Abstract
We think strategically whenever there are interactions between our decisions and other people’s decisions. In order to decide what we should do, we must first reason through how the other individuals are going to act or react. What are their aims? What options are open to them? In the light of our answers to these questions, we can decide what is the best way for us to act. Most business situations are interactive in the sense that the outcome of each decision emerges from the synthesis of firm owners, managers, employees, suppliers, and customers. Good decisions require that each decision-maker anticipate the decisions of the others. Game theory offers a systematic way of analysing strategic decision-making in interactive situations. It is a technique used to analyse situations where for two or more individuals the outcome of an action by one of them depends not only on their own action but also on the actions taken by the others (Binmore, 1992; Carmichael, 2005; McMillan, 1992). In these circumstances, the plans or strategies of one individual depend on their expectations about what the others are doing. Such interdependent situations can be compared to games of strategy. Games can be classified according to a variety of categories, including the timing of the play, the common or conflicting interests of the players, the number of times an interaction occurs, the amount of information available to the players, the type of rules, and the feasibility of coordinated action. Strategic moves manipulate the rules of the game to a player’s advantage. There are three types of strategic moves: commitments, threats, and promises. Only a credible strategic move will have the desired effect.
Key Terms in this Chapter
Payoff: A payoff is a number, also called utility, that reflects the desirability of an outcome to a player, for whatever reason. When the outcome is random, payoffs are usually weighted with their probabilities. The expected payoff incorporates the player’s attitude towards risk.
Maximin: Maximin is solely a one-person game strategy, that is, a principle which may be used when a person’s “competition” is nature or chance. It involves choosing the best of the worst possible outcomes.
Probability Theory: The use of statistics to analyze past predictable patterns and to reduce risk in future plans.
Rationality: A player is said to be rational if he seeks to play in a manner which maximises his own payoff. It is often assumed that the rationality of all players is common knowledge.
Game Theory: Game theory is the formal study of decision-making where several players must make choices that potentially affect the interests of the other players.
Dominant Strategy: A strategy dominates another strategy of a player if it always gives a better payoff to that player, regardless of what the other players are doing. It weakly dominates the other strategy if it is always at least as good.
Common Knowledge: A fact is common knowledge if all players know it and know that they all know it, and so on. The structure of the game is often assumed to be common knowledge among the players.
Mixed Strategy: A mixed strategy is an active randomisation with given probabilities that determine the player’s decision.
Nash Equilibrium: A Nash Equilibrium, also called strategic equilibrium, is a list of strategies, one for each player, which has the property that no player can unilaterally change his strategy and get a better payoff.
Zero-Sum Game: A game is said to be zero-sum if, for any outcome, the sum of the payoffs to all players is zero. In a two-player zero-sum game, one player’s gain is the other player’s loss, so their interests are diametrically opposed.
Perfect Information: A game has perfect information when, at any point in time, only one player makes a move and knows all the actions that have been made until then.