~CoN - Queen's U

B ~CoN

1\

--------------

-! do ~ 1. (15 points) Consider the following normal-form gafm)e:

b E +1 I.(\.???t?'J.:2?.DII'- '1 ~

i="V

. ~ ? olon~ d (f)cJ 01'>1" "'" f

do~'~cd"~ irr F

;. 61 B -I- ~c-

(a) (10 points) Find all pure and mixed strategy Nash equilibria (if any). ee, F) un "rlA./l- N~

(b) (5 points) Find not be considered).

~

p~CU"

the pure-strategy rnimuax for each player (i.e., mixeu strategies

\ I )vq? ?..?~lC

= = ~ b ~ "-~V'1 ~ ~I 31

S ~ ~ 1'\ I'V'-"'o)(: ::.. ~ '" , ~,~ I ~,

== 3>

Heed

2. (15 points) Consider the following dynamic game.

(0,0)

(2,2)

e, (a) (5 points) Find all subgame-perfect equilibria in this game. Pl~a..r \ ;

p~/2..( 2 : 1)

A 0,0

(b) (10 points) Find all pure and mixed strategy Nash equilibria in this game.

which ones are subgame-perfect

-D I)2,~2. I ) -?>

aud which ones are not.

(IS ,D)

A

(c ,Dj

1

/:P

Identify

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Lasf perl~ /

s:.w /-1-(;."'-'";

SI2-c.~ fer,'cPd#

a.. p~eA"

plCUf''; -4 In K..I2- ?I'-~(//~

pe...de-J.- l.OO\A.\~ \>\.ot- (~1(J1AUI,iA) If~C-CU(-pAM/.tl.U.AL f)1rhuMI-!- fAJ/l/p (,?I.h~C.~..S'._PP.['c.1PhQ..IoJl-T~Lv.\6~,..~.Q.f.e~D'..~,) .

$ ~lGN \) ~ b_~x ~J -J

L.U~

(:':>,'""l,A..

b_~ lS ~

ht4~t

b:ci o...Y't"\o~

> 0 Q\...;.> ,

;J

I'OV_vI\:o:.;.:~::'.Dl2 ( 9_~\)() t u.:l~

?~~ 8..~.,x

21 _H J N.

\S ~

~t \;I \\."

-G~ o..:.-m4 ~) --~ rJ . ~

IT((~IIVIG\):= E ( G,+&'Z,-+- .. -tG-,.J - "&(8_1)""'~)(

j I 9, \

t"V

~B_,~O\,~')1'D\}~IJ~~e_\

~t

l = [G. + E=c G. + - T 1m I g, ~ ~

~e~,--',fh.d) - E (B l 8-,;",')1 &, ~ a.~"')]

?[F(~)r-'

l;;,(9,r 1,;(1:l.+?+8NIe.,:\hJ--,!J.N59,)

- JI.B? .?UP) _Fd"F"-N'("fJ'~JJ] FN-'(tS;) "'-'

j t;) :: [9/ -r (1(-1)

{;N(f)z/~z.

< e:;) __

F'v/-'(it)

l(}J13re) dFAH{e) 7 FN-/( P.

t {I' f _ r t :: [ 8, {N-I)

8z. (BJ.)J (}2.

~ ;:(~)

FN-II(f}~) J.J 73(O)dF1.J-II8-)] FN-J(~)I

/V

I\;

= {},FIJ-I(fJ~)1- (tv-/) F ";-2(8;) .?&1pz.frB.}df).?. - J:'t3( ())dFAl-I;B-)

~.o. c.

IV

- IV

::::

;;>TTI(G-,'{}I~

d{)/

B7 -; G-t

-

\f{fJ,)

(), (tv-r) FN-~{p,)f(f)t) -I- 0'-/) (N-2) F S,

+ (/(~J)FtJ-2{9-I) fJ.,ft{}-,) -r

(];el .

N-3( ).1-

. f. ()~ fa:J"l.)d 8-2..

~ [rr3!)eN-I) F#-2 (rf') -pI. ())~

0 ==

(N-Z) ~Q/ Bz ff9z.)dB2,

F(@/)

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