Teoria de Juegos
September 23, 2022 | Author: Anonymous | Category: N/A
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^O^ „ 90;5 „ I „ Ofvlstohknoþf gl Cplrknocfls OO \fov. Ycfkbg @lrmíf Uknc Jkvolr
Wlmk 9 Kfëbosos gl glnosocfls 9.; 9.9 9.9.; 9.9.;.;
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Oftrcgunnoþf Wcmk gl glnosocfls, lf bk ofvlstohknoþf gl cplrknocfls Nbkso`onknoþf gl bcs mcglbcs gl tcmk gl glnosocfls Lblmlftcs gl bk tcmk gl glnosocfls
9.9.;.9 9.9.;.>
Urcnlgomolftc pkrk lbikjc prcnlsc gl glnosoþf Wcmk gl glnosocfls ofnlrtogumirl
9.9.;.7 Wcmk gl glnosocfls ikjc Yolshc K. Nrotlroc glb vkbcr lsplrkgc I. Ëricbls gl glnosoþf N. Wlcrlmk gl Ikyls lf bk tcmk gl glnosocfls Ljlmpbc Mkrtof‟s ^lrvonl ^tktocf lstë
ncfsoglrkfgc pkrtonopkr, lb prþxomc ofvolrfc, lf lb flhcnoc gl quotkr bk folvl. Mkrtof pulgl ncmprkr ufk nunaobbk kgotkmlftc pkrk su nkmoþf pond-up c uf nkmoþf quotkfolvls pkrk trkikjc plskgc. Glspuïs gl kfkbozkr bk sotuknoþf, Mkrtof lfnulftrk qul nukbquolr kbtlrfktovk slrë ufk ofvlrsoþf rlftkibl so aky flvkgks `ulrtls. ^o bks flvkgks scf mcglrkgks, bk rlftkiobogkg pulgl slr plqulûk y so bks flvkgks scf muy bohlrks, pulgl tlflr pïrgogks. Lf bk tkibk sohuolftl sl mulstrkf bks hkfkfnoks y bks pïrgogks
Bks prcikiobogkgls gl bcs lstkgcs scf U(s;) = 5.7, U(s9) = 5.> U(s>) = 5.>. ^upcfhk qul Mkrtof glnogl lsplrkr akstk slptolmirl kftls gl tcmkr ufk uf k glnosoþf. Bks prcikiobogkgls lstomkgks gl qul lf slptolmirl akhk uf `ríc fcrmkb (F) c uf `ríc oflsplrkgc (O) scf bks sohuolftls:
k) Ncfstruyk uf ëricb gl glnosoþf pkrk lstl prciblmk. i) ³Nuëb ls bk glnosoþf rlncmlfgkgk so Mkrtof fc lsplrk akstk slptolmirl3 ³Nuëb ls lb vkbcr lsplrkgc3 ; ‒\f pkís ls hrkfgl scbc nukfgc sus ofhlfolrcs ksí bc quolrlf”
^O^ „ 90;5 „ I „ Ofvlstohknoþf gl Cplrknocfls OO \fov. Ycfkbg @lrmíf Uknc Jkvolr ------------------------------------------------------------------------------------
n) ³Nuëb ls lb vkbcr lsplrkgc gl bk of`crmknoþf plr`lntk3 g) ³Nuëb ls bk lstrktlhok þptomk gl glnosoþf so fc sl tcmk bk glnosoþf sofc akstk qul sl akyk gltlrmofkgc lb nbomk lf slptolmirl3 ³Nuëb ls lb vkbcr lsplrkgc gl lstk lstrktlhok3 glnosocfls N. Wlcrlmk gl Ikylrs lf bk tcmk gl glnosocfls Nkrkntlrístonks: ^l kpbonk lf tlcrlmk gl ikylrs lf lb prcnlsc gl glnosocfls. ^l kntukbozk lb vkbcr gl bks prcikiobogkgls K procro ncfvortoïfgcbks lf prcnknogkgls K. •
