$/RWKULQJHU6WU'.|OQ*HUPDQ\7HOHSKRQH $ $/RWKULQJHU6WU'.|OQ*HUPDQ\7HOHSKRQH $

/RWKULQJHU6WU'.|OQ*HUPDQ\7HOHSKRQH - PDF document

pamella-moone . @pamella-moone

371 views
Uploaded On 2016-05-19

About Share Download

/RWKULQJHU6WU'.|OQ*HUPDQ\7HOHSKRQH - PPT Presentation

03LVFXVVLRQ3DSHU7KHSDSHUFULWLFLHVHOURG ID: 326524

)*'LVFXVVLRQ3DSHU7KHSDSHUFULWLFL]HV$[HOURG

Link:

Copy

Embed:

<iframe width="560" height="315" src="https://www.docslides.com/embed/326524" frameborder="0" allowfullscreen></iframe>

Download Presentation from below link

Download Pdf The PPT/PDF document "/RWKULQJHU6WU'.|OQ..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.

Presentation Transcript

/RWKULQJHU6WU'.|OQ*HUPDQ\7HOHSKRQH)D[03,)*'LVFXVVLRQ3DSHU(0DLOPSL#PSLIJNRHOQPSJGH,661¥+RPH3DJHKWWSZZZPSLIJNRHOQPSJGH'HFHPEHU 03,)*'LVFXVVLRQ3DSHU7KHSDSHUFULWLFL]HV$[HOURGªVPHDVXUHRIFRQIOLFWZKLFKLVEDVLFDOO\DPHDVXUHRIWKHFRQIOLFWRILQWHUHVWDQGGRHVQRWDFFRXQWIRUWKHSRWHQWLDOIRURYHUWFRQIOLFWIXOEHKDYLRUEDVHGRQKRZWKHDFWRUVDUHVWUDWHJLFDOO\LQWHUSRVLWLRQHG'LIIHUHQFHVEHWZHHQWKHWZRGLPHQVLRQVRIFRQIOLFWDUHLOOXVWUDWHGDQGLWLVVKRZQKRZERWKGLPHQVLRQVDUHQHFHVVDU\IRUDWKHRU\RIFRQIOLFW&RQIOLFWLVFRQFHSWXDOL]HGDVDVWUXJJOHIRUSUHIHUUHGHTXLOLEULDLQ[JDPHVZLWKDWOHDVWWZRHTXLOLEULD$QHZPHDVXUHRIFRQIOLFWIRUWKLVFODVVRIJDPHVEDVHGRQWKHFRQFHSWRIULVNOLPLWLVGHYHORSHGLQERWKDVWDWLFDQGDUHSHDWHGJDPHVHWWLQJ7KHULVNOLPLWDSSURDFKPHDVXUHVWKHDFWRUVªLQFOLQDWLRQWRLQDFRQFLOLDWRU\RUFKDOOHQJLQJZD\7KLVLVGLIIHUHQWIURP$[HOURGªVDSSURDFKZKLFKPHDVXUHVWKHLQFRPSDWLELOLW\¥DQGKHQFHWKHFRQIOLFW¥RIWKHDFWRUVª:HVKRZWKDWKLJKHULQFRPSDWLELOLW\RISUHIHUHQFHVEHWZHHQWKHDFWRUVGRHVQRWQHFHVVDULO\LPSO\WKDWWKH\DUHPRUHLQFOLQHGWREHKDYHFKDOOHQJLQJO\)XUWKHUPRUHZHVKRZWKDWWKHPRUHDFWRUVYDOXHIXWXUHSD\RIIVLQWHUPVRISUHVHQWSD\RIIVWKH,QGLHVHP%HLWUDJZLUG$[HOURGV.RQIOLNWPD‰NULWLVLHUWZHOFKHVDOV0D‰GLHVWUDWHJLVFKH(QWVFKHLGXQJGHU$NWHXUHIUNRQIOLNWKDIWHV9HUKDOWHQXQEHUFNVLFKWLJWOl‰W(VZHUGHQ8QWHUVFKLHGH]ZLVFKHQGHQEHLGHQ'LPHQVLRQHQYRQ.RQIOLNWYHUGHXWOLFKWXQGZLU]HLJHQGD‰EHLGH'LPHQVLRQHQLQHLQHU.RQIOLNWWKHRULHZLFKWLJVLQG.RQIOLNWZLUGKLHUDXIJHID‰WDOV6WUHLWXPEHYRU]XJWH*OHLFKJHZLFKWHLQ[6SLHOHQ:LUHQWZLFNHOQHLQQHXHV.RQIOLNWPD‰ZHOFKHVDXIGHP.RQ]HSWGHU5LVLNRJUHQ]HULVNOLPLWDXIEDXWXQGVWHOOHQHVLQHLQHPVWDWLVFKHQXQGLQHLQHPZLHGHUKROWHQ6SLHOYRU'DV0D‰PL‰WGLH%HUHLWVFKDIWGHU$NWHXUHVLFKLQHLQHU.RQIOLNWVLWXDWLRQNRQ]LOLDQWRGHUKHUDXVIRUGHUQG]X(VXQWHUVFKHLGHWVLFKGDPLWYRQ$[HOURGV0D‰ZHOFKHVDXIGLH8QYHUHLQEDUNHLWHQ¥XQGVRPLWGHQ.RQIOLNW¥]ZLVFKHQDE]LHOW:LU]HLJHQGD‰HLQHJU|‰HUH8QYHUHLQEDUNHLWGHU3UlIHUHQ]HQQLFKWQRWZHQGLJHUZHLVHHLQHDXVJHSUlJWHUH1HLJXQJ]XNRQIOLNWWUlFKWLJHP9HUKDOWHQLPSOL]LHUW:HLWHUKLQZLUGJH]HLJWGD‰GLH$NWHXUHXPVRVWlUNHU]XNRQIOLNWKDIWHP9HUKDOWHQQHLJHQMHK|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ªVSD\RIILIWKHILUVWDFWRUUHFHLYHVKLVEHVWSD\RIIDQG7KLVILUVWTXHVWLRQUHIHUVRQO\WRWKHGLYHUJHQFHRISUHIHUHQFHVDQGWKHUHIRUHWR:KDWPLJKWDQDFWRUZLQLIVKHVXFFHVVIXOO\FKDOOHQJHVKHURSSRQHQWDQGZKDW7KLVVHFRQGTXHVWLRQZKLFKDOVRUHIHUVWRVWUDWHJLFFRQVLGHUDWLRQVUHJDUGLQJKRZDQDFWRUFDQLPSURYHKHURZQSD\RIIE\H[KLELWLQJDJJUHVVLYHUHFDOFLWUDQWVWXEERUQRUKDUGKHDGHG¥LHFRQIOLFWIXO¥EHKDYLRUSURFHHGVEH\RQGWKHVLPSOHILUVWTXHVWLRQRIKRZSUHIHUHQFHVGLYHUJH7KHFUXFLDOGLIIHUHQFHEHWZHHQWKHWZRTXHVWLRQVLVWKDWWKHILUVWGHDOVZLWKODWHQWRIWHQKLGGHQFRQIOLFWVRILQWHUHVWDQG2QHGUDZEDFNWROLPLWLQJDWWHQWLRQRQO\WRWKHLQWHUHVWGLPHQVLRQRIFRQIOLFWLVWKDWWKHOLQNEHWZHHQFRQIOLFWDQGEHKDYLRUEHFRPHVXQFOHDU&RQVLGHUIRUH[DPSOH$[HOURGªVVWDWHPHQWZKLFKZHUHIHUWRDVKLVSURSRVLWLRQFRQFHUQLQJFRQIOLFWIXOEHKDYLRUWKDW§RWKHUWKLQJVEHLQJHTXDOWKHPRUHFRQIOLFWRILQWHU 0RKU+DXVNHQ&RQIOLFW,QWHUHVWDQG6WUDWHJ\HVWWKHUHLVWKHPRUHSUREDEOHLWLVWKDWFRQIOLFWIXOEHKDYLRUZLOOUHVXOW¨&UXFLDOKHUHLVKRZ§FRQIOLFWIXOEHKDYLRU¨LVGHILQHG$[HOURGIUHTXHQWO\UHIHUVWRDSULVRQHUªVGLOHPPDLQZKLFKFRQIOLFWIXOEHKDYLRULVZHOOGHILQHG+RZHYHUKHSURFHHGVWRDUJXHWKDWKLVSURSRVLWLRQFRQFHUQLQJFRQIOLFWIXOEHKDYLRUKROGVQRWRQO\LQDSULVRQHUªVGLOHPPDEXWLQDOOFDVHV8QIRUWXQDWHO\$[HOURGGRHVQRWH[SOLFLWO\GHILQHFRQIOLFWIXOEHKDYLRULQJHQHUDOVRFLDOVLWXDWLRQV5DWKHUKHVWDWHV$[HOURG§7KHVSHFLILFPHDQLQJRIFRQIOLFWIXOEHKDYLRUZLOOGLIIHUIURPRQHSROLWLFDOSURFHVVWRDQRWKHURIFRXUVHEXWXVXDOO\WKHUHDUHW\SHVRIEHKDYLRUZKLFKDUHFOHDUO\FRQIOLFWIXODQGKHQFHVRPHK\SRWKHVHVDUHHDV\WRVSHFLI\¨:HZLOOLOOXVWUDWHWKHVHSRLQWVRYHUWKHQH[WVHFWLRQVTXHVWLRQLQJWKHYDOLGLW\RI$[HOURGª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ªVDUJXPHQWWKDWVWUXJJOHIRUSUHIHUUHGHTXLOLEULDLVDFUXFLDOFKDUDFWHULVWLFIRUH[DPSOHDWWKHVWDUWXSRIPRVWVRFLDOLQVWLWXWLRQV.QLJKWKROGVWKDWLQVWLWXWLRQVDUHFUHDWHGWRVROYHWKHVHFRQIOLFWVRYHUSUHIHUUHGHTXLOLEULDDQGWKDWWKHRXWFRPHRIWHQWLOWVLQIDYRURIWKHVWURQJHUSOD\HU0RVWLQVWLWXWLRQVDUHGHVLJQHGWRUHJXODWHVRFLDOOLIHLQWKHORQJWHUP7KHSOD\HUVªVWDNHVLQWKHFRPSHWLWLRQIRUWKHSUHIHUUHGLQVWLWXWLRQDOGHVLJQPD\WKXVEHKLJKGHSHQGLQJRQWKHWLPHKRUL]RQRIWKHSOD\HUV7KLVSRLQWLVHODERUDWHGIXUWKHULQ6HFWLRQZKLFKGHDOVZLWKWKHUHSHDWHGJDPHVHWWLQJ,WLVWKLVLPSRUWDQWUROHSOD\HGE\%DWWOHRIWKH6H[HVVLWXDWLRQVLQUHDOVRFLDOOLIHZKLFKMXVWLILHVRXUIRFXVRQWKH%DWWOHRIWKHKH7KHULVNOLPLWDSSURDFKPHDVXUHVWKHDFWRUVªLQFOLQDWLRQWRLQDFRQFLOLDWRU\RUFKDOOHQJLQJZD\:HVKRZWKDWKLJKHULQFRPSDWLELOLW\RISUHIHUHQFHVEHWZHHQWKHDFWRUVGRHVQRWQHFHVVDULO\LPSO\WKDWWKH\DUHPRUHLQFOLQHGWREHKDYHFKDOOHQJLQJO\)XUWKHUPRUHZHVKRZWKDWWKHPRUHDFWRUVYDOXHIXWXUHSD\RIIVLQWHUPVRISUHVHQWSD\RIIVWKHJUHDWHUWKHLULQFOLQDWLRQZLOOEHWREHKDYHFKDOOHQJ7KHDUWLFOHLVGLYLGHGLQWRILYHVHFWLRQV6HFWLRQLOOXVWUDWHV$[HOURGªVPHDVXUHRIFRQIOLFW6HFWLRQSURSRVHVDQHZPHDVXUHRIFRQIOLFWEDVHGXSRQWKHFRQFHSWRIULVNOLPLWV+DUVDQ\L¥HPSOR\HGLQDVWDWLFDQGDUHSHDWHGJDPHVHWWLQJ6HFWLRQFRPSDUHVWKHWZRFRQFHSWVPRUHULJRURXVO\DQDO\]LQJWKHHI 03,)*'LVFXVVLRQ3DSHUIHFWVRIVOLJKWFKDQJHVRIWKHJDPHVWUXFWXUHRQWKHFRQIOLFWPHDVXUHVDQGVKRZLQJWKDWWKHUHVXOWVPD\EHFRQWUDGLFWRU\6HFWLRQSXWVWKHUHVXOWVRIWKHSUH(YDOXDWLRQRIWKH0HDVXUHRI&RQIOLFWRI,QWHUHVW$[HOURGªVDSSURDFKWRFRQIOLFWIRFXVHVRQ§WKHVWDWHRILQFRPSDWLELOLW\RIWKHJRDOVRIWZRRUPRUHDFWRUV¨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ªVDSSURDFKFDQEHVWEHLOOXVWUDWHGE\DJUDSKLFUHSUHVHQWDWLRQRIWKHJDPH)LJ7KHDUHDRIMRLQWGHPDQGDERYHWKHPLQLPD[SD\RIIVLVWKHUHFWDQJOHLQWKLVH[[E\WKHEHVWSD\RIIHDFKDFWRUFDQSRVVLEO\REWDLQXQGHUKLVPRVWIDYRUDEOHFLUFXPVWDQFHVOLJKWO\VKDGHGLQ)LJ7KHDUHDRIXQIHDVLEOHMRLQWGHIIII4,32,2 