Deliverable 04 – Worksheet
1. Market research has determined the following changes in market shares based on the
different combinations of music choices for the two clubs: if both clubs play country, the new
club (Club 1) does very well with a 24% increase in market share. If Club 1 plays country and
the competing club (Club 2) plays rock, Club 2 gets a 12% increase in market share. If these
choices are reversed, Club 2 does even better and gets an 18% increase in the market share.
Lastly, if both clubs play rock, Club 1 does better and gets a 6% increase in market share. This
results in the following payoff matrix:
Club 2
Country Rock
Country (24, -24) (-12, 12)
Rock (-18, 18) (6, -6)
Use this payoff matrix to determine if there are dominant strategies for either player. Find any
Nash equilibrium points. Show all of your work.
CLUBS’ CHANGES IN MARKET SHARES 3
Enter your step-by-step answer and explanations here.
From the payoff matrix we get that there are dominant strategies for Club 1 and competing club
(Club 2). The cost and benefit incentives do not based on other club’s action. The dominant
strategies of both Club 1 and Club 2 are best and are unaffected by either actions. We get that
each club knows the optimal strategy of the other club which possible but almost pointless
(Aumann, 2016).
The dominant strategy for club one is that whenever club two plays county music or rock music
then it must plays either and from the playoff matrix we get that Club 1 gets an increase of 24%
in market share if both are playing country music. Club 1 does it better and get 6% increase in
market share when both clubs are playing rock music. The dominant strategy is therefore fix for
Club 2 to choose country music the club 1 will choose county music 24>-18.
Another dominant strategy is fix for club two to choose rock music and club 1 will choose
rock because -12<6 . Club 1 doesn’t have dominant strategy, because club 1 looks for better
pay offs.
For club two to have dominant strategy, then it must play a different music choice from music
choices club one is playing. From the playoff matrix when club one is playing country then
Club 2 will play a different music which is rock and Club 2 get 12% increase in market share.
Whenever club one is playing rock music then club two plays country then club two gets 18%
increase in the market share. Club 2 will choose rock because -24<12 and fix club 1 to choose
rock Club 2 will choose country. Meaning Club 2 doesn’t have dominant strategy, because club
2 looks for better pay offs because club 2 looks for better pay offs.
Noting that club one will get better percentage of market share than club two when both clubs
plays same music choices. Club two dominant strategies of getting better percentage increase in
market share than club 1 is when both clubs plays different music choices.
CLUBS’ CHANGES IN MARKET SHARES 4
To get Nash Equilibrium using determinant strategy we consider Row player’s payoff and
to check if column chooses high (Aumann, 2016). It is in row’s best interest to chooses
high because 24>-18, and if column choose low, row will also choose high because 12>-
6.So choosing high row’s dominant strategy. We can do the same analysis for column
player to get the same results that is 18>-6 and 6> -18.
Checking country and country that is (24, -24) in this case club 2 would move to country,
rock which is better payoff (12). So, this is not a Nash equilibrium point. Country rock
represented in (-12, 12), in this case club 1 will want to move to (rock, rock) (6, -6)
because 6 is better payoff then -12. So, this is not a Nash equilibrium point.
Rock, country represented (-18, 18), in this case club 2 would move to rock, rock which is
better payoff (6). So, this is not a Nash equilibrium point. Check (rock, rock) (6, -6) in this
case club 2 would want to move to (rock, country) (-18, 18), which is better payoff for
club 2. So, this is not a Nash equilibrium point.
General overview from the playoff matrix suggest that any time both clubs are playing
same music choice the club 1 will always emerge to get better percentage increase in
market share. This happens to be best scenario and actually strategy for club 1.
Any time both clubs are playing different music choices then club 2 gets better percentage
increase in market share .this happens to be good strategy for club 2.
First we take
CLUBS’ CHANGES IN MARKET SHARES 5
2. Use the payoff matrix from number 1 to determine the optimum strategy for Club 1.
Show all of your work.
CLUBS’ CHANGES IN MARKET SHARES 6
Enter your step-by-step answer and explanations here.
Calculation of optimal strategies of club 1 we use the mixed strategy of
The play off matrix
If club 1 uses the mixed strategy the expected payoff is if club 2 uses column one and if
club 2 uses column two. Equating these we get
Solving,. If we consider another play matrix
Solving we get.
This last solution gives the best strategy for club 1 and it obvious that using this strategy it
give club 1 to carry the day making better percentage in of market share than club 2 on the
average no matter what club 2 does.
3. Find and interpret the value of the game.
CLUBS’ CHANGES IN MARKET SHARES 7
Enter your step-by-step answer and explanations here.
Considering the two playoff matrix that is
.This gives a solution of and considering another payoff matrix
and this gives a solution of
From these two payoff matrixes we get is the best value giving optimal strategy
for club 1 eve though remaining fraction that is for club will not affect determine
club 1 to get its optimal strategy.
Playoff matrix that give solution of cannot give optimal strategy to club one but
remainder of the fraction that is gives an optimal strategy to club 2 because
CLUBS’ CHANGES IN MARKET SHARES 8
4. Working in parallel your co-worker wants to make the recommendation that the new club
owner should always follow the schedule shown below. Do you agree or disagree with
this strategy? Explain your reasoning.
Wednesday Thursday Friday Saturday Sunday
Country Rock Country Rock Country
Enter your step-by-step answer and explanations here.
Wednesday-County music: From the playoff matrix this good because club is likely
to counter this strategy of club 1 by playing country music and once both clubs are
playing county music then club 1 makes better percentage increase in market share.
Thursday-Rock: : This is good as per the playoff matrix where we have seen if club
1 play rock music and club 2 will play rock music the club 1 carry the day by
making better percentage increase in market share
Friday-County: this scenario same as one of Wednesdays provided club 2 play
same county music and club 1 get better percentage increase in market share. In
addition the day will yield better percentage increase because on Friday there are
many people starting weekend retreat
Saturday-Rock: This is best because on Saturday multitude will take a weekend
retreat and it is obvious fro playoff matrix club be will even get better percentage
increase in market share
Sunday-County: On this day is likely to be same scenario as Friday or Monday and
its automatic as we have seen from playoff matrix that club 1 will get better
percentage increase in market share once club 2 play same that is county music
CLUBS’ CHANGES IN MARKET SHARES 9
References
Aumann, R. (2016). Values of non-atomic games. [Place of publication not identified]: Princeton
University Pres.
Leonard, R. (2012). Von Neumann, Morgenstern, and the creation of game theory. Cambridge:
Cambridge Univ. Press.
Morgenstern, O. The collaboration between Oskar Morgenstern and John von