Unfortunately, "Game Theory" is a huge field. If you want to limit things down to just "Algorithmic Game Theory" there are tons of courses and resources out there...

http://www.cis.upenn.edu/~mkearns/teaching/cgt/

http://www.math.mcgill.ca/~vetta/CS764.dir/

http://www.cs.cornell.edu/courses/cs684/2004sp/

http://theory.stanford.edu/~tim/f04/364a.html

http://www.wisdom.weizmann.ac.il/~naor/COURSE/agt-fkn.html

http://www.cs.berkeley.edu/~christos/games/cs294.html

http://zoo.cs.yale.edu/classes/cs455/

http://www.daimi.au.dk/~bromille/AGT/index.html

http://www.cs.duke.edu/courses/fall06/cps296.2/

http://www.inf.ed.ac.uk/teaching/courses/agta/

3-4 years ago I watched the Ben Polak/Yale Game Theory course on Youtube, very well explained, and it was a great refresher for me https://www.youtube.com/playlist?list=PL6EF60E1027E1A10B

Not exactly an "online course", but these notes (used for an undergrad course on games) I found quite readable: http://math.ucr.edu/home/baez/games/

Not strictly online, but this course is very good. Unfortunately, a little pricey.

http://www.thegreatcourses.com/courses/games-people-play-gam...

I don't know about best, but there are a couple of MOOCs on coursera titled "Competitive strategy" and "Advanced competitive strategy" by Tobias Kretschmer of Ludwig-Maximilians-Universität München. They deal with with game theory from a business point of view and are pretty good starting point.