II1,13,4 Table 2.1 Battle of the sexes Actor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inimax Point Fig. 2.1 Diagram for the battle of the sexes game in Table 2.1, assuming pure strategies 1234Minimax Point Fig. 2.2 Diagram for the battle of the sexes game in Table 2.1, assuming mixed strategies 03,)*'LVFXVVLRQ3DSHU2YHUWKHIROORZLQJSDJHVZHSUHVHQWDQDOWHUQDWLYHZD\WRGHILQHWKHUHOHYDQWDUHDV6LQFHRXUDUJXPHQWVGRQRWUHIHUPHUHO\WRWKHLQFRPSDWLELOLW\RIGHPDQGVZHSUHIHUPRUHJHQHUDOODEHOVWKDQ$[HOURGªV§DUHDRIMRLQWGHPDQG¨DQG§DUHDRIXQIHDVLEOHMRLQWGHPDQG¨,Q$[HOURGªVPHDVXUHWKHDUHDRIMRLQWGHPDQGDSSHDUVLQWKHGHQRPLQDWRU+HQFHLWVHUYHVDVDVWDQGDUGRIPHDVXUHDQGZHUHIHUWRLWDVWKH§XQLWDUHD¨$[HOURGGHILQHVWKHDUHDRIWKHXQIHDVLEOHMRLQWGHPDQGDSSHDU$0HDVXUHRI&RQIOLFW%DVHGXSRQWKH&RQFHSWRI5LVN/LPLWV7KLVVHFWLRQSUHVHQWVDPHDVXUHRIFRQIOLFWEDVHGXSRQWKHFRQFHSWRIULVNOLPLWVLQWURGXFHGE\+DUVDQ\L¥7KLVPHDVXUHFODULILHVWKHGLVWLQFWLRQEHWZHHQFRQIOLFWRILQWHUHVWDQGFRQIOLFWIXOEHKDYLRUZLWKLQDJDPHWKHRUHWLFDOIUDPHZRUN0RUHVSHFLILFDOO\WKHULVNOLPLWPHDVXUHRIFRQIOLFWDFFRXQWVEHWWHUIRURYHUWVWUDWHJLFFRQIOLFWIXOEHKDYLRUWKDQ$[HOURGªVPHDVXUHEHFDXVHWKHIRUPHULQYROYHVFRQVLGHULQJWKHDFWRUVªSHUFHSWLRQRIHDFKRWKHUªVUHFDOFLWUDQFHDQGDJJUHVVLRQ,QWKLVVHFWLRQUHFDOFLWUDQFHLVGHILQHGDVWKHWKUHDWRIVZLWFKLQJIURPDQHTXLOLEULXPVWUDWHJ\WRDQRWKHUVWUDWHJ\RUWKHWKUHDWRIQRWIROORZLQJVXLWLIWKHRWKHUDFWRUVZLWFKHVIURPDQHTXLOLEULXPVWUDWHJ\WRDQRWKHUVWUDWHJ\7KHDSSURDFKDSSOLHVRQO\WRJDPHVZLWKWZRRUPRUHHTXLOLEULDVLQFHLWFRQFHSWXDOL]HV7KH5LVN/LPLW$SSURDFKLQD2QH6KRW*DPH&RQVLGHUWKHEDWWOHRIWKHVH[HVJDPHLQ7DEOHUHSHDWHGLQ7DEOHZKLFKLQFOXGHVYDULDEOHSD\RIIVXVHGODWHUIRUJHQHUDOL]DWLRQDDQGEUHIHUWRDFWRULª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ªVH[SHFWHGSD\RIIRIDFKDOOHQJHDVS'HILQHWKHYDOXHRISZKLFKPDNHVDFWRULQGLIIHUHQWEHWZHHQKHUFRQIOLFWIXOVWUDWHJ\DQGKHUILUVWVWUDWHJ\DVS ZKLFKJLYHVS,IWKHSUREDELOLW\WKDWDFWRUUHPDLQVKDUGKHDGHGLVKLJKHUWKDQS WKHQDFWRUZRXOGQRWWU\WRFKDOOHQJHDFWRU7KXVU