Ch14 - CHflpTEE r4 Hid-l Let player I be the labor union...

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Unformatted text preview: CHflpTEE r4 Hid-l Let player I be the labor union with strategy i being to decrease its wage demand by 10(1-1)‘. Let player II he the management with strategy i being to increase its offer by 10(i-1)‘. The payoff matrix is: I‘M-Z .LabgL the. products respectweug Adena B.Th.cn the strategies -Por' each Tncxmw‘Y-acturer are: 4— Nev-mat éeuetopmemh oi? botk products 1— OMK cleutLppment 0% ‘3th A 3- Omsk deveLaP-memt of- product 3 Let RPWWW J. . The pusofi mtTCX then becomes. Cabana Wximltmis ‘3 ‘3‘ thn Hence, both mafia-Faefurers shou Ld use Tiar‘ynml ' dwewpmcnt amd l with Cncrease hrs share 0F tht erét by] a; [4‘1 [LU-3', Each 110.53,:- has the Sat-me semiang set. A strateng mt Speecfifi the first chip chosen mafia:- cada- posstbte Fursth b3 the. oppm‘n't ,ehotces 013m an! that ochsForemmple, a tgpceal strategg is l“Puck c: first-.113 opponent chooses “1,136:qu “AK... IS oPpG‘hf'ht Unease: Wilma“; am! 19.11? opponent damcsbpmkhmtk; when, i-sr L: 1,1,5 id.j¢,k£Z-§ v0.1.3? There are Sohorces For I. come _For each t_ 3 worms of 'covdct'flomluatmtegt'es, lemming al1 ddottl‘nct stmbegces.?a.tgo¥s are deterwhd iron the, tobte (QUL wet PagoH's are gather-“lac, O or —}Qoldep¢mdmfi 0% whether Pbfler J- WL'YIS 3b£1ne5,wun5 1 fume “yd tees ltcmt IQEl as I Strategies 4, 5 and 6 of player II are dominated by strategy 3. W or” 3 his 3 ' Strategies 4, 5 and 6 of player I are dominated by strategy 3. Strategy 1 of player II is dominated by strategy 3. Strategy 1 of player I is dominated by strategy 3. Strategy 2 of player 11 is dominated by strategy 3. Strategy 2 of playerl is dominated by strategy 3. Therefore, the Optimal strategy is for the labor union to decrease its demand by 204 and for management to increase its offer by 205'. A wage of $1.35 will be decided. I 5» A3 5 [a H mm _ . _ .415 a- mm“ .“5 H 155; l‘iL-Z. (a) Strategy 3 of player I is dominated by strategy 2. Strategy 3 of player II is dominated by strategy 1. Strategy 1 of playerl is dominated by strategy 2. Strategy 2 of player If is dominated by strategy 1. Therefore, the optimal strategy is for player Ito choose strategy 2 and player [I to choose strategy 1 resulting in‘a payoff of 1 to player 1. 