The video game industry isn't one to let bankable franchises slip through its fingers. As a result, the 2010s have seen plenty of legacy brands continue to flourish that were started the decade prior or even long before then, with age old classics like The Legend of Zelda proving they're not ready for retirement yet, and big hitters like God of War proving they have what it takes to grow and evolve with the times.
Of course, players crave new things, especially if there's a new console generation in sight, and the PS4 and Xbox One launching in 2013 brought with them a whole host of original new franchises. There have been some stinkers in there, but when the decade is taken as a whole, a good chunk of the games that define the past 10 years come from franchises birthed during this period.
Also, just so I'm not arguing the criteria in each entry, a 'franchise' only counts if two games have been released this decade and sub-series from established brands launched this decade totally count as well.