Microsoft’s high-stakes bid for Yahoo has turned into a chess game. Monday morning, Yahoo officially declined Microsoft’s offer to buy the company for $31 a share, or $44.6 billion.

“After careful evaluation, the board believes that Microsoft’s proposal substantially undervalues Yahoo, including our global brand, large worldwide audience, significant recent investments in advertising platforms and future growth prospects, free cash flow and earnings potential, as well as our substantial unconsolidated investments,” Yahoo’s statement said. “The board of directors is continually evaluating all of its strategic options in the context of the rapidly evolving industry environment and we remain committed to pursuing initiatives that maximize value for all stockholders.”

The architect of the takeover bid is Christopher P. Liddell, who joined Microsoft just two years ago as chief financial officer. “You have to be disciplined and ruthless,” he told The New York Times last week. “We should see acquisitions as a way of growth. We should not be embarrassed at all.”

Hard-Ball Maneuvers

Microsoft executives and their Wall Street advisers spent the weekend strategizing on their next moves, the Times said. Among the options: raise the offer price; convince Yahoo’s large institutional shareholders to pressure the board; take a “tender offer” directly to shareholders; or, to really play hard ball, launch a proxy war to force out Yahoo’s current board and elect Microsoft’s own slate.

Given the weakness of Yahoo’s stock price and its relative share of the online advertising market, many observers thought the company was outmaneuvered by Microsoft. A year ago, former CEO Terry Semel rejected an offer for $40 a share but appears to have done little to shore up the company’s defenses since then. Despite calls for Semel’s removal, the Yahoo board was slow to act.

Yahoo’s rejection is “understandable,” said Charles King, principal analyst for Pund-IT, in a telephone interview. Founder Jerry…