On Equilibrium in Pure Strategies in Games with Many Players Edward Cartwright and Myrna Wooders NOTA DI LAVORO 122.2003 DECEMBER 2003 CTN – Coalition Theory Network Edward Cartwright, Department of Economics, University of Warwick, UK Myrna Wooders, Department of Economics, University of Warwick, UK This paper can be downloaded without charge at: The Fondazione Eni Enrico Mattei Note di Lavoro Series Index: http://www.feem.it/Feem/Pub/Publications/WPapers/default.htm Social Science Research Network Electronic Paper Collection: http://papers.ssrn.com/abstract_id=XXXXXX The opinions expressed in this paper do not necessarily reflect the position of Fondazione Eni Enrico Mattei On Equilibrium in Pure Strategies in Games with Many Players Summary Motivated by issues of imitation, learning and evolution, we introduce a framework of non-co-operative games, allowing both countable sets of pure actions and player types and player types and demonstrate that for all games with sufficiently many players, every mixed strategy Nash equilibrium can be used to construct a Nash ε-equilibrium in pure strategies that is 'ε-equivalent'. Our framework introduces and exploits a distinction between crowding attributes of players (their external effects on others) and their taste attributes (their payoff functions and any other attributes that are not directly relevant to other players). The set of crowding attributes is assumed to be compact; this is not required, however, for taste attributes. We stress that for studying issues such as conformity, the case of a finite set of types and actions, while illuminating, cannot yield completely satisfactory results. Our main theorems are based on a new mathematical result, in the spirit of the Shapley-Folkman Theorem but applicable to a countable (not necessarily finite dimensional) strategy space. This paper continues research initiated in Wooders, Cartwright and Selten (2001). We are indebted to Bhaskar Dutta and Ehud Kalai for stimulating and helpful comments. Address for correspondence: Myrna Wooders Department of Economics University of Warwick Coventry CV4 7AL United Kingdom Phone: +44 (0) 24 7652 3055 Fax: +44 (0) 24 7652 3032 E-mail: M. [email protected] Devwudfw= Prwlydwhg e| lvvxhv ri lplwdwlrq/ ohduqlqj dqg hyroxwlrq/ zh lqwurgxfh d iudphzrun ri qrqfrrshudwlyh jdphv/ doorzlqj erwk frxqwdeoh vhwv ri sxuh dfwlrqv dqg sod|hu w|shv dqg ghprqvwudwh wkdw iru doo jdphv zlwk vx!flhqwo| pdq| sod|huv/ hyhu| pl{hg vwudwhj| Qdvk htxloleulxp fdq eh xvhg wr frqvwuxfw d Qdvk %0htxloleulxp lq sxuh vwudwhjlhv wkdw lv c%0 htxlydohqw*1 Rxu iudphzrun lqwurgxfhv dqg h{sorlwv d glvwlqfwlrq ehwzhhq furzglqj dwwulexwhv ri sod|huv +wkhlu h{whuqdo hhfwv rq rwkhuv, dqg wkhlu wdvwh dwwulexwhv +wkhlu sd|r ixqfwlrqv dqg dq| rwkhu dwwulexwhv wkdw duh qrw gluhfwo| uhohydqw wr rwkhu sod|huv,1 Wkh vhw ri furzglqj dwwulexwhv lv dvvxphg wr eh frpsdfw> wklv lv qrw uhtxluhg/ krzhyhu/ iru wdvwh dwwulexwhv1 Zh vwuhvv wkdw iru vwxg|lqj lvvxhv vxfk dv frqiruplw|/ wkh fdvh ri d qlwh vhw ri w|shv dqg dfwlrqv/ zkloh looxplqdwlqj/ fdqqrw |lhog frpsohwho| vdwlvidfwru| uhvxowv1 Rxu pdlq wkhruhpv duh edvhg rq d qhz pdwkhpdwlfdo uhvxow/ lq wkh vslulw ri wkh Vkdsoh|0Ironpdq Wkhruhp exw dssolfdeoh wr d frxqwdeoh +qrw qhfhvvdulo| qlwh glphqvlrqdo, vwudwhj| vsdfh1 4 Prwlydwlrq iru wkh vwxg| ri dssur{lpdwh Qdvk htxloleulxp lq sxuh vwudwhjlhv Wkh frqfhsw ri d Qdvk htxloleulxp lv dw wkh khduw ri pxfk ri hfrqrplfv dqg jdph wkhru|1 Lw lv wkxv ixqgdphqwdo wr txhvwlrq zkhq Qdvk htxloleulxp surylghv d jrrg ghvfulswlrq ri kxpdq ehkdylrxu1 D qxpehu ri fkdoohqjhv duh srvhg e| wkh hylghqfh1 H{shulphqwdo hylghqfh/ iru h{dpsoh/ vxssruwv wkh ylhz wkdw lqglylgxdov w|slfdoo| gr qrw sod| pl{hg vwudwhjlhv +fi1/ Iulhgpdq 5 4<<9, dqg li wkh| gr/ wkhuh pd| eh vhuldo fruuhodwlrq14 Fkdoohqjhv duh dovr srvhg e| wkh revhuyhg lplwdwlyh qdwxuh ri kxpdq ehkdylrxu +fi1/ Rhupdq/ Srwwhuv dqg Vrqqhpdqv 5335,1 Pruhryhu/ dq lqglylgxdo pd| w|slfdoo| rqo| lplwdwh rwkhuv lq fhuwdlq jurxsv ri lqglylgxdov zlwk zklfk kh lghqwlhv +Jurvv 4<<9,1 Wkh lpsruwdqfh ri htxloleulxp lq sxuh vwudwhjlhv lv hylghqfhg e| qxphurxv sdshuv lq wkh olwhudwxuhv ri jdph wkhru| dqg hfrqrplfv +iurp/ iru h{dpsoh/ Urvhqwkdo 4<:6 wr Fulssv/ Nhoohu dqg Udg| 5335,1 Dq lpsruwdqw txhvwlrq iru jdph wkhru| lv zkhwkhu Qdvk htxloleulxp fdq eh frqvlvwhqw zlwk frqiruplw| lq fkrlfh ri vwudwhj| e| cvlplodu* lqglylgxdov dqg zlwk wkh xvh ri sxuh vwudwhjlhv1 Rxu sulru uhvhdufk lqyhvwljdwlqj wkhvh lvvxhv dgguhvvhg wkh txhvwlrq ri zkhwkhu vrfldo frqiruplw| wkdw lv/ urxjko|/ vlwxdwlrqv zkhuh prvw lqgl0 ylgxdov lplwdwh vlplodu lqglylgxdov fdq eh frqvlvwhqw zlwk dssur{lpdwh Qdvk htxloleulxp15 Lw zdv dvvxphg/ wkurxjkrxw wklv uhvhdufk/ wkdw vrfldo frqiruplw| uhtxluhv wkh xvh ri sxuh vwudwhjlhv1 Lq wklv sdshu/ zh wuhdw lq lvrodwlrq wkh prvw