There are dozens and dozens of books on game theory, of which a handful stand out as indispensable to grasping the theory’s essential features. Those that I found most useful and illuminating:
Camerer, Colin. Behavioral Game Theory. Princeton, N.J.: Princeton University Press, 2003.
Gintis, Herbert. Game Theory Evolving. Princeton, N.J.: Princeton University Press, 2000.
Kuhn, Harold W. and Sylvia Nasar, eds. The Essential John Nash. Princeton, N.J.: Princeton University Press, 2002.
Luce, R. Duncan and Howard Raiffa. Games and Decisions. New York: John Wiley & Sons, 1957.
Williams, J.D. The Compleat Strategyst: Being a Primer on the Theory of Games of Strategy. New York: McGraw-Hill, 1954.
Von Neumann, John and Oskar Morgenstern. Theory of Games and Economic Behavior. Sixtieth-anniversary Edition. Princeton, N.J.: Princeton University Press, 2004.
Two other readable books were very helpful:
Davis, Morton D. Game Theory: A Nontechnical Introduction. Mineola, NY: Dover, 1997 (1983).
Poundstone, William. Prisoner’s Dilemma. New York: Anchor Books, 1992.
For the rich and complex historical context of the social sciences into which game theory fits, an excellent guide is:
Smith, Roger. The Norton History of the Human Sciences. New York: W.W. Norton, 1997.
And for a comprehensive account of attempts to apply physics to the social sciences:
Ball, Philip. Critical Mass: How One Thing Leads to Another. New York: Farrar, Straus and Giroux, 2004.
A few additional books and articles of relevance are listed here; many others addressing specific points are mentioned in the notes.
Harman, P.M. The Natural Philosophy of James Clerk Maxwell. Cambridge: Cambridge University Press, 1998.
Henrich, Joseph, et al., eds. Foundations of Human Sociality: Economic Experiments and Ethnographic Evidence from Fifteen Small-Scale Societies. New York: Oxford University Press, 2004.
Macrae, Norman. John von Neumann. New York: Pantheon Books, 1991.
Nasar, Sylvia. A Beautiful Mind. New York: Simon & Schuster, 1998.
Watts, Duncan J. Six Degrees. New York: W.W. Norton, 2003.
Ashraf, Nava, Colin F. Camerer, and George Loewenstein. “Adam Smith, Behavioral Economist.” Journal of Economic Perspectives, 19 (Summer 2005): 131–145.
Ball, Philip. “The Physical Modelling of Society: A Historical Perspective.” Physica A, 314 (2002): 1–14.
Holt, Charles and Alvin Roth. “The Nash Equilibrium: A Perspective.” Proceedings of the National Academy of Sciences USA, 101 (March 23, 2004): 3999–4002.
Morgenstern, Oskar. “Game Theory.” Dictionary of the History of Ideas. Available online at http://etext.virginia.edu/DicHist/dict.html.
Myerson, Roger. “Nash Equilibrium and the History of Economic Theory.” 1999. Available online at http://home.uchicago.edu/~rmyerson/research/jelnash.pdf.
After the manuscript for this book was completed, a new review article appeared exploring the game theory-statistical mechanics relationship in depth:
Szabó, György and Gábor Fáth. “Evolutionary Games on Graphs,” http://arxiv.org/abs/cond-mat/0607344, July 13, 2006.