1+1 1'41'2‘ B Strategy 1 of player 11 is dominated by strategy 3. Strategy 2 of player I is dominated by both strategies 1 and 3. Strategy 2 of player 11 is dominated by strategy 3. Strategy 1 of player I is dominated by strategy 3. Therefore, the optimal strategy is for player I to choose strategy 3 and player 11 to choose strategy 3 resulting in a payoff of I to - player 11. {HZ-3 Strategy 1 of player II is dominated by strategy 3. Strategy 4 of player II is dominated by strategy 2. Strategies 1 and 2 of player I are dominated by strategy 3. Strategy 2 of player II is dominated by strategy 3. Therefore, the optimal strategy is for player I to choose strategy 3 and-player II to choose strategy 3 resulting in a payoff of 1 to player II. Para. 1: uses shaky a. The fam 35 Shaun gal-A saddkpaim} (3,3) FIW 11: ms S‘h’arhiauf .7. The. page. is Stable. wE‘H'i saddlapo‘m‘l' (3,2,) l<~max_ VI: ; F’Qa—E H565"- sturkgy I that flag?!“ I use; slmkfly 3- M’B "I , flayed I 1495 Sit-m»ka 3am Viz-é (13) P423 [00 Strategy 1 of player II is dominated by strategy 3. Strategy 3 of player I is dominated by strategies 1 and 2. Strategy 2 of player II is dominated by strategy 3. Strategy 2 of player I is dominated'by strategy 1. Therefore, the optimal strategy is for player I to choose strategy 1 and player II to choose strategy 3 resulting in a payoff of l to player I. Wmn Maximum: 1% 0 5 . t-wutn Hence, u“: 0 wow» ‘Poic‘rcgcom 1 Manes Issue a and qaoUticLom Ii ULSIth Issue 2 . (b) LS‘t pcj=?§wcnnthcj or {niches election [:OFWLcl'ucwxmlg Then the patio“: mm: becomes 5kmth '3 01r- 1’0Lc’cccxam1 chemimtesl big strategica- Stratum a. o? 'l’oLct‘L‘u‘am’l domt mica by: smteml. Stratujies‘i and 3 0? “Po LCthcaL-n’i dorm-notth b3 stmtcggal. Hemee,sumtnai-c dommot’ced simmer“ acves no Lew“ ?oL¢rccham 1. Mung Issue 1 cum-J Pout-coma» IE moms issue a. T Kvanv-e,'polih;cxam IL com prevent ‘PoLcfiqiom 1 Wm warm.qu or tun-sq. (C) = i 4 I WC'YL 0" tie 0 5? T’otcttm-n 11 wLLL wen Timex the pagoFF mahmx becomes ILL-'1‘ I‘m-7 to Min [comma mmch = o = H ' - cm MERowmanmofl _ Hence the mtntmo-x cater-Can gums «:0 L'PchtcdanI cannot win).’PaLcth£an-\1 each use an“ Esau: onnd ?0Lci:cc£o.n 1} cam LLse ISSuc 1 or 3.HDvJ¢\1€", Mince. Issue 1 OWers ’PoLcticLan 1 has Dial-41 (Memos o-F wcnm‘nq ,lme shouts! use that ama hope ’Poub-LLComfi which an err-or amd also LLScs Issue 4- 142-8 Advamkafles: It- provides the best posscblc guarantee 97" what the war-5t outwme (A11 be, r‘equr‘aHess OF how sdel-F—ultus the. Opponent PW}; the game-Thmhm til: reduces the v‘csk 0F vex-L1" undescmble, album“ 50 a. Whilmmm. M1 I?“ aver-q Lowsarvmhve Wpr‘oaok, amd1HflLNFore, lit Maw} weld Hr Hum the best fifimties £01- 0 I cr-I. Stratcces £0? [.4 er]: 4—1: mar-1 mam. l-Bet on head; or- tail. - 5. ’P 5 on heads, bet catsuit: m S'Er‘a’ccgies 4 arm-J 3 of pager I are dommied b5 simiqu a .ELCminaicwnas the dom3nated Strategies we obtqcm the pas-50F? table. 1 1 4 :1 ' 1 0 5 '1 5/; 0 1+1? Column mmxcmum 5/; 5 tram MLn[coh.Lm mum] at Mmfilou minimal , thmkre {:here. [.5 W0 Saddle pom-rt. fc cfll’ke/ p’wer dun a pure SMW:7, '"w “Hue.