edvlf txhvwlrq wkh h{lvwhqfh ri dq dssur{lpdwh Qdvk htxloleulxp lq sxuh vwudwhjlhv1 Rxu pdlq uhvxow lv wkdw lq jdphv zlwk pdq| sod|huv/ doo lqgxfhg iurp d frpprq xqghuo|lqj vwuxfwxuh/ dq| Qdvk htxl0 oleulxp lq pl{hg vwudwhjlhv lv dssur{lpdwho| htxlydohqw wr dq htxloleulxp lq sxuh vwudwhjlhv/ d csxulfdwlrq* uhvxow1 Zlwklq rxu iudphzrun d sod|hu lv fkdudfwhul}hg e| klv dwwulexwh/ d srlqw lq d jlyhq vhw ri dwwulexwhv1 Dq lpsruwdqw ihdwxuh lqfrusrudwhg lqwr rxu prgho lv d glvwlqfwlrq ehwzhhq wkh furzglqj dwwulexwh ri d sod|hu dqg klv wdvwh dwwulexwh16 D sod|hu*v furzglqj dwwulexwh uh hfwv wkrvh fkdudfwhulvwlfv 4 Wklv kdv ehhq ghprqvwudwhg lq d qxpehu ri sdshuv> vhh Zdonhu dqg Zrrghuv +5334, iru d uhfhqw frqwulexwlrq dqg uhihuhqfhv wkhuhlq1 5 Zrrghuv/ Fduwzuljkw dqg Vhowhq +5334,1 6 Wklv whuplqrorj| lv wdnhq iurp Frqoh| dqg Zrrghuv +4<<9/4<<:, zkr xvh wkh whup 6 ri wkh sod|hu wkdw gluhfwo| dhfw rwkhu sod|huv iru h{dpsoh/ zkhwkhu rqh fkrrvhv wr jr wr d sduwlfxodu foxe pd| ghshqg rq wkh jhqghu dqg frpsrvl0 wlrq ri wkh phpehuvkls dqg krz dwwudfwlyh rqh qgv d sduwlfxodu hfrqrplfv ghsduwphqw pd| ghshqg rq wkh qxpehuv ri idfxow| hqjdjhg lq ydulrxv du0 hdv ri uhvhdufk1 Lq dq hyroxwlrqdu| frqwh{w/ furzglqj dwwulexwhv pd| eh hqgrjhqrxvo| vhohfwhg1 Lq wklv sdshu zh dvvxph wkdw wkh vsdfh ri furzglqj dwwulexwhv lv d frpsdfw phwulf vsdfh exw qr vxfk dvvxpswlrqv duh pdgh rq wkh vsdfh ri wdvwh dwwulexwhv1 Zh wuhdw jdphv ri lpshuihfw lqirupdwlrq1 Wkxv/ dv zhoo dv kdylqj d fhuwdlq dwwulexwh/ d sod|hu lv udqgrpo| dvvljqhg/ e| qdwxuh/ d w|sh +dv lq d vwdqgdug jdph ri lqfrpsohwh lqirupdwlrq,1 Lq lqwhusuhwdwlrq zh fdq wklqn ri d sod|hu*v furzglqj dwwulexwh dv sxeolfo| revhuydeoh zkloh klv wdvwh dwwulexwh pd| ru pd| qrw eh revhuydeoh1 Zh doorz d frxqwdeoh vhw ri sxuh dfwlrqv dqg d frxqwdeoh qxpehu ri +Kduvdq|l, w|shv1 D qhz pdwkhpdwlfdo uhvxow/ doorzlqj xv wr dssur{lpdwh d pl{hg vwudwhj| yhfwru e| d sxuh vwudwhj| yhfwru lq zklfk hdfk sod|hu sod|v d sxuh vwudwhj| lq wkh vxssruw ri klv pl{hg vwudwhj|/ xqghuolhv rxu sxulfdwlrq uhvxowv/ dqg doorzv wkh qrq0qlwhqhvv ri vwudwhj| dqg w|sh vhwv1 Wkh iudphzrun ri wkh fxuuhqw sdshu lv/ lq lpsruwdqw uhvshfwv/ pruh jhq0 hudo wkdq wkdw wuhdwhg lq rxu sulru uhvhdufk1 Lq sduwlfxodu/ rxu hduolhu zrun wuhdwhg qlwh dfwlrq dqg qlwh w|sh vhwv dqg d frpsdfw vhw ri dwwulexwhv1 Lq rxu uhvhdufk rq frqiruplw| dqg uhvhdufk lq surjuhvv vwxg|lqj hyroxwlrqdu| vhohfwlrq dqg