LVWKHULVNOLPLWRIDFWRU,WLVWKHKLJKHVWULVNRIDFRQIOLFWWKDWVKHLVZLOOLQJWRWDNHE\FKDOOHQJLQJDFWRU,QWKHVDPHZD\ZHGHILQHWKHULVNOLPLWIRUDFWRU*LYHQWKDWDFWRUFKRRVHVKHUVHFRQGVWUDWHJ\WKHH[SHFWHGSD\RIIWRDFWRULIKHGRHVQRWJLYHLQLVSDQGKLVULVNOLPLWWKHQLVU ¥¥7KLVLVWKHKLJKHVWSUREDELOLW\RIFRQIOLFWDFWRULV2IFRXUVHWKHULVNOLPLWVDUHWKHVDPHIRUERWKDFWRUVVLQFHWKHJDPHLVV\PPHWULF5HFDSLWXODWLQJWKHKLJKHVWULVNDFWRULVZLOOLQJWRWDNHE\FKDOOHQJLQJDFWRULVIII II1,1d1,d23,4b1,a2 Table 3.1 Two-person two-strategy gameActor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ª7KLV\LHOGVDGHJUHH& RIFRQIOLFWZKLFKLVWZLFHDVODUJHDV$[HOURGªV$[HOURGªV VKRZQLQ)LJ+RZHYHULIPL[HGVWUDWHJLHVDUHH[FOXGHGIURPWKHDQDO\VLVVRWKDWUDQGRPL]DWLRQEHWZHHQWKHWZRSD\RIIVDQGLVQRWSRVVLEOHWKHQ$[HOURGª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ctor 21234 (a ,b )Threat Point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pcpab12122+-³ &RQVLGHUSDVWKHSUREDELOLW\WKDWDFWRUVWLFNVWRKHUVHFRQGVWUDWHJ\DIWHUVKHKDVFKDOOHQJHGDFWRULHDIWHUDFWRUKDVDFWXDOO\FKDOOHQJHGWKHHTXLOLEULXPpcpab21211+-³ Crrababacac11221122()()()()FDQEHFRQVLGHUHGWKHPD[LPXPGHJUHHRIFRQIOLFWEHWZHHQWKHDFWRUVLHWKH 03,)*'LVFXVVLRQ3DSHU7KH5LVN/LPLW$SSURDFKLQD6XSHUJDPH6RIDUZHKDYHDQDO\]HGRQHVKRWJDPHVRQO\+RZHYHUDQH[WHQVLRQWRPXOWLVWDJHJDPHVZLOOVKRZWKDWWKHGHJUHHRIFRQIOLFWLVVKDSHGE\WKHSOD\HUVª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ªVDQDO\VLVRIWKHFKDLQVWRUHSDUDGR[ZKHUHSOD\HUVHDUO\LQDUHSHDWHGJDPHPD\VHHNWRDFTXLUHDUHSXWDWLRQIRUEHLQJ§WRXJK¨RU§UHFDOFLWUDQW¨RUVRPHWKLQJHOVH$VLVZHOONQRZQIURPWKH§IRONWKHRUHP¨PDQ\GLIIHUHQWHTXLOLEULXPSDWKVFDQEHVXVWDLQHGE\PDQ\GLIIHUHQWVWUDWHJLHVLQDQLQILQLWHO\UHSHDWHGJDPH2QHH[DPSOHZRXOGEHWRDOWHUQDWHWKHVWUDWHJLHVRIFKDOOHQJHDQGIRUJLYHQHVVDFFRUGLQJWRVRPHSDWWHUQ2XUDSSURDFKLQWKLVSDSHUKRZHYHULVWRIRFXVRQVLWXDWLRQVLQZKLFKDUHSXWDWLRQDUJXPHQWSOD\VDUROHVRWKDWWKHFKDOOHQJHUHLWKHUFKDOOHQJHVDOOWKHWLPHRUQRWDWDOO:HEHOLHYHWKDWVXFKVLWXDWLRQVRFFXUIUHTXHQWO\LQUHDO Actor 2Actor 1Actor 2Actor 1Actor 1Actor 2 t=2t=T(a ,b ) 