31 1 , 1 SystemsEngineering—Theory&PracticeJan.,2011:1000-6788(2011)01-0151 -07 :; :A #$ $% & % & ' ( , , , (
,
100044;
,
100044)D /, , ! " !"#
< " !E 2 F 3 H $=G "$=IZ ;%!T"%,#&'$-(0U)4V)5W*1+!X*Y+ +,, -. $"#"(N/: O, - 0$! 1 .R S ,'2364567,,!#$$8789Æ9:;):;<;,?>J> )2??! (@A $@A *+BCDE,B" !"#FGC,,"#KL?M LP?MQ,;[\]^P; #$;" !"#; /"Simulationofcollectivedecision-makingwithincompleteinformationXIONGFei,LIUYun,SIXia-meng,CHENGHui(KeyLaboratoryofCommunication&InformationSystems,BeijingJiaotongUniversity,Beijing100044,China;SchoolofElectronicsandInformationEngineering,BeijingJiaotongUniversity,Beijing100044,China)AbstractTostudyindividualinteractionsanddescribeopiniondynamicsandconsensusformationonInternet,,thepaperpresentsapaymentmatrixwithincompleteinformationbasedonhumanself-confidence,,memoryofagentsisintroduced,andtheacquaintanceforneighbors’,,andcanserveasreferenceforguidingpublicopiniononInternet. Keywordscollectivedecision-making;opiniondynamics;evolutionarygametheory;incompleteinforma-tion;humanself- a
# d e b" c
c on fid ence1_ `
,
,
,
,
, , , , “ ” , 90% “ ” , ,
! " * # ' : '&2!*#00 & 9-0 , 7- '22: + " * ' (6, 09#720 12"); #" (4102047); $ %! (08WL1101);(JXKJD20090001); !$ " # #$(2009GJA00048);2010%% !!(CXJJ1007); $&% Æ;-,+ ' (2009YJS007):&((1985–),$,)& #, *''()(%!)+*&,' ;(+(1955–),),)&, *,)&#-+,(1984–),),)& #, *''*&,' +(% ()...
1D06A:54 </6E 2 .
>* #9 0%=096F -:=1 %.6 ' @ : 77(E/743 @ ;0 ) 1 :> !27>A 33 1 2 $ 7 -/(/,& 0) 31 ,
.1+,- 12 32 ./ , , 2 45 634567
153" ,4, 528;473#41? 4 & 9 :@7 A3 0; /; 88 8 589 6:7;,8
!9"%:6,<9 < =>,; <==?,?@39 B
73# F: A B B B< A * ,C
D A E6D39; <G?FC,[1],2A B B+ $ , GC@>G[2] C,<@9D EDF9 DJ?KB + US!PEFGH2HA ESznajd[3–4], @@DEF@I
AI AE[5–6][7–8],,DeffuantAE[9]L: M HegselmanRB :
P K U7 C ,A4 H : AB WH A: H :: A E
2 3D K E
Kn?-KBrFauSseBABE[10]4 ,IG D JA, ,NJ
OPHK4,.LAI D MN[11–12] , B <A -O #9[13–14] Q [15],8: LL Q T6J,1R,RM $ @,M 7 AH:S [16–17] CDAE=N G , 4NO ,
D UB9 :
V+ 7 / @ I 4G <HLP = MQ
K K TP @QPZ SI T B B , $ @F8 9 ? @. V 079 43 SO A,
G== F ,G2,7 0IR ,8 U ,V4 P * Q2 , TJ 1 Q $$
2500S, , ,123 [18–19] OX SO PQBY U1B9@ 2 73W2VF %WX[