— Piaf, and “KM? ‘6 3+4ij M Inc/L « M7 a; +0 Cw: h «CW flaw—+1. war 41) wag}: 1A3 5mm.» oat mad flf'mfijh; u: «44_ e—FP'ECM f21¥1\f1 + F21x7-Y1 + {‘1‘ qul +f‘flK‘IYL /. Lie"? '5’ buff (’th Fret-LL'I-4f6 M‘s-‘39 \I‘+ Y1 :} “OLA aflJ-JOHJHM -I cm (i).- VlfrhV-fin :25“. :é-ifl—x-L) CW w s" m = mm») {31): \IILAE : Y1 fgl (:04. J71 I“ T13 "" I; h +2; {l‘hJ 1: 5' S‘ 1} $1. + "q 14.9-1 5L2 (4—an = 5%; n) (x'L x; x;,x.‘:) = tog/3' 03,5) and W 5/3 + 3' :0? >951 => %, = => L11. L31).; (#3, 4/3,) :4-5 3x1+U~XO = 1%1-1'1 LIX, a -x1+1 2;th mam. 2w) aha V: 335 31KH1.3+\5.3L‘*1*1)=8/5 {'05- 053‘4‘1 1) 1%‘3'8/5 1H5“ 4- I5; = Us :3. Lahgilgg): Limo, 'w) 1431-30,) Shkay 3 0F film’qu 1'5 dominakd by I reducing fie Mk {D5 4 . 30km. daesmt awdm butter-Hos I.Ma»kdm$-nol* swim Mafia 4.. 30% docs Mot swcm mast-rm &.kad.oas net swim MW' 5.3-ohm i085 not swim lama 31.M0wk does 1nd: Mm MSW Let {:he PW-joCF entrees be the tot-a1 Pawn Won an all fine; events when at gcuem Wrap smfeg “5 are used btd the tea-MS — Then We p410“: who; becomes: 4 N {L 3 Sfmfejxj 2 OP AJ. Team dominated b3 stmkagtj 1} Sfmtegg’l OF Ga.N.Tea7n domtwated be} strategg 6’- ' “1":55) Expected 13ch OFF => :41”: g at. +43 “-xt=141lx:"ol x3: 4/‘1 amd V=l2'/£ WM (a; (ma) £(¥1+4a)+~1§(—¥1+43) g 1:. 1/; Fov- 04m! =91“! +131} my:- 13 4.431;.12 5"; Q ‘jqfio ' 13:34]: Iggg 1/: Thai“ Cs) J'on shoutd Alwags Sue-m the back-stroke and ahould SWL'W'I the butter-Hal 09‘ breastamu sack wdfln probe-MUN 1’2- 4'Lso, Mar-k shoufd mtwaugs chm the mtterfl—u}. and should swcm the backstroke 0r breaststroke each weft; thabch‘hj 1’3. And the I'LJ'. Team can cxpect {'0 act 134/; pants an the {uhch wants. (in) The stmtggcgs For the We teams are as £71 part (a)- Let p“. -3 ‘m CF My” Fer partta};t\mj: :5,AJ.Team wens 31/; 4:55 aids {tor partta13tha£65,A.J.T¢amLoses The pm, ofiF mamx btwmes Stratqu 51 01: AJ. Team dominq‘l'ed bg shuregg 1.. Strutqu ‘I 0? SN Team dominated lag stmiegqa. After tLt‘rnihah'Yq Hne dominated strategies the. N II 131/; CS added to each chm-4,151: OptimaL Strategies an: unchanged.13uri‘hermore, the mafi- Mabn‘x 0? part to.) is obtained. Hence the strategies Swan in part at.) are stilt optimal and mama-1:9;- o l4.H-L!Lc756nce John and Mar-k are the best: swcmmers cm 'lahelir mspectcue teamsJ Hug welt alum-.15 Swim in two event-a since the, tea-m a», do no he Eter- CF they} :5ow in (mtg one or m events.He.