0RKU+DXVNHQ&RQIOLFW,QWHUHVWDQG6WUDWHJ\OLIH7KXVZKLOH)LJPLJKWQRWFRYHUDOOWKHSDWKVREVHUYHGLQSUD[LVLQRXURSLQLRQLWLOOXVWUDWHVSODXVLEOHHTXLOLEULXPSDWKVWKDWDUHREVHUYHGRIWHQHQRXJK*LYHQWKHHTXLOLEULXPSDWKLQ)LJDFWRUPLJKWWU\WRHQIRUFHWKHSD\RIIDLQKHUSUHIHUUHGHTXLOLEULXPEE\FKDQJLQJWRKHUVHFRQGVWUDWHJ\DQGVWLFNLQJWRLWIRUVHYHUDOSHULRGVUDWKHUWKDQJLYLQJLQDQGUHFHLYLQJE$FWRUPLJKWZLWKVWDQGWKHFKDOOHQJHRUJLYHLQ,QHYHU\WLPHSHULRGLQZKLFKQHLWKHUDFWRUJLYHVLQHDFKUHFHLYHVF)XWXUHSD\RIIVDUHGLVFRXQWHGDQGWKHVXFFHVVRIDFWRUªVFKDOOHQJHLVXQFHUWDLQ7KHFUXFLDOTXHVWLRQIRUDFWRULVZKHQWREDFNGRZQIURPKHUFKDOOHQJH'HILQHIRUDFWRUDWLPHSHULRGIDIWHUZKLFKVKHFHDVHVWRHPSOR\KHUFKDOOHQJLQJVWUDWHJ\LIDFWRUKDVQRWFRQFHGHGEHIRUHWLPHSHULRG'LVFRXQWLQJIDFWRURIDFWRU7KHSUHVHQWYDOXHRIDSD\RII[LQSHULRGWIRUIRUdW¥7/DVWSHULRGRIWKHJDPH1RSD\RIIVDUHUHFHLYHGDIWHUWLPHSHULRG7I3HULRGRIODVWFKDOOHQJHRIDFWRU$FWRUGRHVQRWFKDOOHQJHDIWHUSHULRGI2EVHUYHWKDWLII WKHQDFWRUGRHVQRWFKDOOHQJHDWDOO,IDFWRUFKDOOHQJHVLQSHULRGIDQGDFWRUKDVQRWFRQFHGHGLQDQ\RIWKHSHULRGVXQWLODQGLQFOXGLQJSHULRGIWKHQHDFKJHWVFLQWKHSHULRGVI$FWRUWKHQFRQFHGHVLQSHULRGIDQGUHFHLYHVELQWKHSHULRGVII7$FWRUUHFHLYHVDLQWKHSHULRGVII7,IDFWRUFKDOOHQJHVLQSHULRGIDQGDFWRUFRQFHGHVLQSHULRGIWKHQDFWRUJHWVFLQI¥DQGDLQIII7$FWRUJHWVFLQI¥DQGELQIII7,IDFWRUFRQFHGHVLQSHULRGHHIWKHQDFWRUJHWVFLQH¥DQGDLQHHIII7$FWRUKDVVRPHRSSRUWXQLW\FRVWWREHDUZKHQVKHEHKDYHVFRQIOLFWIXOO\XSWRDQGLQFOXGLQJSHULRGI,IVKHJLYHVLQIURPWKHYHU\EHJLQQLQJLHLIVKHGRHVQRWFKDOOHQJHDWDOOVKHZRXOGUHFHLYH7KHUHIRUHWKHH[SHFWHGDGGLWLRQDOJDLQJIVKHUHFHLYHVLIVKHFKDOOHQJHVLQHYHU\WLPHSHULRGXQWLODQGLQgfapcpbpbtft221212()(()p)=-++-åååådddd 03,)*'LVFXVVLRQ3DSHU1RWHWKDWJI $OVRQRWHWKDWWKHULVNOLPLWVGHULYHGZLWKLQWKHVWDWLFDQDO\gTpapcb21212111(|)()==-+-_7 LVWKHDGGLWLRQDOJDLQZKLFKDFWRUH[SHFWVWRUHFHLYHLIVKHFKDOOHQJHVDFWRULQSHULRGLQDJDPHZKLFKLVSOD\HGRQO\RQFH7 UDWKHUWKDQJLYLQJLQ:HFDQGHULYHWKHULVNOLPLWUDVGHILQHGLQHTXDWLRQLIZHVROYHWKH$VVXPHQRZWKDWWKHLQWHUDFWLRQFRQWLQXHVIRUDORQJWLPHLHWKDW7EHFRPHV lim()()()(()(()())apbpcp---+-22121221212111apbpcp21221212111()(()()---+-LVODUJHURUVPDOOHUWKDQ]HUR+HQFHVHWWLQJWKLVWHUPHTXDOWR]HURDOORZVXVWRGHWHUPLQHWKHULVNOLPLWIRUDFWRUZKHQWKHJDPHLQ)LJLVSOD\HGDQLQIL