Abstract
In this chapter we introduce the concept of game theory and its use as a decision making tool in a competitive situation among players. We define and describe some different types of games and solution methodologies. We present the assumptions regarding these different types of game. We define and represent the different types of games between two players as either total conflict or partial conflict. We present solution techniques to both total conflict and partial conflict games. We present both pure strategy and mixed strategy solutions. We discuss the Nash equilibrium.
TopIntroduction
Conflict has been a central theme in human history. Conflict arises when two or more individuals with different views, goals, or aspirations compete to control the course of future events. Game theory studies competition. It uses mathematics and mathematical tools to study situations in which rational players are involved in conflict both with and without cooperation. According to Weins (2003), game theory studies situations in which parties compete, and also possibly cooperate, to influence the outcome of the parties' interaction to each party's advantage. The situation involves conflict between the participants called players because some outcomes favor one player at the possible expense of the other players. What each player obtains from a particular outcome is called the player's pay-off. Each player can choose among a number of strategies to influence his pay-off. However, each player's pay-off depends on the other players' choices. According to Straffin (2004) rational players desire to maximize their own payoffs. Game theory is a branch of applied mathematics that is used in the social sciences (most notably in economics), business, biology, decision sciences, engineering, political science, international relations, operations research, applied mathematics, computer science, and philosophy. Game theory mathematically captures behavior in strategic situations in which an individual’s success in making choices depends on the choices of others. Although initially developed to analyze competitions in which one individual does better at another’s expense, game theory has grown to treat a wide class of interactions among players in competition.
Key Terms in this Chapter
Game Theory: The study of competitive games between two or more players each having multiple strategies they might play.
Nash Equilibrium: It is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally.
Dominance: A strategy A dominates a strategy B if every outcome in A is at least as good as the corresponding outcome in B . A player should never play a dominated strategy.
Pure Strategy: A course of action available to a player.
Movement Diagrams: For total conflict games in each row, draw an arrow from an entry to the smallest entry in that row. In each column, draw arrows to the largest entry in each column. When all arrows point to a payoff (or payoffs), these payoffs describe the pure Nash equilibrium.
Partial Conflict Game: A game between two or more players where the sum of the payoffs for each pair of strategies are not always equal to 0 or 100.
Total Conflict Game: A game between two or more players where the sum of the payoffs for each pair of strategies are always equal to 0 or 100.