RT B ; < NMS\WT YN6
4 > *[20–21],Newman-Watts
$,.L$
AH:73
[22]Mare3 4 D e ffu an t A E; D< ,? Q1Y3,7 T I Q X46 ,
Z9Z[ X @I ] ,PU MareQ1AE D<,=N \P 6 XZ [ Q62\ \ 9P Q _; < N@\ 4 *,73 U - ]F^W < ` BB,Y , I V4 ,]O] Q 2D V )Q 1^ AH: 23 PU >GMN 25f6g78Deffuant a AE , σ [
0 1: E,0
1
_;*0 σ> , ^ ,8σ<,
Y \6 i : @EFjF : c ^S
8a; < ]<@ 1% 1N, d \] O @ B
i Z RC`[; ja <Z kd4[ D=3 aE|σ F− lσ|R9 F<=ε,
b Y: i
j ZOb.:jiσ=σ+µ·(σ−σ),σ=σ−µ·(σ−σ)(1)ijijjjiµ
Z[=Ei,µ∈(0,],
/H^_`,cµ= >h?@A
b ,<9 4a
c% _ \ BfbB% Qd^1 A@EI T i:: @EF
[b\Q1 Q1j ;<d
s=S:PC ;s=S:\ 5 12,8gH`a F<;%d ,ZO N\ ,e7 P;< 23 cfE ;<eZ,N\eS;,1 `adDJ cfE,2ABB c 2[22–23](a>0,b>0):1)u=−a+1/d,X PC ;2)u=b,X \ ;3)u=a+1/d,X PPC ;4)u=−b,X P\
K Sh 99 1 = N7 ^ QP 2 c3 , 2 &(c,][:Q^1c.()d_deÆ`aG153i
j# Q1n[,iahj /Z[
n(a+1/d)P,P jjjPC @S[22] % PIC%d ig\
,Y:,] iahj8 i_ZP[j
f2%d
Æ ,*H4 Hhi
j % 6
q
q,q <=g ijjL1−q
. bah,ZO(a+1/d)q·(1−q) j,
@
j:>;< i_ c i cY3 1O[.1JmKLMnNoOPpi :1 @
:Z[ RB AjefSjefS12iefS−aP+P/d+aP+P/d−aP−bQ+P/d1iijjijiiefSbQ+aP+P/d−bQ2ijjij,P=Q=(1−q)·q,Q=P=q·(1−q) Vh9,
L j , D4 k `ad43, GQ1 D4 k
:∗s=QKV Q2(S , S ),-X]d^≤P/(aP+bQ)4d≤P/(aP+bQ);11iiijjj∗s=(S,S),Xd≤P/(aP+bQ)4d≥P/(aP+bQ);12iiijjj∗s=(S,S),Xd≥P/(aP+bQ)4d≤P21iii, 0IO4 % /6(aP+bQ);jjj∗s=(S,S),Xd≥P/(aP+bQ)4d≥P/(aP+bQ) 22iiijjj,Q1d e;<D4 k 8 4PQ KVf,14E :^ Q%@
m j
6Kji ;R4i<T 4 0I,Q= 2Q 28 0Q %1QdR1 T D*
4 QQ2 HX Q k7 A* \,7 f2:> Q 0 i q,H 0j ,i 8k0 O 42qdh" fF(q) lOQ1
Q2 b\“Q%1: ”, gPÆ fV2E P VE @,0 % 6 Æhig f O45 n40= “%: ”N\ , O P,O D4 k
gi: k
; 2<#
8d _VjS , % kD4q % 6h q,_V oK k,qVE HLHF(q) "@ ,Xd≤P/(aP+bQ) Y jT2N\,i1PC k , iHiiis ig
ip(s)=F(q=q)p(s|q=q,d)+F(q=q)p(s|q=q,d)(2)ijHijHjLijLp(s|q=q,d),p(s|q=q,d)
00q
q
d N\;<s ig ;VijHijLiji f P Ca ] OPl mm A <E= ,qHd <=1/(a+bq(1−q)/(1−q)q)n
9q
b1/(a+bq(1−HLHLLLq)/(1−q)q q U V rlW
AQBli4CKjKkFl D4
4 ] k k H c [ Q17jmX, ,# bQ+p QG21 P @ I ,:O>4<5
ip:G><0 o[ h ;"Q<k1N8G\ d+ % Q Q 1 g6 gi ikf , O4 n;0= GQ1AE D,6J QT, i :> Q1 ,k5,"8N\
S4X ;,4c[Q1:: aqS Q1 BB +Q1,O k
D,Z ,, % 6 i4 -ORn,b:> O<= i 4 % ig t−1 TpG
t−1F(q=q) t T, i j Q1 N\iHlVtsE ;l <" ,H@
g i k hig,
