ECON 1001

Tutorial 10

Q1)A dominant strategy occurs when

A) One player has a strategy that yields the highest payoff independent of the other player’s choice.

B) Both players have a strategy that yields the highest payoff independent of the other’s choice.

C) Both players make the same choice.

D) The payoff to a strategy depends on the choice made by the other player.

E) Each player has a single strategy.

Ans: A

• Let’s illustrate this by an example:• Player 1’s dominant strategy is {Top}, because it

gives him a higher payoff than {Bottom}, no matter what Player 2 chooses.

• Player 2’s dominant strategy is {Right}.

2

1Left Right

Top (100, 30) (80, 90)

Bottom (60, 60) (70, 100)

• Therefore, a dominant strategy is a strategy that yields the highest payoff compared to other available strategies, no matter what the other player’s choice is.

• A rational player will always choose to play his dominant strategy (if there is any in the game), because this maximises his payoff.

• The other strategy available to the player that yield a payoff strictly smaller than that of the dominant strategy is called a ‘dominated strategy’ (e.g. Player 2’s [Left})

• Dominant strategies may not exist in all games. It all depends on the payoff matrix.

Q2) The prisoner’s dilemma refers to games where

A) Neither player has a dominant strategy.B) One player has a dominant strategy and the

other does not.C) Both players have a dominant strategy.D) Both players have a dominant strategy which

results in the largest possible payoff.E) Both players have a dominant strategy which

results in a lower payoff than their dominated strategies.

Ans: E

• The prisoner’s dilemma is a coordination game.

• Both players have a dominant strategy, but the result of which is a lower payoff than the dominated strategies.

2

1 Confess Deny

Confess (-3, -3)* (0, -6)

Deny (-6, 0) (-1, -1)

Q3) MC for both Firms M and N is 0. If Firms M and N decide to collude and work as a pure monopolist, what will M’s econ profit be?

A) $0

B) $50

C) $100

D) $150

E) $200

Ans: C

P

Q

Demand

• The monopolist maximises profit by producing a quantity where MC = MR, and set the price according to the willingness to pay (Demand)

• The profit-max output level is 100, and the profit will be $200.

• Since each firm is halving the quantity, they each earns an econ profit of $100.

P

Q

Demand

100

$2

Q4) If Firm M cheats on N and reduces its price to $1. How many units will Firm N sell?

A) 200

B) 150

C) 100

D) 50

E) 0

Ans: E

P

Q

Demand

100

$2

• If Firm M cheats and charges $1/unit, the quantity demanded by the market would be 150.

• At this point, M is charging $1 and N is charging $2 for the same product.

• All customers will buy from Firm M, and hence, Firm N will have no sales at all.

• Firm M is going to make a profit of $150.

P

Q

Demand

100

$2

$1

150

• If Firm N is allowed to respond to Firm M’s cheating, it may lower is price to $0.5/unit, the quantity demanded by the market would be 175.

• At this point, if M is charging $1, all customers will buy from Firm N, and hence, Firm M will have no sales at all.

• Firm N is going to make a profit of $75.

• … The story continues

P

Q

Demand

100

$2

$1

150

Q5) The game has ? Nash Equilibrium.

A) 0

B) 1

C) 2

D) 3

E) 4

Ans: C

• Let’s look at the payoff matrix to find out the N.E.

• {C, C} and {D, C} are the Nash Equilibria.

• Hence, there are 2 N.E. in this game.

• The N.E. is also known as pure strategy N.E., the adjective “pure strategy” is to distinguish it from the alternative of “mixed strategy” N.E. A mixed strategy N.E. is a N.E. in which players will randomly choose between two or more strategies with some probability.

Jordan

LeeComedy Documentary

Comedy (3, 5) (1, 1)

Documentary (2, 2) (5, 3)

Q6)By allowing for a timing element in this game, i.e., letting either Jordan or Lee buy a ticket first and then letting the other choose second, assuming rational players, the equilibrium is ? , based on ? .

A) Still uncertain; who buys the 2nd ticket.

B) Now determinant; who buys the 1st ticket.

C) Now determinant; who buys the 2nd ticket.

D) Still uncertain; who buys the 1st ticket.

E) Now determinant; who is more cooperative.

Ans: B

• By allowing a timing element, the game is now a sequential game.

• That means, one player moves first, and buys the first ticket.