•
∘U ΑD/Q ∛= ∘U………..(;)
Ukrk kpbonkr sl glil slhuor lb sohuolftl prcnlgomolftc: Ncfstruor ufk mktroz gl cislrvknocfls (Q) Bk mktroz gl cislrvknocfls, tolfls lxplromlftcs (O), rlbknocfkgcs ncf bcs lstkgcs gl fkturkblzk ( ΑD) rlbknocfkgcs ncf prcfþstoncs, lfnulstks g, gktcs aostþroncs, ltn ^l ofnurrl lf ncstcs glb lxplromlftc (Q), N Bulhc kpbonkr bk lstrktlhok mktlmëtonk: •
•
•
∅ T , Α] ∙ ∙ …… ;
Gcfgl Cpt: so bk mktroz ls gl ilfl`onocs, lftcfnls. Cpt: mkxomozkr Cpt: so bk mktroz ls gl ncstcs/plrgogks, lftcfnls. Cpt: C pt: mkxomozkr
Ljlmpbc Mkrtof‟s ^lrvonl ^tktocf lstë
ncfsoglrkfgc pkrtonopkr, lb prþxomc ofvolrfc, lf lb flhcnoc gl quotkr bk folvl. Mkrtof pulgl ncmprkr ufk nunaobbk kgotkmlftc pkrk su nkmoþf pond-up c uf nkmoþf quotkfolvls pkrk trkikjc plskgc. Glspuïs gl kfkbozkr bk sotuknoþf, Mkrtof lfnulftrk qul nukbquolr kbtlrfktovk slrë ufk ofvlrsoþf rlftkibl so aky flvkgks `ulrtls. ^o bks flvkgks scf mcglrkgks, bk rlftkiobogkg pulgl slr plqulûk y so bks flvkgks scf muy bohlrks, pulgl tlflr pïrgogks. pïrgogks . Lf bk tkibk sohuolftl sl mulstrkf bks hkfkfnoks y bks pïrgogks
9 ‒\f pkís ls hrkfgl scbc nukfgc sus ofhlfolrcs ksí bc quolrlf”
^O^ „ 90;5 „ I „ Ofvlstohknoþf gl Cplrknocfls OO \fov. Ycfkbg @lrmíf Uknc Jkvolr ------------------------------------------------------------------------------------
Bks prcikiobogkgls gl bcs lstkgcs scf U(s;) = 5.7, U(s9) = 5.> U(s>) = 5.>. ^upcfhk qul Mkrtof glnogl lsplrkr akstk slptolmirl kftls gl tcmkr ufk uf k glnosoþf. Bks prcikiobogkgls lstomkgks gl qul lf slptolmirl akhk uf `ríc fcrmkb (F) c uf `ríc oflsplrkgc (O) scf bks sohuolftls:
k) Ncfstruyk uf ëricb gl glnosoþf pkrk lstl prciblmk. i) ³Nuëb ls bk glnosoþf rlncmlfgkgk so Mkrtof fc lsplrk akstk slptolmirl3 ³Nuëb ls lb vkbcr lsplrkgc3 n) ³Nuëb ls lb vkbcr lsplrkgc gl bk of`crmknoþf plr`lntk3 g) ³Nuëb ls bk lstrktlhok þptomk gl glnosoþf so fc sl tcmk bk glnosoþf sofc akstk qul sl akyk gltlrmofkgc lb nbomk lf slptolmirl3 ³Nuëb ls lb vkbcr lsplrkgc gl lstk lstrktlhok3 ^CB\NOCF Lblmlftcs gl bk tcmk gl glnosocfls L;: tcmkgcr gl glnosocfls: Mkrtof L9: Lstkgcs gl fkturkblzk Α;: flvkgks `ulrtls Α9: mcglrkgks Α>: flvkgks scf muy bohlrks •
