{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 " Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 } } {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "restart;\na:=6: b:= -2: c:=-3: d:=1:\nu:=(p, q)->a*(1-p)*(1-q)+b*(1-p)*q+c*p*(1-q)+d*p*q: \ncollect(u(p, q), q); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&,&!\") \"\"\"*&\"#7F'%\"pGF'F'F'%\"qGF'F'\"\"'F'*&\"\"*F'F*F'!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "U1:=p->minimize(u(p, q), q=0 ..1);\ns:=maximize(U1(p), p=0..1);\npe:=solve(U1(p)=s, p);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#U1GR6#%\"pG6\"6$%)operatorG%&arrowGF(-%)m inimizeG6$-%\"uG6$9$%\"qG/F3;\"\"!\"\"\"F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#peG# \"\"#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "plot(U1, 0..1 );" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG 6$7U7$\"\"!$!\"#F(7$$\"+;arz@!#6$!+Q&3Y$>!\"*7$$\"+XTFwSF.$!+wmP()F17$$\"+$Q*o]RFD $!*&=$z9)F17$$\"+\"=lj;%FD$!*Y/4](F17$$\"+V&RC'F17$$\"+R\"3Gy%FD$!*ev:l&F17$$\"+.T1&*\\FD$!*p2[,&F17$$ \"+(RQb@&FD$!*\"[Q`VF17$$\"+=>Y2aFD$!*C9wx$F17$$\"+yXu9cFD$!*Emd:$F17$ $\"+\\y))GeFD$!*XOL^#F17$$\"+i_QQgFD$!+;U%[)=FD7$$\"+!y%3TiFD$!+gcuw7F D7$$\"+O![hY'FD$!*))eb,'FD7$$\"+4FEnlFD$!*s=@)HFD7$$\"+#Qx$omFD$!(W'R: F17$$\"+y)Qjx'FD$!)!*\\q)*F17$$\"+u.I%)oFD$!*O.(e>F17$$\"+(pe*zqFD$!*F G'>PF17$$\"+C\\'QH(FD$!*J%yWcF17$$\"+8S8&\\(FD$!*71iX(F17$$\"+0#=bq(FD $!*&Qm\\$*F17$$\"+2s?6zFD$!+'['3?6F17$$\"+IXaE\")FD$!+x+*QJ\"F17$$\"+l *RRL)FD$!+pfa+:F17$$\"+`<.Y&)FD$!+y&G9p\"F17$$\"+8tOc()FD$!+#eI2)=F17$ $\"+\\Qk\\*)FD$!+k%zY0#F17$$\"+p0;r\"*FD$!+7X/aAF17$$\"+lxGp$*FD$!+*)* eBV#F17$$\"+!oK0e*FD$!+7%zCi#F17$$\"+<5s#y*FD$!+:*[W!GF17$\"\"\"$!\"$F (-%'COLOURG6&%$RGBG$\"#5!\"\"$F(F(Fh[l-%+AXESLABELSG6$Q!6\"F\\\\l-%%VI EWG6$;Fh[l$F^[lF(%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "patron:=proc(autre::integer)\nif rand(3)()<2 then 1 e lse 0 fi;\nend proc:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 172 "pa t_int:=proc(autre::integer)\nglobal P_N, P_1;\nif autre=-1 then P_N:=0 ; P_1:=0; rand(2)(); \nelse P_N:=P_N+1; P_1:=P_1+autre;\n if P_1/P_N> 2/3 then 1 else 0 fi\nfi;\nend proc:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "syndicat:=proc(autre::integer)\nif rand(5)()<3 then 1 else 0 fi;\nend proc:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "s yn_bete:=proc(autre::integer)\nif autre=0 then 0 else 1 fi;\nend:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 172 "syn_int:=proc(autre::intege r)\nglobal S_N, S_1;\nif autre=-1 then S_N:=0; S_1:=0; rand(2)(); \nel se S_N:=S_N+1; S_1:=S_1+autre;\n if S_1/S_N>2/3 then 0 else 1 fi\nfi; \nend proc:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 325 "annee:=proc (p, s)\nlocal k, x, ox, y, sc;\nsc:=0; x:=-1; y:=-1;\nfor k from 1 to \+ 10000 do\n ox:=x; x:=p(y); y:=s(ox);\n if x=0 and y=0 then sc:=sc+6; \n elif x=0 and y=1 then sc:=sc-2;\n elif x=1 and y=0 then sc:=sc-3; \n elif x=1 and y=1 then sc:=sc+1;\n else ERROR(\"partie invalide\") ; fi;\n# print([x, y, sc]);\nod;\nsc;\nend proc:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 24 "annee(pat_int, syn_int);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#!#d" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "S_N ;S_1;P_1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"%****" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"%)e'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"%xm" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "maximize(u(x, 3/5),x=0..1); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"'\"\"&" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}}{MARK "13 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }