- The standard reference on Algorithmic Game Theory is the book by Nisan, Tardos, Roughgarden, and Vazirani.
Algorithmic Game Theory
- Another book on AGT is by Kevin Leyton-Brown from UBC and Yoav Shoham from Stanford:
Multi-Agent Systems: Algorithmic, Game-Theoretic and Logical Foundations
A free electronic copy has been made available by the authors as well:
I think there are half a dozen books by Roughgarden with "Twenty Lectures on Algorithmic Game Theory" being one of the best books for beginners. All Books are available on amazon.
If you're interested in lecture notes and video lectures on Algorithmic Game Theory, then I would strongly urge you to have a look at Tim Roughgarden's course website:
Algorithmic Game Theory (CS364A), Fall 2013
His lectures are amazing and surprisingly easy to grasp, especially considering the theoretical nature of the subject matter.
There's also a sequel course on Mechanism Design if you're interested:
Frontiers in Mechanism Design (CS364B), Winter 2014
If you're looking to brush up on a few game theory fundamentals you could go through the following two courses offered by Coursera:
Introductory Course on Game Theory
Advanced Applications of Game Theory: Auctions and Social Choice Theory