Question

Consider the following
**2 period** sequential game. There are two players,
Firm 1 and Firm 2. They pro- duce identical goods and these goods
are perfect substitutes. The inverse demand function in this market
is given by *P* = 12 *−* (*q*1 + *q*2).
Firm 1 moves first and choose its output *q*1. Firm 2
**observes** Firm 1’s decision of *q*1 and then
chooses its output *q*2.\

- Suppose that the cost function of both Firm 1 and 2 is given by
*C*(_{i}*q*) = 8_{i}*q*. Find all subgame perfect Nash equilibria._{i} - Now suppose that the cost function of both Firm 1 and 2 is
given by
*C*(_{i}*q*) = 8_{i}*q*+ 3 when_{i}*q*0. So both firms face a variable cost of 8 and a fixed cost of 3 if they choose to produce. If a firm chooses to produce nothing (_{i}>*q*= 0) then its total cost is 0. Find all subgame perfect Nash equilibria._{i}

Answer #1

A) P=12-q1-q2

A firm Profit Maximize at where MR= MC

MR2=12-2q2-q1

MC2==∆TC/∆Q=8

MR2=MC2

12-2q2-q1=8

Q2=2-0.5q1{ best response function of firm 2}

Putting Q2 into demand,

P=12-q1-(2-0.5q1)=10-0.5q1

MR1=10-q1

MC1=8

10-q1=8

Q1=10-8=2

Q2=2-0.5q1=2-0.5*2=1

P=12-2-1=9

B) Because fixed cost doesn't effect Profit Maximizing quantity, so the profit Maximizing ( or loss minimization) quantity of both firm will be same as before.

But Profit of firm 1=2-3=-1

Firm 2=1-3=-2

So both firm will be better off by not producing.but firm 1 moves first ,he knows if he choose q1=2, then firm 2 won't enter.

If q1=2 and q2=0( won't enter)

P=12-2-0=10

And firm 1 Profit

Profit of firm 1=(10-8)*2-3=1

Profit of firm 2=0( better than if it Produce)

So Subgame perfect nash equilibrium, Q1=2 and q2=0

A product is produced by two profit-maximizing firms in a
Stackelberg duopoly: firm 1 chooses a quantity q1 ? 0, then firm 2
observes q1 and chooses a quantity q2 ? 0. The market price is
determined by the following formula: P ( Q ) = 4 ? Q , where Q =
q(1) +q(2) . The cost to firm i of producing q i is Ci( qi ) =
q^2)i . (Note: the only difference between this problem and...

There is a Cournot duopoly competition between Firm 1 and Firm
2. The inverse demand function is given by P(Q)=100-q, where
Q=q1+q2 and qi denotes the quantity produced by firm i for all iÎ
{1, 2} and the cost function is given by ci(qi)=10qi. Describe this
problem as a normal-form game. Find pure-strategy Nash Equilibria
for both firms.

From problem 2 please answer and explain questions 1 , 2 and 3
thanks. Class Game Theory: topic, theory and illustrations.
Problem 2
An industry is currently monopolized by a single firm (the
"incumbent" or firm 1). A second firm (the "challenger") is
considering entry, which entails a positive cost F =
$729 in addition to its production cost. If the
challenger stays out, then its profit is zero, whereas if it
enters, the firms simultaneously choose outputs (as in...

Consider a Cournot model with two firms, firm 1 and firm 2,
producing quantities q1 and q2, respectively. Suppose the inverse
market demand function is: P = 450 – Q where Q denotes the total
quantity supplied on the market. Also, each firm i = 1,2 has a
total cost function c(qi) = 30qi. a) What is the Nash equilibrium
of this Cournot game ? What is the market prices ? Compute each
firm’s profit and the industry profit. b)...

Consider the following game: Two firms simultaneously decide
whether or not to enter a market. Each firm must pay a fixed entry
cost of c if it decides to enter. After making their entry
decisions, each firm observes whether or not its rival entered, and
then chooses a production level. If both firms enter, production
levels are chosen simultaneously. Market demand is given by p(q) =
8 − Q, where Q is the total market production. If a firm enters...

1. Consider the Leader-Follower game in which two firms each
choose a quantity qi to bring to the market, but in sequence. Firm
1 chooses q1, and then being informed of q1, firm w then chooses
q2. The market has an inverse demand function P(Q) = 100 - Q, where
Q = q1 + q2. Assume each firm has a constant marginal cost of
10.
(a) Solve by backward induction, state complete contingency
plans for both firms.
(b) Compute the...

Two firms, firm 1 & firm 2, in a Stackelberg sequential
duopoly are facing the market demand given by P = 140 – 0.4Q, where
P is the market price and Q is the market quantity demanded. Firm 1
has (total) cost of production given by C(q1) = 200 + 15q1, where
q1 is the quantity produced by firm 1. Firm 2 has (total) cost of
production given by C(q2) = 200 + 10q2, where q2 is the quantity
produced...

Three oligopolists operate in a market with inverse demand given
by p (Q ) = a −Q , where Q = q1 + q2 + q3, and qi is the quantity
produced by firm i. Each firm has a constant marginal cost of
production, c and no fixed cost. The firms choose their quantities
dy- namically as follows: (1) Firm 1, who is the industry leader,
chooses q1 ≥ 0; (2) Firms 2 and 3 observe q1 and then
simultaneously...

1. There are two players: A government, G, and a firm, F . The
firm can choose to invest in a Research and Development project,
action R, or not, action N . If the firm chooses R, it gets a
payoff of pπ − c, where p is the level of patent protection given
to the firm, π are the profits generated by the invention to a
monopolist, and c is the cost of research. So if p = 1,...

Alexander and Eliza are playing a sequential game of perfect
information.
Alexander moves first and he chooses between Up and Down. If
Alexander chooses Up, it is Eliza’s turn and she chooses between
Left and Right. If Eliza chooses Left (after Alexander chose Up)
the game ends and Alexander gets a payoff of 4 whereas Eliza gets a
payoff of 3. If Eliza chooses Right (after Alexander chose Up),
then it is Alexander’s turn again and he chooses between In...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 16 minutes ago

asked 19 minutes ago

asked 28 minutes ago

asked 34 minutes ago

asked 39 minutes ago

asked 56 minutes ago

asked 57 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago