Chapter 4 Static Games of Incomplete Information.ppt

Chapter 4
Static Games of plete Information
This chapter begins our study of games of
plete information, also called Bayesian
games. Recall that in a game plete infor-
mation the players’ payoff functions mon
knowledge. In a game of plete information,
in contrast, at least one player is uncertain about
another player’payoff function. mon
example of a static game of plete informa
-tion is a sealed-bid auction: each bidder knows
his or her own valuation for the good being sold
but does not know any other bidder’s valuation;
bids are submitted in sealed envelopes, so the
players’ moves can be thought of as simultaneous.
Most economically interesting Bayesian games,
however, are dynamic. As we will see in Chapter
5, the existence of private information leads
naturally to attempts by informed parties -
municate(or mislead) and to attempts by unin-
formed parties to learn and respond. This are
inherently dynamic issues.
一、Theory: Static Bayesian Games and
Bayesian Nash Equilibrium
(一)An Example: petition
under Asymmetric Information
…
C1(q1)=Cq1 , common knowledge,but
C2(q2)=? , firm 2’s private information
Firm 2 knows its cost function and firm 1’s, but
firm 1 only knows its cost function(does not know
firm 2’s cost function). All of this mon
knowledge.
Firm 1 knows: firm 2’s cost function is C2(q2)=
CHq2 with probability θ and C2(q2)= CLq2 with
probability 1- θ, where CL < CH.
common knowledge
q2*(CH) will solve
[a-q1*-q2-cH] q2
q2
q2*(CH)=
a - q1*- cH
2
max
(1)式:
q2*(CL) Will solve
[a-q1*-q2-cL] q2
max
q2
q2*(CL)=
a - q1*- cL
2
q1* Will solve
[a-q1-q2*(CL)-c] q1
[a-q1-q2*(CH)-c] q1
(1-θ)
θ
+
{
}
max
q1
(2)式:
q1* =
(1- θ)[a-q2*(CL)-c]+ θ[a-q2*(CH)-c]
2
(3)式
The solutions to 1 ,2 and 3 are
q2*(CH)=(a-2CH+C)/3 + (1- θ)(CH – CL )/6
q2*(CL)= (a-2CL+C)/3 –θ(CH – CL )/6
q1* =[a-2C+ θCH +(1- θ)CL ]/3
不完全信息下古诺竞争的贝叶斯NE
与完全信息下古诺竞争的NE作比较:
令a=8,C=2,CH=3, CL=2
不完全信息(θ=50%):
q2*(CH)= , q2*(CL)