b i% VE pG:it−1t()F(q=q)p(s |qb,d )iHHtt−1tiF∑q=q|F(q=q),s=(3)iHiHitt−1F(q)p(s|q,d)iiii
jQ1 i At,
b i% 6 pG qi,p(s|q=q,d)igp?0Ij % i 9K,i N\;< 7 f2j % iHi,8" j pGt−1F(q=q)mojH∑tt−1tp(s|q=q,d)=F(q)p(s|q=q,q,d)(4iHjiHjiiqj
1 5O4
" \fE4]t _@ AG; A X EA4n 4 sEF% 6<=
-b/(/,& 0) 31 ,m 2 3 W q ,^4 Q rH48,
.m3":βp
q r3>"G6,0Lβ ig
b > ,7 Q <= 3Y sZ[\t:N t ] =^, t _r4=,L, o n Q2 Q1 MN \ jT
b,q=,qH,ca:b=1:12 ,: @pS2Nbo,o_0 t @N
3
.1m =U^ Q >2h ? @ A\D EIkF 8l1
X fq BB, HA
200,k8 @ f,F(q)
50% H,9Z3[2 6
\, 12000 T0 `\,43\ @I 8Q2 18000 T Z,4@, p\! ^2 k8 f ÆA^, Q2 Q1 `\ 40% s;@I, σ
[,1] @=,60% σ [0,] @
Y , Q\ 28I; < @ JiI Kg ; oK k E
2500, HR u! [
b , Q2 , > G T80000,q #
50%
I,k8 H90% Y @I,8Q2 r425%L [<; Q2 -]^, ss<;
66 ,8 t q
b Q2 Q1 AE
Z[a ^s\ % , X] Q Æhig f,LM Ft F P,qQ%d ,uR<
q @,Z[ L,ZO Q2 =>^HvP
\ ൈ҄/200ൈ҄/200(a)^c.()u(b)c.()ປಆྐ༏҂ປಆྐ༏05001000150020002500۱ุ240%oijNwkKLlm۱ุܴܴׄׄ۱ุܴׄ
Q
x u1 D 1Cvy jfX n3 4wEk x 6t Sw C @ 1D B j Df Jj E] uy! EvfRE nE w&(x,]:^c.()d_deÆ`aG155,
N64 uSB
10Vm=1,2,···,10 rmV sv[−∑,],t? Cn/Nl(m)=n/NOv) wx
f uvnwx t Zmkk≤m
jlS(m )= m/C10COBv8wU
f Dj E Dj E ,,4V QESBjyR, y=B;Y:, @I\ k ^3 ,2500 ,k8 @ f,O[MN
![>G = "^
Lw, Q2 BB X,0 , % h 4
6 Dj E,
xF,,? f V XjSF(q)
20% , Q2 Q2 Q1 Dj EB` Q2 QH, Y ,Q2 BB Dj E F(q)҂ປಆྐ༏, F(qH)=20%ປಆྐ༏, F(qH)=20%҂ປಆྐ༏, F(qH)=50%ປಆྐ༏, F(qH)=50%҂ປಆoྐ༏p, Fx(qHq)=20%ປಆྐ༏200, F(qH)=20%҂ປಆྐ༏, F(qH)=50%ປಆྐ༏, F(qH)=50%1000xB 9 RGu S
B6 V 8 Dy1<0 1214161820123456789103bcKൈL҄/4N000, iX d UF 6 BB , ;qN t f UF , p ES lRuuൈ҄/80004KLrsp,,u p HA-OzR. B
uE z a\ k B iE.^S X' jW WA y z6v ,4FD43lj z: `ad\R, 7 uv ^4,k8 @ f, Q2 ,
SF ,p E\u,uSp HA
R 8Q2 Q1,`\r:d RSx9 ,4p, jES X\ C . , 5
X
q n
-{YQ:WT < 00RX: >4 ; %D j ,6E HA2500,F(q)
,O[MN
![ h = BBH, , X . p EQ
7 yf pG O , 7 QT23, Y,u Q -ORQ,bO4 ,y C D ` \Q1
Q2 Q1 4QT Q2 SQ2 -]e%, Z[ 6,4QT Q2 BBX Dj E pE 9YQT:Q2 2,βy4 < =# ` \ 0=RQ y2 . Q E2 / Q E
=I , Q Q 2 = g ,0^ Q % . R,Z[ 6r:\9,] i% pGF(q=q)≈0 F(q=q)≈1,H6iiHiHS 8 0f b C: > Q6,j,6F(q)\
\R,!E % 6 . BB -OR[,= g\F(q)HH %, =< =g A \w
{b, β= 0 ."1
M9Nw40%,β=
970% 4ZPwUa] PQ :{x , D9 % Q2 <A, I Q1 , Q2 BB F ,p E\u,7 p HAD,73 Q2 BB 23 :[
i A BBQ1 ,6J QT, I