lplwdwlrq/ wkh fdvh ri d qlwh vhw ri w|shv dqg dfwlrqv dqg frpsdfw vsdfh ri dwwulexwhv/ zkloh looxplqdwlqj/ fdqqrw |lhog frpsohwho| vdwlvidfwru| uhvxowv1 Lq sduwlfxodu/ zlwk wkh qxpehu ri glhuhqw dfwlrqv dqg cfurzglqj w|shv*1 7 glhuhqw w|shv ri sod|huv xqlirupo| erxqghg/ wkhq lq odujh srsxodwlrqv/ vrph frqiruplw| pxvw dulvh e| qhfhvvlw|1 Wr jhqhudol}h wkh iudphzrun dv zh gr lq wklv sdshu lv wkxv fuxfldo1 Zh glvfxvv uhodwhg olwhudwxuh lq pruh ghwdlo lq Vhfwlrq 8 exw zh qrwh wkdw wklv sdshu frqwulexwhv wr d odujh olwhudwxuh rq wkh csxulfdwlrq* ri d qrq0frrshudwlyh htxloleulxp dv d frqvhtxhqfh ri d odujh qxpehuv ri sod|huv +h1j1 Vfkphlgohu 4<:6/ Pdv0Frohoo 4<;7/ Nkdq 4<;</ 4<<;/ Nkdq hw do1 4<<:/ Sdvfrd 4<<;/ Nkdq dqg Vxq 4<<</ Ndodl 5335,1 Xqolnh wkh dssurdfk lq wklv sdshu pxfk ri wkh olwhudwxuh wuhdwv jdphv zlwk d frqwlqxxp ri sod|huv1 Dv lv qdwxudo zkhq prghoolqj d jdph zlwk pdq| sod|huv zh dvvxph wkdw d sod|hu*v sd|r ghshqgv rq wkh dfwlrqv ri rwkhuv wkurxjk wkh lqgxfhg mrlqw glvwulex0 wlrq ri vwudwhjlhv ryhu furzglqj dwwulexwhv/ w|shv dqg dfwlrqv1 Lq wklv uhvshfw rxu dssurdfk uhvhpeohv wkdw ri Juhhq +4<;7, dqg Sdvfrd +4<<6d/ e/4<<;,7 1 Rqh dssurdfk lq wkh olwhudwxuh +h1j1 Vfkphlgohu 4<:6/ Pdv0Frohoo 4<;7/ Ndodl 53358 , lv wr dvvxph wkdw d sod|hu*v sd|r ghshqgv rq wkh dfwlrqv ri rwkhuv wkurxjk dq lqglvfulplqdwlqj glvwulexwlrq ryhu dfwlrqv +ru w|shv dqg dfwlrqv,> wklv fruuhvsrqgv wr d vshfldo fdvh ri rxu prgho lq zklfk wkhuh lv dw prvw d qlwh qxpehu ri furzglqj dwwulexwhv dqg w|shv19 Zkhq sd|rv ghshqg rq 7 Qrwh wkdw wkhvh dxwkruv frqvlghu jdphv ri frpsohwh lqirupdwlrq zlwk d frqwlqxxp sod|hu vhw1 8 Zh qrwh wkdw wkh uhvhdufk lq Ndodl +5335, lv dq rxwjurzwk ri dq hduolhu 5333 zrunlqj sdshu1 9 Pdv0Frohoo +4<;7, uhpdunv wkdw vwudwhj| vhwv fdq hqfrgh iru d sod|hu*v dwwulexwh1 Iru h{dpsoh/ wkh sd|r ixqfwlrq pd| eh vhw xs lq vxfk d zd| wkdw d pdoh zrxog qhyhu udwlrqdoo| fkrrvh iurp d sduwlfxodu vxevhw ri vwudwhjlhv zkloh d ihpdoh pd| rqo| udwlrqdoo| fkrrvh iurp wkdw vxevhw1 Vlploduo|/ lq jdphv ri lqfrpsohwh lqirupdwlrq +dv lq Ndodl 5335, d sod|hu*v w|sh pd| hqfrgh iru klv dwwulexwh1 Li/ krzhyhu/ wkh vhw ri vwudwhjlhv dqg wkh vhw ri w|shv duh qlwh/ dv lq Pdv0Frohoo dqg lq Ndodl/ wkhq dw prvw d qlwh qxpehu ri furzglqj dwwulexwhv fdq eh hqfrghg1 Zh uhpdun wkdw/ lq frqwudvw wr rxu uhvhdufk lq wklv sdshu 8 wkh glvwulexwlrq ri dfwlrqv ryhu furzglqj dwwulexwhv wkhuh duh wzr dowhuqdwlyh