-nce,cF_ewher does not SwC‘m Eh (:hc Fer-st event) the butterth,He wCLL swab} Sow fine but two events. Tbm; the strategies {-‘or- the AI. team are : 4-30hn embers the butterth amd than enters the back-5mm regardless OI yum-gum Park enter-s I {the bufichUj. Liohn enters the. butterqu and than 5ow5 the backatroke. C9 Max-K enters the Eadie-FELL}, but chms breaststroke C? Mark does not. 5. John em'tm the bung-m; and then swcms breast- shake. EC Mow-k tankers the bufioqu1mI: ch'nns {-Me backst'r‘okc (J? Mark does not. 11. john ant:ch the butiorFLusaLhd the-n sworn-5 like breastsbr‘oke mew-Mess o'F wkelrhu- Marke'ntcrs We buttchLg. -5.John dogs 'hut swim the buEtUHAj flhnd, the,“ enters both the bmshtmke amd the Mmm_ The skatcgtes (lor- the 6..N.Teonm are, as alcove but with-the- Fotes 0? 30km amd Mark ravaged. T he 0 PF moder L1‘5 {4'}? 1119A (a) (amt) 5Wtcg¢1 5 0? 6.N.Teann domcnates out! "others. SL'nce {he {Esau-£7143 page“ Mai-rm vs.- 3 . _ 3» t?— G.N- Team uses Shrdegg .3»J LC MIN 3 \N‘C‘h , regardtess 053 H1: shutqu 1; Chosen be} an: LII. Team. (at) SWRQH 2 o? AITeam dominates shutegces {,3,4I. I Thusch the coach Por- Has G-N Tea'rn' MM} choose 0mg 0? lnt‘s stmkfices at whalch the coach Cor Hue A-J.Teo.m should clacose u’ldncr atmth 9- th- ‘54 The pave: mm: becomgs (apt-er epwm‘nah‘ng {the Wdhafed strait-slits 0? Al Team).- A._ - 1 a 5 t, ' _ -Thus,cF khe mm For L—he AlTeaim knows that the Wher- coadn. has a tandem»; ho 311er Mark Ch butter-R“ and backswokc mom 0H1!“ Hanna bust— Stroke) that mums coLmnn { 95 More Mikel»; {a be (Jensen than colMTnh ’1. Thergfiore‘ the coach for“ Hat 45.73am should (1400.5: Strateglj 5L. H-H H54 Aéclbng 5 to the Entries 0; tabLe 19.6 we obtmm the Paulo’r‘F tau; 1 A a 3 1 3 ‘1 5 .‘L 5 3' O The, mew Unan- qummmcng moéel For pLagerI 1:5: Moxémnc X5 ' subject ho SKA-3545 30 x1 «via-:3 30 x.* “a *1 X‘ I. Thc, new Lenmr programequ modeL For pmger‘jl 55: chtmfizc lja subject to bgfi ggfigrlfl £0 3%. + 4L5; - by, é 0 ‘31 * ‘11 '* ‘13 2 i 1‘5" '1'” ‘3‘! ‘5‘! ’}0 Based om the ch¥ormakion given En Sect-ma 13.5, the. optimat soLutLOhs $91» these newmodeb am: (xfmgmgh (1/44, Hm , 55/40 amo‘ 05?.152,3:,3:).(0Mc.‘m,5%00 Note 'lzhOLt x3": afi6 (LL30 542%: =v+5 where V is the orcacml game vatuc. 2. Mud man X1. subjectto 5&*1&*3?‘3"¥H?0 5x.+3x, mac L 11 +axa+lmflwo 5 K14: 11+ X3 SJ. 1. x1 x5 “"30 Optimal Solution 1 : J olve Automatically by the Simplex Method: VaLue of the Objective Function: Z = 2.36842105 Variable X1 0.05263 X2 0.?3684 X3 0.21053 X4 2.36842 {4J1 Solve Automatically by the Simplex Method: [1153 73’ rhsufie. 21; 30 Add 3 1'2: Lac}: ) en‘H‘Ll; 03C Hue whim-139.. 1’9- SHLP‘EC'E f0: ¥Xr 4-2)“! - If 5x,+3xz + 61:3 wt, a0 L) Optimal Solution Value of the Objective Function: Z = 3 .79166567 1115-“! 97,0 insane 955 ea add ‘r’v‘o édclx {"479 0F He fable. Solve Automatically by the Simplex Method: I) Optimal Solution WIMIJR .