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Game Theory in Operation Research | Graphic Method of Game Theory | Game Theory in Hindi | Operation Research Game Theory

The graphic method in game theory (used in operations research) is a graphical solution technique for solving two-person, zero-sum games, where the payoff matrix has a dimension of 2 × n or m × 2. This method helps determine the optimal strategies for both players and the value of the game without requiring complex computations like linear programming.

Key Features of the Graphic Method:

1. Applicability:
• The game must have two players (Player A and Player B).
• One player (say, Player A) has two strategies, while the other player (Player B) can have multiple strategies (or vice versa).
2. Steps Involved:
• Step 1: Plot the payoffs for Player A (or Player B) on a graph, considering one player’s strategies as the x-axis and the payoffs as the y-axis.
• Step 2: For each strategy of the opposing player, draw straight lines representing the corresponding payoffs.
• Step 3: Identify the minimum of the maximum payoffs for Player A (or vice versa for Player B) by observing the intersection point of the lines.
• Step 4: The intersection point represents the value of the game and the optimal mixed strategy proportions.
3. Purpose:
• It helps in determining the saddle point (if it exists) and solving mixed-strategy games when no pure strategy solution is available.
4. Limitations:
• It works efficiently only for games involving two strategies for one player and multiple strategies for the other. For larger matrices, numerical or linear programming methods are preferred.

I hope this video will help you understand the graphic method of game theory.
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JOLLY Coaching


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