Notes on Game Theory

The Theory of Games was born suddenly in 1944 with the publication of Theory of Games and Economic Behaviour by John von Neumann and Oskar Morgenstern. Their choice of title was a little unfortunate, since it quickly got shortened to Game Theory, with the implication being that the domain of applications consists merely of parlour games. Nothing could be further from the truth. In fact, the authors hoped that their theory might form the basis of decision making in all situations where multiple decision makers can affect an outcome, a large class of situations that includes warfare and economics. In the years since 1944, the only part of Game Theory where a notion of solution has been developed that is powerful enough to discourage further theoretical work is the part where there are exactly two players whose interests are in complete opposition. Game theorists refer to these games as two-person zero sum TPZS games. TPZS games include all parlour games and sports where there are two people involved, as well as several where more than two people are involved. Tic-tac-toe, chess, cribbage, backgammon, and tennis are examples of the former. Bridge is an example of the latter there are four people involved, but only two players sides. Team sports are also examples of the latter. Many of these games were originally conceived in imitation of or as surrogates for military conflict, so it should come as no surprise that many military problems can also be analyzed as TPZS games.