1. For the game, identify the saddle point and determine the corresponding optimal strategy for each player. 4
3 6
5 The saddle point is the in row and column .
The optimal strategy is for R to always choose row and for C to
always choose column .
2. For the game, identify the saddle point and determine the
corresponding optimal strategy for each player. 3
4 −
2
−
4 1
−
5 The saddle point is the in row and column .
The optimal strategy is for R to always choose row and for C to
always choose column .
3. Determine the optimal strategy for the situation by
representing it as a game and finding the saddle point. State your
final answer in the terms of the original question.
In an ongoing price war between Burger Haven (locally owned)
and MacArches (a chain), both restaurant managers plan to
change the price of a hamburger by 10¢. If they both raise their prices, there will be no change in their market shares, but if they
both lower their prices, the chain's national advertising will
ensure that MacArches gains 5% of the market. Again because of
advertising, if Burger Haven lowers their price and MacArches
raises their price, Burger Haven will gain only 3% of the market,
but if Burger Haven raises their price and MacArches lowers their
price, MacArches will gain 7% of the market. Use this information
to decide what the managers should do.
MacArches
L
R
Burger Haven L R %
% %
% What does L represent?
L represents lowering the price by 10¢.
L represents raising the price by 10¢.
What does R represent?
R represents lowering the price by 10¢.
R represents raising the price by 10¢.
The saddle point is the in row and column . What should the managers do?
Burger Haven should lower its prices, while MacArches raises its
prices.
Both restaurants should lower the price.
MacArches should lower its prices, while Burger Haven raises its
prices.
Both restaurants should raise the price.
4. For the game and mixed strategies, find the expected value.
Let G = 4
2 −5
3 , r=
1 2 1
2
and c = 1
2
1
2 5. For the 2 × 2 game, find the optimal strategy for each player.
Be sure to check for saddle points before using the formulas. 9
4 −
1
9 For row player R:
r1 =
r2 =
For column player C:
c1 =
c2 =
Find the value v of the game for row player R.
v=
Who is the game favorable to?
The game is favorable to the row player.
The game is favorable to the column player.
This is a fair game.
6. Represent the situation as a game and find the optimal
strategy for each player. State your final answer in the terms of
the original question.
A farmer grows apples on her 500-acre farm and must cope with
occasional infestations of worms. If she refrains from using pesticides, she can get a premium for "organically grown"
produce and her profits per acre increase by $400 if there is no
infestation, but they decrease by $100 if there is. If she does use
pesticides and there is an infestation, her crop is saved and the
resulting apple shortage (since other farms are decimated) raises
her profits by $300 per acre. Otherwise, her profits remain at
their usual levels. No worms r1
r2
c1
c2
v Worms =
=
=
=
= How should she divide her farm into a "pesticide-free" zone and a
"pesticide-use" zone? (Round your answers to two decimal
places.)
The farmer should set aside acres for pesticide-free apples and
use pesticide on the other acres.
What will be her expected increase in profits per acre with this
strategy?
This strategy will increase her expected profits by $ per acre.

 

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Status NEW Posted 18 Aug 2017 05:08 AM My Price 10.00

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