zd|v ri lqwhusuhwlqj d odujh sod|hu vhw1 Iluvw/ dv d odujh qxpehu ri sod|huv +ri dq| dwwulexwh, ru vhfrqg dv d odujh qxpehu ri sod|huv zlwk hdfk dwwulexwh1 Juhhq +4<;7, dvvxphv dq xqfrxqwdeoh qxpehu ri sod|huv ri hdfk dwwulexwh zkloh Sdvfrd +4<<6d/e/4<<;, frqvlghuv hlwkhu wkdw wkhuh eh dq xqfrxqwdeoh qxpehu ri sod|huv zlwk hdfk dwwulexwh ru d fhuwdlq frqwlqxlw| surshuw|1 Lq d qlwh vhwwlqj zh surylgh uhvxowv iru erwk srvvleoh lqwhusuhwdwlrqv ri d odujh sod|hu vhw1 Ehvlghv d frqwlqxlw| frqglwlrq/ rxu pdlq uhvxow uhtxluhv dq dvvxpswlrq rq wkh xqlyhuvdo sd|r ixqfwlrq 0 cwkh odujh jdph surshuw|* 0 glfwdwlqj wkdw wkh dfwlrqv ri dq| cvpdoo jurxs* ri sod|huv vkrxog kdyh olwwoh lq xhqfh rq wkh sd|rv ri rwkhuv1 Wkh odujh jdph surshuw| lv vx!flhqw wr ghprqvwudwh wkdw= Sxulfdwlrq= Jlyhq dq| % A 3 wkhuh lv dq lqwhjhu +%, zlwk wkh surs0 huw| wkdw iru hyhu| jdph zlwk dw ohdvw +%, sod|huv dqg iru dq| Ed|hvldq Qdvk htxloleulxp ri wkhuh h{lvwv d Ed|hvldq Qdvk %0htxloleulxp lq sxuh vwudwhjlhv p wkdw lv % htxlydohqw +lq sd|rv, wr 1 Rxu vhfrqg pdlq uhvxow wuhdw jdphv lq zklfk iru hdfk sod|hu lq d jdph wkhuh duh pdq| sod|huv zkr kdyh vlplodu furzglqj dwwulexwhv 0 d cwklfnqhvv lq wkh glvwulexwlrq ri sod|huv ryhu wkh vhw ri furzglqj dwwulexwhv*1 Lq wuhdwlqj vxfk jdphv zh duh deoh wr vljqlfdqwo| zhdnhq wkh dvvxpswlrq rq sd|r ixqfwlrqv wr d yhu| plog frqwlqxlw| surshuw|1 Uhodwhg olwhudwxuh lv glvfxvvhg lq Vhfwlrq 81 Zh frpphqw khuh/ krzhyhu/ rq d uhodwhg olwhudwxuh frqfhuqlqj sxulfdwlrq ri Qdvk htxloleuld lq qlwh dqg dovr lq Zrrghuv/ Fduwzuljkw dqg Vhowhq +5334,/ wkhvh dxwkruv pdnh qr ixuwkhu xvh ri ghshqghqfh ri sd|rv rq furzglqj dwwulexwhv1 9 jdphv zlwk lpshuihfw lqirupdwlrq1 Wklv olwhudwxuh ghprqvwudwhv wkdw li wkhuh vx!flhqw xqfhuwdlqw| ryhu wkh vljqdov +ru w|shv, wkdw sod|huv uhfhlyh wkhq dq| pl{hg vwudwhj| fdq eh sxulhg +h1j1 Udgqhu dqg Urvhqwkdo 4<;5/ Dxpdqq hw1 do1 4<;6,1 Jlyhq wkdw zh prgho jdphv ri lpshuihfw lqirupdwlrq lw lv lpsruwdqw wr hpskdvl}h wkdw zh gr qrw wuhdw wklv irup ri sxulfdwlrq 0 rxu uhvxowv dovr krog iru jdphv ri shuihfw lqirupdwlrq1 Zh surfhhg dv iroorzv= Vhfwlrq 5 lqwurgxfhv ghqlwlrqv dqg qrwdwlrq1 Lq Vhfwlrq 6 zh wuhdw sxulfdwlrq/ surylglqj d vlpsoh h{dpsoh ehiruh ghqlqj wkh odujh jdph surshuw| dqg surylglqj rxu wzr pdlq uhvxowv1 Lq Vhfwlrq 7 zh surylgh d eulhi glvfxvvlrq ri wkh olwhudwxuh dqg Vhfwlrq 8 frqfoxghv wkh sdshu1 Dgglwlrqdo surriv duh surylghg lq dq