Pure Strategy - Math Problem Example

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…

Download full paper File format: .doc, available for editing

GRAB THE BEST PAPER91% of users find it useful

Read Text Preview

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

Extract of sample "Pure Strategy"

Download file to see previous pages

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.

...Download file to see next pages Read More

CHECK THESE SAMPLES OF Pure Strategy

The Current State of Internationalisation

The global maximiser uses Pure Strategy when formulating growth plans.... For an SME deciding to internationalise, the internationalist strategy appears most suitable.... An internationalist strategy is used by a company with a secure position within its home market/nation....

10 Pages (2500 words) Essay

Microeconomic Theory

1.... The required game tree can be drawn as follows: Figure 1.... :The game tree 1.... ) If a = ?... , the game tree will become as follows: Figure 2: game tree with a=1/2 Note that player 2 will know with certainty that player 1 has played A if the game ends and he gets ?... hellip; without having to make a move....

5 Pages (1250 words) Essay

Economics game theory paper

More precisely, the implication of the players being intelligent is that if we are able to infer that a given strategy is optimal for any particular player subject to the strategy choice of the rival players, then each and every player of the game will be able to draw the same inference as well (Kreps, 1990)....

5 Pages (1250 words) Essay

Commercial Aviation Management Functions

Seat inventory control under horizontal competition (airlines competing for customers on a single flight leg) and vertical competition (airlines flying different flights on a multi leg itinerary) is usually achieved by a Pure Strategy Nash... Commercial Aviation Management Functions Introduction When deregulation of the US and EU airline industries began in the 70's and 90's respectively, competition increased with many airlines jumping into the fray and started to offer customized services to improve performance and revenue for which they started to use yield management systems for inventory control (Rose, 2012; Knorr and Zigova, 2004)....

6 Pages (1500 words) Essay

Perfect Game Theory of Equilibrium

The game theories will term these as Pure Strategy equilibrium in non-zero game of Nash equilibrium (McCain 78).... In game 1, the correct sub-game starts at player2's decision join; the condition that 2's choices are Nash equilibrium strategy lowers or reduces the prerequisite that 2 takes the action that yields in the highest induce, thus, player 2 must play 1; these deductions are only possible because there exist a finite extensive form of the game, therefore exists a sub-game perfect Nash equilibrium....

3 Pages (750 words) Essay

Stalins Achievement as A Military Leader: An Analysis of the Second World War

Through his strategy making, Stalin knew that Hitler would not wage war against a United European force, so he tried to convince Chamberlain, the then British Prime Minister to join unite the two countries.... The strategy behind this was the closeness of Finland's border to Leningrad, which made it vulnerable to attack....

6 Pages (1500 words) Essay

Economic questions

Because of this, a mixed-strategy Nash equilibrium shows that the dealer would average about 100 deals, meaning the officer would be able to stop an average of 70 deals.... In this game, Player One decides how to split the money/good between them and the other player.... Player Two can then reject or accept the… If the second player rejects the proposal, neither player gets anything....

4 Pages (1000 words) Assignment

The Game Theory and Long Run Marginal Cost in Microeconomics

Pure Strategies: To solve the game we first of all look for a Pure Strategy.... If there is a Pure Strategy, A plays i and B play j (say), then the ijth element (the payoff to A per play) is called a saddle point.... Mixed Strategies and Dominance: If there is no Pure Strategy then we look for a mixed strategy which means each player mixes their options in certain proportions.... Our object is to find the best strategy for each player....

7 Pages (1750 words) Term Paper