In the second position of the ranking, you have Baidu still number two since a couple of years. According to ComScore, the market share of Baidu in December 2012 was 8.2%.
Yahoo was second in search in 2007 (1) but was overtaken by Baidu. The firm had a market share of 4.9% the last month of year 2012.
The Russian firm Yandex is now doing better than Microsoft! 2.8% for Yandex Search Engine against 2.5% for Bing.
The competitive advantage will be in Mobile Search. All the search engines are working hard on that to make search pleasant convenient, and fast on every type of device. For instance, Baidu signed a partnership with Orange to expand its presence in Africa and Middle East.
Wall Street Journal
(1) ComScore, January 24, 2008, URL: http://www.comscore.com/Insights/Press_Releases/2008/01/Baidu_Ranked_Third_Largest_World_Wide_Search_Engine