This topic examines the nature of game theory, why it is relevant for managerial decision making, and how it determines decisions. The starting point is an explanation of the nature of game theory in terms of the inter-dependence of decision making, and its wide range of applications in real life. Different types of game and their elements are described. The prisoner’s dilemma illustrates some of the counterintuitive aspects of game theory. Static and dynamic games are analysed, and the different types of equilibrium: dominant strategy equilibrium, iterated dominant strategy equilibrium, Nash equilibrium, subgame perfect Nash equilibrium and mixed strategy equilibrium. Cournot, Bertrand and Stackelberg types of oligopoly and their strategy implications are analysed, and comparisons are drawn between them and with perfect competition and monopoly. Games with uncertain outcomes and repeated games are discussed, along with commitment strategies and credibility. Limitations of standard game theory are discussed, such as the existence of bounded rationality and social preferences. Aspects of behavioural game theory are introduced to account for these factors.

We introduce the notion of a mathematical game. We give examples and classify them into various types, such as two-person games vs. n-person games (where n > 2), and zero-sum vs. constant-sum vs. variable-sum games. We carefully delineate the assumptions under which we operate in game theory. We illustrate how two-person games can be described by payoff matrices or by game trees. Using examples, including an analysis of the Battle of the Bismarck Sea from World War II, we develop the notions of a strategy, dominant strategy, and Nash equilibrium point of a game. Specializing to constant-sum games, we show the equivalence between Nash equilibrium and saddle point of a payoff matrix. We then consider games where the payoff matrix has no saddle point and develop the notion of a mixed strategy, after a quick review of some basic probability notions. Finally, we introduce the minimax theorem, which states that all constant-sum games have an optimal solution, and give a novel proof of the theorem in case the payoff matrix is 2 x 2.