• •
Urcikiobogkgls K procro UΑ;): 5.7 UΑ9): 5.> U(Α>): 5.> L>:L7 • • •
ΑD
k;: ncmprkr ufk nunaobbk kgotkmlftc
Α;
Α9
Α>
Flvkgks `ulrtls UΑ;): 5.7
Mcglrkgks UΑ9): 5.>
flvkgks scf muy bohlrks U(Α>): 5.>
>5 5=;9 Ukrk k9: ncmprkr uf nkmoþf quotkfolvls
T , Α] 8555∘ 5.7 + 95555.> + ∙ ∙?5 ?555 55∘∘ 5.> 5.>5 5=855 ^us ^us D=;,9,>
Lftcfnls rllmpbkzkmcs lf bk lnuknoþf
∅ T , Α]=(;9
5.>< 5.09 ;.55
5.>5 5.>; ;.55
5.>< 5.58 ;.55
7 ‒\f pkís ls hrkfgl scbc nukfgc sus ofhlfolrcs ksí bc quolrlf”
^O^ „ 90;5 „ I „ Ofvlstohknoþf gl Cplrknocfls OO \fov. Ycfkbg @lrmíf Uknc Jkvolr ------------------------------------------------------------------------------------
Lftcfnls ΑD Q
;: `roc fcrmkb(F):5.1 9: `roc oflsplrkgc (O):5.9 sumk
Α;
Α9
Α>
Flvkgks `ulrtls UΑ;): 5.7
Mcglrkgks UΑ9): 5.>
flvkgks scf muy bohlrks U(Α>): 5.>
5.>< 5.09 5.?8
5.>5 5.>; 5.0;
5.>< 5.58 5.79
Α;
Α9
Α>
Flvkgks `ulrtls UΑ;): 5.7
Mcglrkgks UΑ9): 5.>
flvkgks scf muy bohlrks U(Α>): 5.>
5.>0 5.07 ;.55
5.7? 5. 5.;8 ;.55
Lftcfnls bk mktroz gl prcikiobogkgls slrë:
ΑD Q
;: `roc fcrmkb(F):5.1 9: `roc oflsplrkgc (O):5.9 sumk
Kpbonkfgc lb tlcrlmk gl Ikylr pkrk citlflr bks prcikiobogkgls K procro
∘U ΑD/Q ∛= ∘U………..(;) Ncf lb lxplromlftc ;4 `roc fcrmkb (F) Ukrk (Α;): flvkgks `ulrtls
•
5.>>0∘ 0 ∘ 5.7 5.;77 5.98 ( Α;; ) 5.>>0∘ 0 ∘ 55..7 + 55..7? 7?∘∘ 55..> + 5.5.1> ∘ 5.> 5.5 5.;78 ( ; ) 5.>>0∘ 0 ∘ 55..7 + 55..7? 7?∘∘ 55..> + 5.5.1> ∘ 5.> 5.): flvkgks muy bohlrks
•
Α> 5.1>.∘ 5.>5 5.97? ( ; ) 5.>>0∘ 0 ∘ 55..7 + 55..7? 7?∘∘ 55..> + 5.5.1> ∘ 5.> 5. ( Α9 ) 5.0077 ∘ 5.7 +5.5 55.. 5.> 5.705 Ukrk (Α>): flvkgks muy bohlrks
•
5.5 ) 5.0077 ∘ 5.7 +5.;8∘5.>5 55.. 5.> 5.705 Lftcfnls bk mktroz gl prcikiobogkgls K pcstlrocro slrë:
ΑD Q
;: `roc fcrmkb(F):5.1 9: `roc oflsplrkgc (O):5.9
Α;
Α9
Α>
Flvkgks `ulrtls UΑ;): 5.7
Mcglrkgks UΑ9): 5.>
flvkgks scf muy bohlrks U(Α>): 5.>
5.98 5.>
5.70 5.;;
sumk
;.55 ;.55
Kpbonkfgc lb tlcrlmk gl ikyls : ncf mktroz gl ilfl`onocs Lxplromlftc `roc fcrmkb akstk slptolmirl
∅ T , Α]
Ukrk k;: ncmprkr ufk nunaobbk kgotkmlftc
T , Α] >
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