the proposal generated buzz in the country’s burgeoning buyout market.

What came next was unprecedented. Bain Capital made a public rival bid for Fuji Soft that was 7% higher, a move that one dealmaker likened to a last-minute extra inning in baseball. It set off a rare open tussle between the private equity giants that has shocked investors.

"I’ve seen lots of private equity activity in Japan. I cannot remember two large firms in a bidding war for an asset of this nature,” said Howard Smith, a portfolio manager at Indus Capital Partners.