Transcript ECON 1001

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
Left
Right
Top
(100, 30)
(80, 90)
Bottom
(60, 60)
(70, 100)
1
• 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
Deny
(-3, -3)*
(0, -6)
(-6,
(-1, -1)
0)
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?
P
Demand
A)
B)
C)
D)
E)
$0
$50
$100
$150
$200
Q
Ans: C
•
The monopolist
maximises profit by
producing a quantity
where MC = MR, and
set the price according
to the willingness to
pay (Demand)
P
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.
$2
100
Q
Q4) If Firm M cheats on N
and reduces its price to
$1. How many units
will Firm N sell?
A)
B)
C)
D)
E)
200
150
100
50
0
Ans: E
P
Demand
$2
100
Q
•
•
If Firm M cheats and
charges $1/unit, the
quantity demanded by
the market would be
150.
P
At this point, M is
charging $1 and N is
charging $2 for the
same product.
Demand
$2
•
•
All customers will buy
from Firm M, and
hence, Firm N will have
no sales at all.
$1
100
Firm M is going to
make a profit of $150.
150
Q
•
•
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
Demand
$2
$1
100
150
Q
Q5) The game has ? Nash Equilibrium.
A)
B)
C)
D)
E)
0
1
2
3
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
Comedy
Documentary
Comedy
(3, 5)
(1, 1)
Documentary
(2, 2)
(5, 3)
Lee
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)
B)
C)
D)
E)
Still uncertain; who buys the 2nd ticket.
Now determinant; who buys the 1st ticket.
Now determinant; who buys the 2nd ticket.
Still uncertain; who buys the 1st ticket.
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
25
X
50
Y
75
100
• 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
25
X
50
Y
Z
75
100
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)
B)
C)
D)
E)
Unpredictable.
Matthew and Dean both get $1,000.
Matthew gets $500; Dean gets $1,500.
Matthew gets $1.5m; Dean gets $1m.
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)
Dean
Y
(500, 1500)
X
Matthew
*
Z
Dean
(1.5m, 1m)
(400, 1.5m)
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)
B)
C)
D)
E)
Any positive number.
More than $1.5m.
Less that $100.
More than $0.5m.
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)
Dean
Y
(500, 1500)
X
Matthew
*
Z
Dean
(1.5m, 1m)
(400, 0.9m)