Question

For each of the following short statements, explain whether it is True or False. If it’s true, explain why. If it’s false, give a counter-examples or explain why it’s false. (a) (b) (c)

(5 points) Suppose in a game a player has three decision nodes, with three possible actions at each node: A,B and C. The player has fewer strategies in a version of the game where C end the game, than in another version of the game where C does not.

(5 points) You can construct an example of a game where a strategy A is weakly dominant, but is also weakly dominated by another strategy B.

(5 points) Because backwards induction always chooses the best option at every decision node, there is always a unique SPNE if a game has any SPNEs.

Answer #1

a) Suppose in a game a player has three decision nodes, with three possible actions at each node: A,B and C. The player has fewer strategies in a version of the game where C end the game, than in another version of the game where C does not.

**FALSE.** The number of strategies remain the same
if C ends the game or any other action. Number of strategies

b) You can construct an example of a game where a strategy A is weakly dominant, but is also weakly dominated by another strategy B.

**TRUE.**

**c)** Because backwards induction always chooses
the best option at every decision node, there is always a unique
SPNE if a game has any SPNEs.

**FALSE.**

Using backward induction, we can find a unique SRNE i .e sequentially rational nash equilibrium. There can be a game which has two SPNE like the following:

Indicate whether the following statement is TRUE or
FALSE and explain your answer:
If one player is the leader in a game it means that s/he
has the first move in the game. The key thing is that this move can
be observed by the follower before making his/her own decision,
otherwise it would be a simultaneous move game that cannot be
solved by backwards induction.

Determine if each of the following statements is true or false.
If it’s true, explain why. If it’s false explain why not, or simply
give an example demonstrating why it’s false. (A correct choice of
“T/F” with no explanation will not receive any credit.)
(a) If two lines are contained in the same plane, then they must
intersect.
(c) Let n1 and n2 be normal vectors for two planes P1, P2. If n1
and n2 are orthogonal, then the planes...

Determine if each of the following statements is true or false.
If it’s true, explain why. If it’s false explain why not, or simply
give an example demonstrating why it’s false
(a) If λ=0 is not an eigenvalue of A, then the columns of A fo
ma basis of R^n.
(b) If u, v ∈ R^3 are orthogonal, then the set {u, u − 3v} is
orthogonal.
(c) If S1 is an orthogonal set and S2 is an orthogonal set...

Problem 1:
For the following, please answer "True" or "False" and
explain why.
In simultaneous move game where one player has a dominant
strategy, then he is sure that he will get the best possible payoff
in a Nash equilibrium.
In a simultaneous game where both players prefer doing the
opposite of what the opponent does, a Nash equilibrium does not
exist.
If neither firm has a dominant strategy, a Nash equilibrium
cannot exist.

Explain whether the following statements are true, false, or
uncertain.a. “An increase in the number of employed workers always means a
reduction in the unemployment rate.”b. “An increase in the unemployment rate always means a decrease
in the economy’s participation rate.”

Is each statement true or false? If true, explain why; if false,
give a counterexample.
a) A linear system with 5 equations and 4 unknowns is always
inconsistent.
b) If the coefficient matrix of a homogeneous system has a
column of zeroes, then the system has infinitely many solutions.
(Note: a homogeneous system has augmented matrix [A | b] where b =
0.)
c) If the RREF of a homogeneous system has a row of zeroes, then
the system has...

True or False: Indicate whether each of the following
statements is true or false and explain why.
4. The industry supply curve could be downward sloping in the
long run.
The market for apartment rentals is in equilibrium when the
rent is $1000 per month and the quantity of apartments rented is
2,000. A rent control law is passed that sets the maximum rent at
$800. If the elasticity of demand for apartments is 1.2 and the
elasticity of supply...

Explain and discuss whether each of the following statements is
true or false (please explain)
The aggregate supply function is upward sloping because at
higher expected price levels, firms wish to produce more
output.
In the medium run output and the price level always return to
their same (original) values after a demand shock.
An increase in the minimum wage will cause an increase in the
natural rate of unemployment with an increase in the equilibrium
real wage.

Indicate whether the following statements are true (T) or false
(F). Explain the false ones
1. Visible light, radio waves, and ultraviolet waves are the
same nature.
2. Electromagnetic waves can travel in a vacuum.
3. The main difference between a radio wave and visible light is
its frequency.
4. The wavelength of the blue color is less than the yellow.
5. Different electromagnetic waves can have different
frequencies, but their speed it's constant.
6. Light will always travel from...

For each of the following statements, identify whether the
statement is true or false, and explain why. Please limit each
response to no more than 2 sentences.
f) A weighted mean is preferred over an unweighted mean (i.e. a
regular sample mean) when each observation has its own unique
weight.
g) A z-score is a percentile.
h) Assuming the population is normally distributed, the standard
deviation of the sampling distribution of the sample mean will
always be less than or...

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