\ : 4- _ juk’ecfi‘ +0 53f,+éi¢z 41'; 1530 Value of the I, -- 1x; +S’x3 4-qu *%30 Objective “nation: Z = 338101266 . a ‘- 3“ .0 $31, 4 9'21 +313 + 2X9 *5 3‘9 Variable £9" t-"22:3,'1',5 2" {fix 4— x + £9 and ~x5 20 X1 0 ' . z 3 X2 0.26582 x5 3.98101 mm. yq L1" 471’*1‘{1’ +Y‘r 1° L" “M *Jy; Wfi 2" [0‘ 5:; =13, 64.23 mm EV" EV}! : ._) SKLJJJJ'WHBJ Inning! {in 3.111% PJR-y’crfi Pmbm' There Fore the. 9805651.: ream»; M be aLermfmfly éescx‘dbeé bu, '— 79: L-x‘ 3/5 5’. x, 1:. 33/3 The. matrcctcons maul be rewnittch as: Xjé'5xw5 3/5éx4$9v'3 x35-(,x1+# 3/93,‘ x1 53/3 x3, 5 5xr3 35/50:.I 41/3 ThemPor-e the Olgc5mic. expressfio-n Go»- the‘ maxemc 2015 Value 0? x5 For- a..th pocht in Hue. lusche region cs: x3 = E- 5x1-3 30v- 3/5 {x15 fly" ‘65‘14'11 {:Ov- 1/41$><1<3/3 H6100: , the optn'qu SoLuh'ox LB -' X: 21%|! Xi: {-1744 1: 11/4” X; a 5 GAO-.3 .. 3/41 (4-H ILLS‘S 11010101111: SIMPLE): "£1000: FINAL TABLEAU Baleq| Coefficient of | Right Var|No| 21 x1 x2 x3 11!. x5 116 11? 110 11:9 3110 | side _|HJ._!%H._—I | | | 1H 111 ‘IM 111 | 2 | 0| 1| 0 0 0 0 0.455 0.545 0 -0.45 -0.5-5 0.182 | 0.152 x2| 1| 0| 0 1 0 0 -0.09 0.091 0 0.091 -0.09 0-364 | 0.3.5:. Kat 2| 0| 0 0 0 1 40-91 -0.09 -1 0.900 0.091 1.636 | 1.636 x1| 3| 0| 1 0 0 0 0.091 -0.09 0 -0.09 0.091 0.636 | 0.636 x3| 4| 0| 0 0 1 0 0-455 0.545 0 -0.45 -0.55 0.182 | 0.152 Til-1e rfrnjlal solujicm rs (“In-KL) :(01336) 0.3M!) wm‘ a lam/OFF: Odaz The {Ph‘nnJ data! 5oht+r0u ,5 (y'Jy-zjys) = (o) aqng 0.545) “1.5-? 105mm saddle points can 6: Found From the LCY'IEQI- programming «Carma Lemon 0’? fine fiflm€,parf'£a) Fouows Prom part (b). Lb)Oorhscder Hue Linear- pmgmmmcng fimMahb-n a; an; problern ’Fw T’Luqu II. Th; 1555' and K915 conshnini's are P£1H1+Pu%a* -" +’Pc-n‘jn ‘5 “jun W131." Yua‘sfl ' ‘ *?kh‘5n {- finn It: rowk. weOLKUg éomtmtes Kiwi-wan p“ Wt" * ' ‘ +'Pim‘fin 4 if)” Kan -- - + 13K.“ ‘3." cww 15,)...3‘ Thad: '55, the. lit-l" constraint cs Néuhda'nt 51:th cl: (:5 (implied bus the, kflmmmcnf. Hmce, eliminah'“q Hekaus Ami naieé pure strutgaces 3?"- Plaflerfmmsfnds [:0 eLCmle-‘E'Yts redunéa-n-t Oonsw‘atnst C'n E‘ne (mnem- Pmfimm p0" pin-“sir 11:. SCMLLay-lg, eLCmimHnol weakLg éomcnal'ed pure stvntefims 901“ NM" 1'1. correspond; ‘70 cL-CWrmh’ng redundant ounsh-Mn'l-s Ch the Lyme“... pmajra'm Pn— ‘PECMScr-I. 56mg We process cannot eLCanalt Feasible 50M- h‘cms or create “rewoth a.“ optimaJ shat-cases Mhhof be ett’mfinaf‘d Mad. 'hew ones cannot be Outed. 14—15 ...
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This note was uploaded on 02/15/2010 for the course IE 220 taught by Professor Storer during the Spring '07 term at Lehigh University .

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Ch14 - CHflpTEE r4 Hid-l Let player I be the labor union...

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