HOMEWORK

SOLUTION TO THE HOMEWORK

一、

Chapter 1

完全信息静态博弈

Static Games

of Complete Information

1

、

In the following normal-form game,what strategies

survive iterated elimination of strictly dominated

strategies ?What are the pure-strategy Nash equilibrium?

L

C

R

T

2,0

1,1

4,2

M

3,4

1,2

2,3

B

1,3

0,2

3,0

纯策略

NE

有

2< /p>

个：

（

M, L

）和（

T, R

）

第二

第一

2

、

Players 1 and 2 are bargaining over how to

split 10 thousand players

simultaneously name shares they would like to

have,s

1

and s

2

,where 0

≤

s

1

,s

2

≤

s

1

+s

2

≤

1,

then the players receive the shares they named;

if s

1

+s

2

＞

1,then both players receive

are the pure-strategy Nash equilibrium of this

game?

纯策略

NE

有无数：

（

S

*

, S

*

2

）

, S

*

1

+ S

*

2

= 1.

3

、

Suppose there are

n

firms in the Cournot oligopoly model,

let q

i

denote the quantity produced by firm i, and let

Q=q

1

+…+ q

n

denote the aggregate quantity on the market .

Let p denote the market-clearing price and assume that

inverse demand is given by p(Q)=a-Q(assuming Q

＜

a,else

p=0).Assume that the total cost of firm i from producing

quantity q

i

is C

i

(q

i

) =cq

i

.That is, where are no fixed costs

and the marginal cost is constant at c,where we assume c

＜

a.

Following Cournot, suppose that the firms choose their

quantities simultaneously. What is the Nash equilibrium?

What happens as n approaches infinity?

q

i

= (a-c)/(n + 1)

*

4

、

Consider a population of voters uniformly

Distributed along the ideological spectrum from left (x=o) to

right(x=1).Each of the candidates for a single office

simultaneously chooses a campaign platform(i.e.,a point on

the line between x=0 and x=1). The voters observe the

c

andidates’

choices,and then each voter votes for the

candidate whose platform is closest to the voter’s position on

thespectrum. If there are two candidates and they