acbc22222()()---(TXDWLRQGHILQHVWKHYDOXHS ZKLFKPDNHVDFWRULQGLIIHUHQWEHWZHHQFKDOOHQJLQJDFWRUDOOWKHWLPHDQGFRQFHGLQJLQWKHILUVWWLPHSHULRGJLYHQWKDWWKHJDPHLVSOD\HGDQLQILQLWHQXPEHURIWLPHV2EVHUYHWKDW(TXDWLRQPD\ (TXDWLRQVDQGDUHGHULYHGDQDORJRXVO\IRUDFWRU$VDPHDVXUHRIFRQIOLFWLQD[JDPHZLWKWZRHTXLOLEULDZKLFKLVSOD\HGDQLQILQLWHQXPEHURI ------ababacbcacbc()()(()())(()())11221111122222 ----11221111(())(()) 0RKU+DXVNHQ&RQIOLFW,QWHUHVWDQG6WUDWHJ\&RQIOLFWRI,QWHUHVWDQGWKH5LVN/LPLW$SSURDFKWR&RQIOLFW7KHULVNOLPLWDSSURDFKTXHVWLRQVWKHFKRLFHRIWZRFUXFLDOSRLQWVLQ$[HOURGª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§LQWHUPHGLDWHVWD\¨IURPZKLFKWKH\PD\FRPSHWHRUVWUXJJOHIRUHLWKHURIWKHWZRHTXLOLEULDDDQGE,QFUHDVLQJFWRZDUGIIII4,31,1 II2,23,4 Table 4.1 Two-person two-strategy gameActor 1 03,)*'LVFXVVLRQ3DSHUWKXVLQGXFHVDQLQFUHDVLQJGHJUHHRIFRQIOLFW&RQIOLFWIRUWKHJDPHLQ7DEOHLVQRWGHILQHGIRUFL $OVRREVHUYHWKDW&GHFUHDVHVDVFDQGFDSSURDFK'HFUHDVLQJFRUFWKHSUREDELOLW\RIWKHDFWRUVªJHWWLQJVWXFNDWWKHFRQIOLFWSRLQWFZKLFKLQFUHDVHVWKHSUREDELOLW\RIWKHLUUHPDLQLQJSHUPDQHQWO\LQRQHRIWKHWZRHTXLOLEULDDDQGE,QWKLVFDVHWKHGHJUHH7KHPHDVXUHRIFRQIOLFWGHFUHDVHVVLQFHWKHSD\RIIVLQWKHFRQIOLFWSRLQWGHFUHDVHZKLFKUHQGHUVFRQIOLFWIXOEHKDYLRUOHVVDWWUDFWLYHWRERWKDFWRUV+HQFHWKHMRLQWPD[LPXPULVNRIDFRQIOLFWWKDWWKHDFWRUVDUHZLOOLQJWRDFFHSWGHFUHDVHVWRR&RQWUDU\WR$[HOURGªVDQDO\VLVWKHSRLQWGHILQHGE\WKHPLQLPD[SD\RIIVGRHVQRWSOD\DQ\UROHKHUH7KHFUXFLDOIDFWRUVDUHWKHSD\RIIVLQWKHWZRHTXLOLEULDWKHDFWRUVVWUXJJOHIRUDQGWKHSD\RIIVLQWKHFRQIOLFWSRLQWZKLFKLVQRZUDWKHUWKDQ+HQFHWKHDQDO\VLVVKRZVKRZWKHULVNOLPLWDSSURDFKOHDGVWRDQRWKHUGHILQLWLRQRIWKHXQLWDUHDDVGHPRQVWUDWHGE\)LJWKDQ$[:HZLOOQRZVKRZWKDWWKHGHILQLWLRQRIWKHXQLWDUHDLQ$[HOURGªVDSSURDFKPD\DOVREHFKDQJHGE\TXHVWLRQLQJWKHFKRLFHRIWKHRXWPRVWSRLQWLQWKHXSSHUULJKWGLUHFWLRQ7KLVLVWKHPD[LPXPDWWDLQDEOHSD\RIIIRUHDFKDFWRULQ$[HOURGªVDQDO\VLV,WLVGHILQHGE\WKHKLJKHVWSD\RIIVLQWKHJDPHDQGLWOLPLWVERWKWKHDUHDRIFRQIOLFWLQJLQWHUHVWDQGWKHXQLWDUHD,WLVREYLRXVWKDWWKLVSRLQWLVYHU\LPSRUWDQWLQ$[HOURGªVDQDO\VLVRIFRQIOLFWLQJLQWHUHVWV+RZHYHUZHZLOOVKRZWKDWVWUDWHJLFUHDVRQLQJPD\UHQGHUWKLVSRLQWLUUHOHYDQWWRR7KLVFDQEHVHHQLQWKHWZRSHUVRQWKUHHVWUDWHJ\JDPHLQ7DEOHZKLFKLQFOXGHVWKHWZRSHUVRQWZRVWUDWHJ\JDPHLQ7DEOHDQGIRUH[SRVLWLRQDOFRQYHQLHQFHSUHVHUYHVWKH 