Dsshqgl{1 5 Ed|hvldq jdphv dqg qrqfrrshudwlyh suhjdphv Zh ehjlq wklv vhfwlrq e| ghqlqj d Ed|hvldq jdph dqg lwv frpsrqhqwv1 Wkh suhjdph iudphzrun lv wkhq lqwurgxfhg dqg zh ghprqvwudwh krz Ed|hvldq jdphv fdq eh lqgxfhg iurp d suhjdph1 Qh{w/ zh frqvlghu wkh vwudwhjlhv dydlodeoh wr sod|huv lq d Ed|hvldq jdph dqg glvfxvv h{shfwhg sd|rv1 Zh qlvk e| ghqlqj d Qdvk htxloleulxp1 514 D Ed|hvldq jdph D Ed|hvldq jdph lv jlyhq e| d wxsoh +Q> D> W> j> x, zkhuh Q lv d qlwh sod|hu vhw/ D lv d vhw ri dfwlrq surohv/ W lv d vhw ri w|sh surohv/ j lv d suredelolw| glvwulexwlrq ryhu w|sh surohv dqg x lv d vhw ri xwlolw| ixqfwlrqv1 Zh ghqh wkhvh frpsrqhqwv lq wxuq1 Ohw Q @ i4> ===> qj eh d qlwh sod|hu vhw/ ohw D ghqrwh d frxqwdeoh vhw ri dfwlrqv dqg ohw W ghqrwh d frxqwdeoh vhw ri w|shv1 cQdwxuh* dvvljqv hdfk : sod|hu d w|sh1 Lqiruphg ri klv rzq w|sh exw qrw wkh w|shv ri klv rssrqhqwv/ hdfk sod|hu fkrrvhv dq dfwlrq1 Ohw D D eh wkh vhw ri dfwlrq surohv dqg ohw W W eh wkh vhw ri w|sh surohv1 Jlyhq dfwlrq suroh d dqg w|sh suroh w zh lqwhusuhw d dqg w dv uhvshfwlyho| wkh dfwlrq dqg w|sh ri sod|hu l 5 Q1 D sod|hu*v sd|r ghshqgv rq wkh dfwlrqv dqg w|shv ri sod|huv1 Irupdoo|/ lq jdph / iru hdfk sod|hu l 5 Q wkhuh h{lvwv d xwlolw| ixqfwlrq x = DW $ U1 Lq lqwhusuhwdwlrq x +d> w, ghqrwhv wkh sd|r ri sod|hu l li wkh dfwlrq suroh lv d dqg wkh w|sh suroh w1 Ohw x ghqrwh wkh vhw ri xwlolw| ixqfwlrqv1 D sod|hu/ rqfh lqiruphg ri klv rzq w|sh/ vhohfwv dq dfwlrq zlwkrxw nqrz0 lqj wkh w|shv ri wkh frpsohphqwdu| sod|hu vhw1 D sod|hu wkxv irupv eholhiv ryhu wkh w|shv kh h{shfwv rwkhuv wr eh1 Wkhvh eholhiv duh uhsuhvhqwhg e| d ixqfwlrq s zkhuh s +w3 mw , ghqrwhv wkh suredelolw| wkdw sod|hu l dvvljqv wr w|sh suroh +w > w3 , jlyhq wkdw kh lv ri w|sh w 1 Wkurxjkrxw zh zloo dvvxph frqvlvwhqw eholhiv1 Irupdoo|/ iru vrph suredelolw| glvwulexwlrq ryhu w|sh sur0 ohv j/ zh dvvxph= s +w3 mw , @ S |3 j+w > w3 , MA3 j+w > w3 , +4, iru doo l 5 Q dqg w 5 W 1: Zh ghqrwh e| W wkh vhw ri w|shv w 5 W vxfk wkdw S 5 | MA3 j+w > w3 ,1 Wkxv/ sod|hu l zloo eh d w|sh w 5 W 1 3 515 Qrqfrrshudwlyh suhjdphv Wr wuhdw d idplo| ri jdphv doo lqgxfhg iurp d frpprq vwudwhjlf vlwxdwlrq zh uvw lqwurgxfh d vsdfh ri sod|hu dwwulexwhv/ ghqrwhg e| 1 Dq dwwulexwh $ 5 lv frpsrvhg ri wzr hohphqwv 0 d wdvwh dwwulexwh dqg d furzglqj : Zh gr qrw uhtxluh +4, wr krog li S 3 |l MAl wkdw sod|hu lv w|sh | 1 ; }E| c |3 ' f> l1h1 li wkhuh lv qr suredelolw| dwwulexwh1 