ࠎୄ༢ඔܴׄ՛ඔ
<1R 5Z 6= X @I _ -/&(9A/I, & 0 )l
31 , A ^\,Z[
,X 4
6 Dj E QT
b EF% ,[ 6BrB:z\ \Q 2Z 87 3S QM2N 4 y,H0 % -OR , Q2 blog4 Q {x KK,
A {Ⴕ࠺ၫ҂ປಆྐ༏,β=Ⴕ࠺ၫ҂ປಆྐ༏,β=࠺ၫ҂ປಆྐ༏ປಆྐ༏ 734MN6
8 1 0 1 231|4?16C 18 ൈ҄/Æ{jβ=β={(qH)6y|s6Bz}/ ~
}P} ~ 7 } | {|2v 3 H %~ * 0$ F+S 1 ;4h 8=HF = 9 -Æ T" } B ~Q ~1 < AQ~)2,zR 8,|q, >A12 aPFW <n ( b|}
,"8|h:~?R} 23l
blog ) ,?6 NO ,R
" a,; # }| }s,,|h ! ~~qf,Y A %'( K[1][J].ComputinginScience&Engineering,2003,5(3):71–75.[2]CastellanoC,FortunatoS,[J].ReviewsofModernPhysics,2009,81(2):591–646.[3]Sznajd-weronK,[J].InternationalJournalofModernPhysicsC,2000,11(6):1157–1165.[4][J].ActaPhysicaPolonicaB,2005,36(8):2537–2547.[5]SoodV,[J].PhysicalReviewLetters,2005,94:178701.[6]DornicI,ChateH,:Theuniversalityclassofthevotermodel[J].PhysicalReviewLetter,2001,87:045701.[7][J].PhysicaA,1999,274:132–139.[8][J].PhysicaA,2000,285:66–76.[9]:Firstimpressioncounts[J].InternationalJournalofModernPhysicsC,2006,17(2):1801–1808.[10]HegselmannR,,analysisandsimulation[J].JournalofArtificialSocietiesandSocialSimulation,2002,5(3):2.[11]ShaoJ,HavlinS,[J].PhysicalReviewLetters,2009,103:018701.[12]BorghesiC,,staggered,andpolarizeddynamicsinopinionforming:Thecontrarianeffect[J].PhysicalReviewE,2006,73:066118.[13]ShenB,[J].InternationalJournalofModernPhysicsC,2007,18(8):1231–1242.ࠎୄ༢ඔ്љੱ
1 &(,]:^c.()d_deÆ`aG157[14][J].PhysicalReviewE,2008,78:036104.[15]LambiotteR,SaramakiJ,[J].PhysicalReviewE,2009,79:046107.[16]StarkHU,TessoneCJ,[J].PhysicalReviewLetter,2008,101:018701.[17]StarkHU,TessoneCJ,-is-faster:Fosteringconsensusformationbyheterogeneousinertia[J].AdvancesinComplexSystems,2008,11(4):551–565.[18]LiPP,ZhengDF,-worldnetwork[J].PhysicalReviewE,2006,73:056128.[19]Kozma1B,[J].PhysicalReviewE,2008,77:016102.[20]AlbertR,JeongH,[J].Nature,1999,401:130–131.[21]YookSH,JeongH,[J].PhysicalReviewLetter,2001,86:5835–5838.[22]MareAD,[J].InternationalJournalofModernPhysicsC,2007,18(9):1377–1395.[23]DingF,LiuY,-evolutionofopinionandstrategyinpersuasiondynamics:Anevolutionarygametheoreticalapproach[J].InternationalJournalofModernPhysicsC,2009,20(3):479–490.
