ECO2007S
Tutorial 1
Due: Friday 5 August 13:00
Please submit under Vula Assignments
Tutorial compiled by: Rinelle Chetty
Tutorial covers: Modules 1, 2.1, and 2.2
Total marks: 60
Question 1 [15 marks]
For each of the following statements, indicate whether you think it is true or false, and provide
sufficient reasoning for your answer.
1.1 Game Theory is the analysis of luck and chance to obtain the highest possible payoffs. [3
marks]
1.2 You have registered for ECO2007S, and you are now trying to choose between the 4 th
and 5th editions of the course textbook. This interaction can be described as a strategic
game. [3 marks]
1.3 Consider two mobile phone companies, Apple and Samsung, who share the majority of
the market in South Africa. Each company needs to decide on whether to advertise or
not. Based on this information, the companies are interacting strategically, and each
company has two strategies available to them. [3 marks]
1.4 A game can be classified by its timing (complete vs incomplete), payoffs (sequential vs
simultaneous), or information (zero-sum vs non-zero sum). [3 marks]
1.5 Screening devices are tools that can be used to show your opponent all your good qualities
and attributes. As part of your justification, provide an example of a screening device. [3 marks]
Question 2 [15 marks]
Consider the interaction between you and your flat mate about the housework in the flat. You
and your flat mate each face a binary choice: to wash the dishes or do the laundry. If you both
wash the dishes, it’s a wasted effort and you each receive a payoff of 6. If you both do the
laundry, you will each receive a payoff of 1. If instead, you split the load between the two tasks,
the household member who washes the dishes will receive 4 while the household member who
does the laundry will receive 9.
Flat mate
You
, 2.1 Copy out the table above and fill in the appropriate strategies and payoffs. [6 marks]
2.2 Solve the game table in Q2.1 using best response by marking off the appropriate payoffs.
Identify the Nash Equilibrium/Equilibria (NE) and NE outcome(s). [6 marks]
2.3 Based on your answer to Q2.2, what type of game is this? Explain your answer fully. [3
marks]
Question 3 [7 marks]
For each of the cells in the game table below, explain why that cell (and its associated strategies)
can or cannot be a Nash equilibrium (NE). Make sure to provide an explanation for every cell.
Given your answer, determine the NE, if it exists. [7 marks]
Player B
Red Orange
Green 23, 54 86, 15
Player A
Blue 37, 19 49, 28
Question 4 [14 marks]
The following game table describes the interactions between two players, each of whom have three
possible strategies available to them. Using the process of successive or iterative elimination of
strictly dominated strategies (IESDS), reduce the game table as far as possible.
Describe each step that you take, making reference to dominant and dominated strategies. Make sure
to evaluate whether each player initially has a strictly dominated strategy. Remember to use the
correct notation to show dominance among players’ strategies.
What strategy/strategies remain after you eliminate all possible strictly dominated strategies?
Is the game dominance solvable?
Player B
E F G
Q 38, 41 56, 91 20, 30
Player A R 27, 25 43, 13 66, 72
S 47, 62 77, 54 29, 18
Tutorial 1
Due: Friday 5 August 13:00
Please submit under Vula Assignments
Tutorial compiled by: Rinelle Chetty
Tutorial covers: Modules 1, 2.1, and 2.2
Total marks: 60
Question 1 [15 marks]
For each of the following statements, indicate whether you think it is true or false, and provide
sufficient reasoning for your answer.
1.1 Game Theory is the analysis of luck and chance to obtain the highest possible payoffs. [3
marks]
1.2 You have registered for ECO2007S, and you are now trying to choose between the 4 th
and 5th editions of the course textbook. This interaction can be described as a strategic
game. [3 marks]
1.3 Consider two mobile phone companies, Apple and Samsung, who share the majority of
the market in South Africa. Each company needs to decide on whether to advertise or
not. Based on this information, the companies are interacting strategically, and each
company has two strategies available to them. [3 marks]
1.4 A game can be classified by its timing (complete vs incomplete), payoffs (sequential vs
simultaneous), or information (zero-sum vs non-zero sum). [3 marks]
1.5 Screening devices are tools that can be used to show your opponent all your good qualities
and attributes. As part of your justification, provide an example of a screening device. [3 marks]
Question 2 [15 marks]
Consider the interaction between you and your flat mate about the housework in the flat. You
and your flat mate each face a binary choice: to wash the dishes or do the laundry. If you both
wash the dishes, it’s a wasted effort and you each receive a payoff of 6. If you both do the
laundry, you will each receive a payoff of 1. If instead, you split the load between the two tasks,
the household member who washes the dishes will receive 4 while the household member who
does the laundry will receive 9.
Flat mate
You
, 2.1 Copy out the table above and fill in the appropriate strategies and payoffs. [6 marks]
2.2 Solve the game table in Q2.1 using best response by marking off the appropriate payoffs.
Identify the Nash Equilibrium/Equilibria (NE) and NE outcome(s). [6 marks]
2.3 Based on your answer to Q2.2, what type of game is this? Explain your answer fully. [3
marks]
Question 3 [7 marks]
For each of the cells in the game table below, explain why that cell (and its associated strategies)
can or cannot be a Nash equilibrium (NE). Make sure to provide an explanation for every cell.
Given your answer, determine the NE, if it exists. [7 marks]
Player B
Red Orange
Green 23, 54 86, 15
Player A
Blue 37, 19 49, 28
Question 4 [14 marks]
The following game table describes the interactions between two players, each of whom have three
possible strategies available to them. Using the process of successive or iterative elimination of
strictly dominated strategies (IESDS), reduce the game table as far as possible.
Describe each step that you take, making reference to dominant and dominated strategies. Make sure
to evaluate whether each player initially has a strictly dominated strategy. Remember to use the
correct notation to show dominance among players’ strategies.
What strategy/strategies remain after you eliminate all possible strictly dominated strategies?
Is the game dominance solvable?
Player B
E F G
Q 38, 41 56, 91 20, 30
Player A R 27, 25 43, 13 66, 72
S 47, 62 77, 54 29, 18
