Tutorial 6
Problem
1.
Aksu is a small village with only two stores: Aigerim’s store and Aizhan’s
store.
Aigerim's store is thinking of having a major sale in the month of
March, but does not know if its competitor store Aizhan's is also planning one.
If Aigerim's has a sale and Aizhan's does not, Aigerim's sales go up by 30%,
but if both stores have a sale simultaneously, Aigerim's sales go up by only
5%.
On the other hand, if Aigerim's does not have a sale and Aizhan's does,
Aigerim's loses 5% of its sales to Aizhan's, and if neither of the stores has a
sale, Aigerim's experiences no gain in sales.
Write a payoff matrix for Aigerim's and find the optimal strategies for both
stores.
Problem
2
.
Akylbek, 12 years old, and Sagyndyk, 15years old, play a game using coins of
50 tenge and 100 tenge.
Each chooses one of the two coins, puts it in their
hand and closes their fist.
At a given signal, they simultaneously open their
fists.
If the sum of the coins is less than 150 tenge, Akylbek gets both coins,
otherwise, Sagyndyk gets both coins.
Write the matrix for the game,
determine the optimal strategies for each player, and find the expected payoff
for Akylbek.
Solution:
Suppose Akylbek is the row player, that is, he plays the rows, and Sagyndyk is
a column player.
If Akylbek shows 50 tenge and Sagyndyk shows 50 tenge,
the sum will be less than 150 tenge and Akylbek will win 50 tenge.
But, if
Akylbek shows 50 tenge and Sagyndyk shows 100 tenge, the sum will not be
less than 150 tenge and Sagyndyk will win 50 tenge or Akylbek will lose 50
tenge.
The following matrix depicts all four cases and their corresponding
payoffs for Akylbek.
Remember a negative value is a loss for Akylbek and a
win for Sagyndyk.
The best strategy for Akylbek is to always show 50 tenge because this way the