Develop a payoff matrix  - Is there a saddle point?  - Determine the promotion strategies of firm A and firm B - Compute the value of the game

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter13: Regression And Forecasting Models
Section: Chapter Questions
Problem 44P
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Assume that two firms are competing for market share for a particular product. Each firm 
is considering what promotional strategies (no promotion, moderate promotion or heavy 
promotion) to employ for the coming period. The market research team of firm A 
develop the following data for varying degree of promotions.
i. No promotion, moderate promotion and heavy promotion for both firms 
will result in no change in the percentage of their market shares
ii. Firm A with no promotion: its market share will show 5% decline in its 
market share when firm B uses moderate promotion and 10% decline 
when firm B uses heavy promotion 
iii. Firm A using moderate promotion: its market share will increase by 12%
when firm B chooses no promotion and 6% growth will be recorded when 
firm B uses heavy promotion.
iv. Firm A using heavy promotion: its market share will increase by 14 when 
firm B uses no promotion and 9% when firm B uses moderate promotion. 
Based on the forgoing information, 
- Develop a payoff matrix 
- Is there a saddle point? 
- Determine the promotion strategies of firm A and firm B
- Compute the value of the game

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