Teoria de Juegos

 

^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 + 95555.> + ∙ ∙?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 

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  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]  >