e¯twlmn ¨ twhPtw ifNnr¹ - mimuw.edu.plagnese/mikro/MIKROSKRYPT3.pdf · 12$ 6 "-6

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m′ =(p′)T x(p, m) w �

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6

m�E!JM[_SÍEGFvSV[4[4L�Ys>PãPTSV[�A/\XF$lpk = 1

2

Lpl = 1

�~Ú�]>[4YEkD);b��A)�tS�a�]aiAd(p) = 400− 100p

�³>;>Yf§:;Va@P�Ah��A/=�LNEMFvS��!m�P6Y�W)sa:Y�L�^áA/Y�W)JG\�L:J`u

K = KmLF(^gL:JG[4[�J w �q]_[4Y�EOD);�YA$\�F,ais>PÎ^�;��A/\ra#;��

c(y) = 16

+ miny=K

16 L

13

K=K

12K + L = 1

6+ 1

2K + y3K−

12m°;ÁP®eV§q]>njL�^ A/Y�W)JM\XL:J

c(y) =

16

+ miny=K

16L

13

12K + L = 1

6+ 3

2y2 �

� W)s>P�[�A>P�;je�FIJbe4§i]>nVAA/Y�W)JM\vA>PyJkDbE!JM[p;c[p;�WiS4[VY�]¨W)s>P�[p;ZD(JG\raminy≥0

c(y)y

= 1m8Y_;I�Iet;

Fc�VW�^ ��W)Ae�]_Y�]�D(Jy = 1

3

m���WXFvSB[p;>Y4§:;jet;�E|{L = 1

9

LK = 1

9

��»yA$[4L:JrP�;>�Q��A)�tS�a�PTSV[�A/\XLd(1) = 300

mUP�LNÃ(Ex[p;QWqSV[4Y�]�D(JM\ra900

;>Y�a�S�P�[_S�E|{f�4WX^��

�������������� �������� Ñw´

·�JGWM;>FhFIAt?_;�EMF!^~S,mTE(Ab\XL:Ã}\(a@;>[VL:J(m_D(JMKX=�L�e4A�^gLO;I\ra@;�\@��W)A>P�;je�F$l�\XL:Ã}[�A_P�LT^�LNJM\XF(Y>;>Â�E|S,m�E(AF>P�L:ÃMY�\XFvSc��Av�VS�a�e4A

d′(p) = 750− 150p�

� ?,;IW)e�F/A}Y�W)sa:Y�L�^ A/Y�WvJM\�LNJ���Aet;>�UD(JM\(a300

m�P�L:Ã!E300 = 750−150p

m�P�L:Ã(E�E(JG[p;�]>\ra@;I=�L\XL:Ã2[p;

p′ = 3���ìY�W)sa:YL�^ÇA/Y�W)JG\�LNJ�^`A/�([�;�F>P�L:ÃMY�\XFvS�����WvAte�]>YEOD(Ã�F_P�LNÃMY�\�Fr;!D)l�E�Fr;Va¯W(]e�[4LNJM[4LNJ

��WG;�EXS��º}W)sa:YAA/Y�W)JM\vA>P�;��q]>[4YEkD);�YA/\XF,ais_P½^�;b��A/\(a@;��

c(y) = 29

+ 3y3,; P�LNÃ(E�Y_;I�Iet;¨�4W�^�;

D(JG\ra8\�Y4§#A$[4[p;�PTSj��W)Ae�]_YA>P2;��Argmaxy≥0 py−c(y)

m4EGFvSV=�Ly = 1

3p

12��­�a#l�eh�q]_[4YEkD);���Aet;>�vS

n;j§#ÃMF!L~aqAs(p) = 300p

12�Ç� Wvs>P�[�A>P�;�ejFIJ`Y�Wvsa¯Y�AtA/Y�WvJM\)A>P�JOD

750 − 150p = 300p12 ,E(A

PTSVF([�;�EMFr;¨E(JG[�Ãp′′ = 7− 2

√6�

� K�WvJ(e�[4L�^ A$YWvJM\XL:J`[�;�WqSV[4Y�]cD(JM\(a�[p;�et;I=]¢jÌ_Ì<;>Y�a�S�P�[_S�E|{Î�4W�^ A´�q]>[4YEkDML°YA/\XF,ais_Pc(y) = 1

6+ 3y2 LV��W)Ae�]_Y�EOD);�Y>;>�Ie4JkDxWvs>P�[p;Q\�L:à Argmaxy≥0 py − c(y)

m�EMFMS4=�Ly = 1

3p�y­�a@l�e

s(p) = 300p.� W)s>P�[�A>P�;je�FIJdKXW)J!e�[4L:AA/Y�W)JG\)A>P�JOD

750− 150p = 300pmUE(AcPTS4F![p;�EGF$;¨E!JM[�Ã

p′′′ = 53

�� eV§q]>njL�^ A/Y�WvJM\�LNJ�E(JG[p;dF![�s>PcD(JM\(a

1mY>;>�Ie;}F��4WX^�WvAtep]_Y�]�D(J

y = 13

m>��W�FMS�[p;>Y4§:;jet;�E|{L = 1

9

LK = 1

9

L�^c;�F/JMWvA_PTS¨FvSV\�Y���»yA/[4LNJ$P2;>����Av�VS�a�PTSV[�A/\XLd(1) = 600

m8P�L:Ã!E�[p;QWqSV[4Y�]D(JG\ra

1800;>Y�a�S�P�[_S�E|{<�4WX^��

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LFuu:EGFvSV=�L

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1 ·√P = 0.25 ·

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√160000

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