Importance of game theory to decisions, Data Structure & Algorithms

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Question:

(a) Discuss the importance of game theory to decisions.
(b) Explain the following:
(i) saddle point,
(ii) two-person zero-sum game.

(c) Two leading ?rms, ABC Ltd and XYZ Ltd, have for years been selling shirts. The manager of ABC Ltd developed the following data for varying degrees of advertising:

(1) No advertising, medium advertising and heavy advertising for both ?rms will result in equal market share.

(2) ABC Ltd with no advertising will obtain 40% of the market with medium advertising by XYZ Ltd and 28% of the market with heavy advertising by XYZ Ltd.

(3) ABC Ltd using medium advertising will obtain 70% of the market with no advertising by XYZ Ltd and 45% of the market with heavy advertising by XYZ Ltd.

(4) ABC Ltd using heavy advertising will obtain 75% of the market with no advertising by XYZ Ltd and 52.5% of the market with medium advertising by XYZ Ltd.

(i) Draw the payoff matrix from the viewpoint of ABC Ltd, showing its market share under different combinations of strategies.

(ii) Obtain the value of the game and the strategies of ABC Ltd and XYZ Ltd in terms of advertising.

(iii) How would your answers to part (c)(ii) change if (4) in the question reads as follows:

(4) ABC Ltd using heavy advertising will obtain 75% of the market with no advertising by XYZ Ltd and 47.5% of the market with medium advertising by XYZ Ltd.


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