Game Theory: Basic Terminology

Following are the key terms related to Game theory.

Player

Each participant (interested party) is called a player.

Strategy

The strategy of a player is the predetermined rule by which a player decides his course of action from the list of courses of action during the game. A strategy may be of two types:

• Pure strategy. It is a decision, in advance of all plays, always to choose a particular course of action. In other words, if the best strategy for each player is to play one particular strategy throughout the game, it is called pure strategy.
• Mixed strategy. It is a decision, in advance of all plays, to choose a course of action for each play in accordance with some particular probability distribution. In other words, if the optimal plan for each player is to employ different strategies at different times, we call it mixed strategy.

Optimal strategy

The course of action which maximizes the profit of a player or minimizes his loss is called an optimal strategy.

Saddle point

A saddle point is an element of the matrix that is both the smallest element in its row and the largest element in its column. Furthermore, saddle point is also regarded as an equilibrium point in the theory of games.

Pay-off

The outcome of playing the game is called pay-off.

Pay-off Matrix

It is a table showing the outcomes or payoffs of different strategies of the game.

Value of the Game

It refers to the expected outcome per play, when players follow their optimal strategy. It is generally denoted by V.

In the subsequent sections of this chapter, we provide several trivial illustrations. It should be noted that we make no pretense about the realism of these illustrations.