1. (Simultaneous Game) In the first-price auction two bidders simultaneously submit a written bid. Amy (player 1) decided to bid an odd number between 1 and 9 (that is, $1, $3, $5, $7, or $9) and Leah (player 2) decided to bid an even number between 2 and 10 (that is, $2, $4, $6, $8, or $10). The bidder who submits the highest bid wins and pays a price equal to her bid. The winning bidder's payoff equals her valuation of the item less the price she pays. The losing bidder's payoff is 0. Assume that Amy's valuation of the item is $8, and that Leah's valuation of the item is $7.

Example: Calculation of the player payoffs for the cases when:

• Amy bids $1 and Leah bids $2. Leah wins and gets the payoff of 7-2=5 and Amy gets the payoff 0.
• Amy bids $1 and Leah bids $10. Leah wins and gets the payoff of 7-10=-3 and Amy gets the payoff 0.

a, Present this game in payoff matrix.

b, Find all Nash equilibria of the game.

2, (Simultaneous Game) Martin and Courtney, a formerly married couple, are deciding whether to attend the alumni reunion party at 6 pm, 7 pm, 8 pm, or 9 pm. The payoff will be 1 if either of them shows up before the other partner, 0 if either of them shows up after the other partner, and -1 if they show up at the same time.

a, Present this game in payoff matrix.

b, Find all Nash equilibria.

3, (Simultaneous Game) Find all and all Nash equilibria profile for the games below.

a.

Player 2

	L	M	N	O
A	2, 2	0, 4	4, 0	3, 3
B	3, 1	1, 3	2, 2	4, 0
C	0, 4	2, 2	3, 1	1, 3
D	4, 0	3, 3	1, 3	2, 2

Player 1 are abcd there was no space to write it on the left side

b.

Van Pelt

	North	South	East	West
Earth	1, 3	3, 1	0, 2	1, 1
Water	1, 2	1, 2	2, 3	1, 1
Wind	3, 2	2, 1	1, 3	0, 3
Fire	2, 0	3, 0	1, 1	2, 2

Sam Parrish

c.

Player 2

	L	M	N	O	P	Q
A	2, 2	1, 1	1, 0	0, 0	0, 1	0, 2
B	1, 1	3, 3	1, 1	0, 2	2, 2	0, 1
C	0, 1	1, 1	2, 2	1, 0	1, 1	0, 0
D	0, 0	0, 2	1, 0	1, 1	1, 0	2, 2
E	1, 0	2, 2	1, 1	0, 1	3, 3	1, 1
F	2, 0	0, 1	0, 0	2, 2	1, 1	2, 2

Player 1

d.

Player 2

	L	M	N	O	P	Q	R	S
A	3, 3	1, 0	1, 0	0, 0	1, 1	0, 1	0, 2	2, 2
B	2, 2	0, 0	1, 1	0, 1	0, 1	1, 0	2, 2	0, 2
C	1, 1	2, 2	0, 0	1, 1	0, 2	2, 2	1, 0	0, 1
D	0, 0	1, 1	2, 2	0, 0	2, 2	1, 1	0, 1	1, 0
E	1, 1	0, 1	2, 2	1, 0	3, 3	1, 2	1, 0	0, 0
F	0, 2	1, 0	1, 2	2, 2	1, 1	3, 3	0, 0	1, 1
G	2, 2	2, 2	0, 1	1, 1	0, 1	0, 0	3, 3	1, 0
H	1, 0	0, 0	1, 0	2, 2	1, 0	1, 1	0, 1	3, 3

Player 1

4, (Monopoly and Cournot competition) The market demand for office paper is P = 400 2Q.

Suppose that there is only one firm in the market, and it has a unit cost and marginal cost of $40. Calculate the monopolist's:

1. profit maximizing quantity
2. price
3. profit

b, Now, suppose that two companies supply office paper, Dunder Mifflin Paper Companyand Michael Scott Paper Company. Each firm has a marginal cost and a unit cost of production that equals to $40. These companies maximize their profits and compete in the market in quantities. Companies can choose any quantity to supply, and they make their quantity choices simultaneously.

i, Derive the best response function of each firm and illustrate both functions in a single graph.

ii, How much does each firm sell in a Cournot equilibrium? iii.What is the market price? iv.What are the firms' profits?

v.Why isn't producing half the monopoly output a Nash equilibrium?