Pure Strategy - Math Problem Example

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Summary

Pure Strategy occurs when the best strategy for each player is to choose the same option for all plays of the game. If there is a pure strategy, A plays i and B plays j (say), then the ijth element (the payoff to A per play) is called a saddle point.
Player A would prefer to have the largest value possible from those highlighted…

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Subject: Science
Type: Math Problem
Level: Masters
Pages: 4 (1000 words)
Downloads: 2
Author: craigtromp

Extract of sample "Pure Strategy"

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Player A would prefer to have the largest value possible from those highlighted. In the diagram this can be seen to occur when the line V = 2 + 7X intersects with V= 6 - 3X which occurs at the point as determined below. Value of the game is as follows.The minimax criteria is to maximise the minimum values. To find the solution for B's strategy we need to identify and solve the 2 by 2 pay-off matrix associated with A's optimal strategy. In this case that will be the columns associated with the lines V= 2 + 7X and V= 6 - 3X.

Hence3962Q3. a) Solution:The transformation is as follows.Total Number of audience = 10000000Total audience size as a pair in each matrix element = 100000Total value of a pair in each matrix element = 10000000/100000 = 100Subtracting half the total value of a pair as computed above from each element of the payoff matrix defined in the question.Half the total value = 50Payoff Matrix SkyCastHistorical DramaComedyContemporaryDramaVarietyMini Series60 - 5058 - 5049 - 5052 - 50RayTVDetective55 - 5052 - 5054 - 5059 - 50Film55 - 5054 - 5047 - 5055 - 50Variety47 - 5054 - 5056 - 5061 - 50Transformed Matrix: SkyCastHistorical DramaComedyContemporaryDramaVarietyMini Series10 8-1 2RayTVDetective 5 2 4 9Film 5 4-3 5Variety-3 4 611b) Solution: SkyCastHistorical DramaComedyContemporaryDramaVarietyMini Series10 8-1 2RayTVDetective 5 2 4 9Film 5 4-3 5Variety-3 4 611Comparing fourth column with the third column 2 > -1, 9 > 4, 5 > -3.

In the diagram this can be seen to occur when the line V = 2 + 7X intersects with V= 6 - 3X which occurs at the point as determined below. The minimax criteria is to maximise the minimum values. To find the solution for B's strategy we need to identify and solve the 2 by 2 pay-off matrix associated with A's optimal strategy. In this case that will be the columns associated with the lines V= 2 + 7X and V= 6 - 3X. Hence The value decides the type of the show to be put out in order to maximise the ratings over the coming TV season.

The value against Detective has more gain (approximately 3.33) and hence it has to be put out in order to maximise the ratings.

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