1234 Threat Point Fig. 4.1 Diagram for the 2x2 game in Table 4.1 0RKU+DXVNHQ&RQIOLFW,QWHUHVWDQG6WUDWHJ\,IDFWRUUHFHLYHVKLVKLJKHVWSD\RIIRIDFWRUJHWVKHUPLQLPD[SD\RIIRIDQGYLFHYHUVD7KHUHIRUHWKHFRQIOLFWRILQWHUHVWLQWKHHQODUJHGJDPHLVZKLFKLVWZLFHZKDWLWZDVLQWKHWZRVWUDWHJ\JDPHLOOXVWUDWHGLQ7DEOHE\WKHGHOLPLWLQJEROGJUD\OLQHV$JUDSKLFUHSUHVHQWDWLRQRI7DEOHLVJLYHQLQ)LJ$FFRUGLQJWR$[HOURGªVPHDVXUHWKHZKROHUHOHYDQWDUHDLVOLPLWHGE\WKHSRLQWV7KHDUHDRIFRQIOLFWLQJLQWHUHVWLVUHSUHVHQWHGE\WKHOLJKWO\VKDGHGWULDQJOHVSDQQHGE\$[HOURGª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ªVDSSURDFK:KDWUHPDLQVLVWRDQDO\]HDGGLWLRQDOGLIIHUHQFHVZKHQWLPHLVH[SOLFLWO\WDNHQLQWRDFFRXQW2EVHUYHWKDWLQ$[HOURGªVDSSURDFKWKHUHLVQRSRVVLELOLW\WRDFFRXQWIRUWKHYDOXDWLRQRIIXWXUHSD\RIIVLHIRUIIIIIII4,32,25,2 Actor 1II1,13,41,1 III1,12,51,1 Table 4.2 Two-person three-strategy game 03,)*'LVFXVVLRQ3DSHUWKHDFWRUª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hreat point, Minimax point Actor 2Actor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§VKDGRZRIWKHIXWXUH¨HPERGLHGLQWKHGLVFRXQWIDFWRUVDIIHFWVWKHPHDVXUHE\FKDQJLQJWKHYDOXDWLRQRIDQH[SHFWHGJDLQLQWKHIXWXUH7KHKLJKHUWKHDFWRUVYDOXHSUHVHQWSD\RIIVUHODWLYHWRIXWXUHSD\RIIVLHWKHVPDOOHUWKHGLVFRXQWIDFDUHWKHPRUHUHOXFWDQWWKH\DUHWRULVNDFRQIOLFW)URPWKHSHUVSHFWLYHRIWKHDFWRUVDQHQJDJHPHQWLQWRDFRQIOLFWFDQEHVHHQDVDULVN\LQYHVWPHQW$QDFWRUPD\WKURXJKFKDOOHQJLQJKHURSSRQHQWDFFHSWDORVVLQWKHSUHVHQWLIVKH 222 Actor 1cba (a -c )(a -c )-(b -c ) (a -c )(b -c )1111(a -c )-(b -c )22222 03,)*'LVFXVVLRQ3DSHU&RQFOXVLRQ6LQFH$[HOURGª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ª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ªLQWHUHVWLQWKHIXWXUHPD\KHOSWRVWDELOL]HFRRSHUDWLYHEHKDYLRUUDWKHUWKDQHQFRXUDJHDJJUHVVLYHDFWLRQZHVKRZWKDWWKH§VKDGRZRIWKHIXWXUH¨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