978-0393919684 Chapter 6 Solution Manual Part 3

U4. (a) The strategic form of the game follows:

Severus = x Severus = y

Pure-strategy Nash equilibria are indicated by double borders. The unique subgame-perfect Nash

equilibrium is (SS, aa, y), with payoffs of (2, 1, 1).

(b) The equilibria (SN, aa, x), (SN, ab, x), and (SN, aa, y) cannot be subgame perfect because

Minerva Minerva

aa ab ba bb aa ab ba bb

NN 1, 3, 1 1, 3, 1 4, 1, 4 4, 1, 4

NN 0, 2, 3 4, 1, 5 4, 1, 4 4, 1, 4

U5. (a) The payoff table is shown below. This game has a dominant strategy equilibrium: (Ads,

Ads).

Pepsi

Ads No ads

(b) See tree below. The subgame-perfect equilibrium is again (Ads, Ads); when both players

(c) This game is a prisoners’ dilemma. The (Ads, Ads) equilibrium is jointly inferior to the

U6. (a) The game table follows:

Vendor 2

A B C D E

(b) Locations A and E are both dominated for both vendors.

175).

(d) In sequential play of the game, the vendor that moves first will choose either B or D and

U7. (a) The strategic form of this game follows:

Lion 3 = Eat Lion 2 Lion 3 = Not Eat Lion 2

Lion 2 Lion 2

Eat Lion

1

Not eat

Lion 1

Eat Lion

1

Not eat

Lion 1

In the equilibria (N, E, N) and (E, N, N), Lion 3 is making a noncredible promise not to eat Lion

U8. (a) The game tree is shown below:

(b) The subgame-perfect equilibrium of this game is (U, UU, RUUR) with payoffs of (5, 5,

(c) The payoff table is shown below. Note that since Frieda appears as the row player and

Big Giant

Urban Rural

Titan Titan

Frieda’s UU UR RU RR UU UR RU RR

UUUU 1, 5, 5 1, 5, 5 5, 2, 5 5, 2, 5 5, 5, 2 3, 4, 4 5, 5, 2 3, 4, 4

UUUR 1, 5, 5 1, 5, 5 5, 2, 5 5, 2, 5 5, 5, 2 4, 4, 4 5, 5, 2 4, 4, 4

(d) There are 18 Nash equilibria in the table; the box with the double borders, (RUUR, UU,

U), is the subgame-perfect equilibrium in the sequential-play game. This equilibrium entails the same set

(c). Forcing Frieda’s to go third here does not change the store’s incentives in this matter, and we end up

U9. (a) Nancy’s best response to Monica’s choice m is

Monica knows Nancy’s best-response rule, so when she chooses her m to maximize her profit she can

plug in (1 + m/4) for n:

3/2.

(b) When m = 2 and n = 3/2 the profits are

In Exercise S10 of Chapter 5, when Monica and Nancy choose their effort levels simultaneously, their

profits are

Both Monica and Nancy make higher profits when Monica commits to an effort level first, but Nancy

experiences a greater increase in her profits. This game thus has a second-mover advantage.

(c) Monica’s best response to Nancy’s choice n is

Nancy knows Monica’s best-response rule, so when she chooses her n to maximize her profit she can plug

Their payoffs are as follows:

As seen in part (b), both Monica and Nancy benefit when one commits to an effort level first, but the one

who moves second benefits more.