• The other player observes any action taken (i.e. knows what ticket has been bought), and then makes his / her decision.

• Actions are not taken simultaneously anymore.

• Whoever chooses an action can now predict how the other player is going to react.

• E.g. If Lee chooses {Comedy}, he can be sure that Jordan will choose {Comedy} as well, because this gives Jordan a higher payoff than picking {Documentary}.

• Therefore, the first mover has the advantage (called First Mover Advantage) to take actions first, hence securing his or her own payoff by predicting the response from the other player.

• A rational (self-interested) player will always pick the action that maximises his or her own payoff (irregardless of others’)

• Hence, if Lee is to move first, he will pick {Documentary}, because {D, D} gives him the highest possible payoff.

• If Jordan is to move first, she will pick {Comedy}, because {C, C} gives her the highest possible payoff.

• Therefore, the result is now determinant, as soon as we know who is buying the 1st ticket.

Q7)Suppose Candidate X is running against Candidate Y. If Candidate Z enters the race,

A) Approximately half of the voters who were going to vote for X will now vote for Z.

B) Fewer than half of the voters who were going to vote for Y will now vote for Z.

C) All of the voters who were going to vote for Y will now vote for Z.

D) Most of the voters who were going to vote for Y will now vote for Z.

E) X will certainly win because Y and Z compete for the same voters.

Ans: D

• Originally, before Z joins the election,

• Assuming voters in between 2 candidates are shared equally.

• Area covered in RED are voters voting for X.

• Area covered in BLUE are voters voting for Y

0 1005025 75

X Y

• With Z joining the election, the area in green are voters voting for Z.

• All voters in the green area used to vote for Y.

• Hence, (D) is the answer.

0 1005025 75

X Y Z

Q8) A commitment problem exists when

A) Players cannot make credible threats or promises.

B) Players cannot make threats.

C) There is a Prisoner’s Dilemma.

D) Players cannot make promises.

E) Players are playing games in which timing does not matter.

Ans: A

• In games like the prisoner’s dilemma, players have trouble arriving at the better outcomes for both players…. Because – Both players are unable to make credible

commitments that they will choose a strategy that will ensue a better outcomes for both players (either in the form of credible threats or credible promises)

• This is known as the commitment problem.

Q9) Suppose Dean promises Matthew that he will always select the upper branch of either Y or Z. If Matthew believes Dean and Dean does in fact keep his promise, the outcome of the game is

A) Unpredictable.B) Matthew and Dean both get $1,000.C) Matthew gets $500; Dean gets $1,500.D) Matthew gets $1.5m; Dean gets $1m.E) Matthew gets $400; Dean gets $1.5m.

Ans: D

• If Dean will indeed goes for the upper branch, then Matthew can either earn $1,000 by choosing the upper branch (i.e., arriving the node Y), or $1.5m by picking the lower branch (i.e., arriving the node Z).

• As Matthew is a rational individual, he will choose a lower branch (i.e., arriving the node Z).

(1000, 1000)

(500, 1500)

(1.5m, 1m)

(400, 1.5m)

Y

Z

X

Matthew

Dean

Dean

*

Q10) Suppose Dean promises Matthew that he will always select the upper branch of either Y or Z. Dean offers to sign a legally binding contract that penalises him if he fails to choose the upper branch of Y or Z. For the contract to make Dean’s promise credible, the value of the penalty must be

A) Any positive number.B) More than $1.5m.C) Less that $100.D) More than $0.5m.E) More than $500.

Ans: D

• If Dean will indeed goes for the upper branch, then Matthew is better off picking the lower branch (i.e., arriving at node Z), because he can then have a payoff of $1.5m (compared to $1000 from the upper branch, i.e. arriving at node Y)

• As Matthew picks the lower branch (i.e., arriving at node Z), there is a tendency for Dean to the lower branch (i.e., arriving the payoff of (400 for Matthew and 1.5m for Dean) -- for a higher payoff (compared with 1m for Dean).

• The penalty of breaching the promise should then be at least $0.5m (say $0.6m). The penalty will reduce the payoff to Dean (becomes 1.5-0.6 = 0.9) when Dean chooses the lower branch at node Z. Thus, Dean will choose the upper branch at node Z.

(1000, 1000)

(500, 1500)

(1.5m, 1m)

(400, 0.9m)

Y

Z

X

Matthew

Dean

Dean

*