An alliance between Google and Yahoo also would face antitrust hurdles because the two companies combined control more than 80 percent of the US search advertising market.
Although Google's superior technology would help boost Yahoo's profits in the short term, some analysts worry it could be a mistake for Yahoo to surrender any control over such a lucrative piece of the online ad market.
Yahoo also has been exploring a possible merger with AOL's Internet operations, but may now have to contend with a competing offer from Microsoft.
Yahoo also might attempt to placate shareholders by buying back stock.
Kessler believes Yang should use some of his estimated $1.9 billion fortune to personally buy more Yahoo stock even though he already owns 54.1 million shares, or 3.9 percent of the company.