Game Theory in Operations Research and Decision Making

The term game represents a conflict between two or more parties .Game Theory may be defined as the body of knowledge that deals with making decisions when two or more intelligent and rational opponents are involved under conditions of conflict and competition. In this course, the students will learn:

• Concept of Game

• Saddle Point

• Dominance Rule

• Modified Dominance Rule

• Oddoment Method

• Graphical Method

• Sub Games Method

• Algebraic Method

• Problem Formulation

Lets discuss some Characteristics of Games

1.The number of competitors is finite.

2. The player act rationally and intelligently.

3. Each player has available to him a finite set of possible courses of action.

4. The players attempt to maximize gains and minimize losses.

5. The outcome of the game is affected by the choices made by all the players.

6. Every participant has the knowledge above the alternatives available to his opponent.

7. A game is played when each player chooses his one course of action.

8. Every combination of courses of action determines an outcome which results in a gain

or loss to each player.

9. There exits a set of rules according to which the value of game will be determined.

Concepts & Terminology in Game Theory

1) Player- Each participant (party) is called a player.

2) Play- A play of the game results when each player has chosen a course of action.

3) Strategy- A rule or set of rules on the basis of which a player selects his alternative. It refers to the total pattern of choices employed by any player.

4) Pure strategy- A pure strategy is a decision always to select the same course of action when a player plays one row all of the time or one column all of the time in case of player 4), he is said to be playing a pure strategy.

5) Mixed strategy - Mixed strategy is a decision to select more than one of his course of action with fixed probabilities. In a mixed strategy, player A will play each of his rows a certain portion of the time and player Y will play each of his columns a certain part of time.

6) Value of the game- The value of the game is the expected gain(or loss) of both the players , if both players use their best strategies.

7) Two person zero sum game-Two person zero sum game are played by two persons, parties or groups, with directly opposing interests . One person’s gain is exactly equal to the loss of another player and therefore the sum total of the gain and loss is equal to zero.

8) Payoff- The outcome of playing the game is known as payoff. It is the net gain or loss the strategy brings to the player.

9) Payoff matrix- The table/matrix representing the outcome or payoff of different strategies of the game is known as payoff matrix.

10) Saddle point-It is known as the equilibrium point of the game. Saddle point is the condition when maximin value is equal to the minimax value.It is called as the value of the game.

11) Maximin Principle-According to this principle, The player adopts a pessimistic attitude. The maximizing player decides to play those strategies corresponding to the maximum of the minimum gains for his different courses of action.

Minimax Principle-The minimizing player selects the strategies, which correspond to the minimum of the maximum losses for his different courses of action, which is referred to as Minimax principle.