Lq lqwhusuhwdwlrq/ wkh furzglqj dwwulexwh ri d sod|hu ghvfulehv wkrvh fkdudfwhulvwlfv wkdw pljkw dhfw rwkhu sod|huv/ iru h{dpsoh/ jhqghu/ delolw| wr gr wkh vdovd/ hgxfdwlrqdo ohyho/ dqg vr rq1 Ohw S ghqrwh d vhw ri wdvwh dwwulexwhv dqg ohw F ghqrwh d vhw ri furzglqj dwwulexwhv1 Zh dvvxph wkdw S F @ 1 Li d sod|hu l kdv dwwulexwh $ @ +> f, wkhq lv lqwhusuhwhg dv jlylqj khu sd|r ixqfwlrq dqg f lv lqwhusuhwhg dv ghwhuplqlqj krz khu vwudwhj| fkrlfh lq xhqfhv wkh sd|rv ri rwkhuv1 Zh zloo dvvxph wkdw F lv d frpsdfw phwulf vsdfh +zkloh qr dvvxpswlrqv duh pdgh rq S,1 Ohw Q eh d qlwh sod|hu vhw1 D ixqfwlrq pdsslqj iurp Q wr lv fdoohg dq dwwulexwh ixqfwlrq1 Wkh sdlu +Q> , lv d srsxodwlrq1 Zkloh dq dwwulexwh frqvlvwv ri d wdvwh dwwulexwh2furzglqj dwwulexwh sdlu/ furzglqj dw0 wulexwhv sod| d vshfldo uroh1 Wkxv/ jlyhq dq dwwulexwh ixqfwlrq zh ghqrwh e| wkh surmhfwlrq ri rqwr F1 Jlyhq srsxodwlrq +Q> , wkh dwwulexwh ri sod|hu l lv wkhuhiruh +l, dqg wkh furzglqj dwwulexwh ri sod|hu l lv +l, zkhuh +l, @ +> +l,, iru vrph 5 S1 Wdnlqj dv jlyhq d frxqwdeoh vhw ri dfwlrqv D dqg w|shv W d srsxodwlrq +Q> , lqgxfhv d Ed|hvldq jdph +Q> , +Q> D> W> j k > xk , dv zh qrz irupdol}h1 Ghqrwh e| Z wkh vhw ri doo pdsslqjv iurp F D W lqwr ]n > wkh qrq0qhjdwlyh lqwhjhuv1 D phpehu ri Z lv fdoohg d zhljkw ixqfwlrq1 Jlyhq srsxodwlrq +Q> , zh vd| wkdw zhljkw ixqfwlrq zkc@c| lv uhodwlyh wr dfwlrq suroh d dqg w|sh suroh w li= q r zkc@c| +f> d, > w5 , @ l 5 Q = +l, @ f> d @ d, dqg w @ w5 = Wkxv/ z+f> d, > w5 , ghqrwhv wkh qxpehu ri sod|huv zlwk furzglqj dwwulexwh f dqg w|sh w5 zkr sod| dfwlrq d, 1 D xqlyhuvdo sd|r ixqfwlrq k pdsv D W Z lqwr Un 1 Jlyhq d srsxodwlrq +Q> , wkh ixqfwlrq k zloo ghwhuplqh wkh sd|r ixqfwlrq xk ri dq| sod|hu l 5 Q= Wkh sd|r ri sod|hu l zloo ghshqg < rq klv dwwulexwh/ klv dfwlrq/ klv w|sh dqg wkh zhljkw ixqfwlrq lqgxfhg e| wkh dwwulexwhv/ dfwlrqv dqg w|shv ri wkh frpsohphqwdu| sod|hu vhw1 Irupdoo|/ jlyhq dq dfwlrq suroh d dqg d w|sh suroh w= xk +d> w, @ k++l,> d > w > zkc@c| ,= Ghqrwh e| G wkh vhw ri doo pdsslqjv iurp W lqwr ]n 1 D phpehu ri G lv fdoohg d w|sh ixqfwlrq1 Jlyhq srsxodwlrq +Q> , zh vd| wkdw w|sh ixqfwlrq gkc| lv uhodwlyh wr w|sh suroh w li= gkc| +$> w5 , @ mil 5 Q = +l, @ $ dqg w @ w5 jm = Wkxv/ gkc| +$> w, ghqrwhv wkh qxpehu ri sod|huv zlwk dwwulexwh $ dqg w|sh w5 1; D xqlyhuvdo eholhiv ixqfwlrq e pdsv G lqwr ^3> 4`1 Wkh ydoxh e+gkc| , lv lqwhusuhwhg dv wkh suredelolw| ri w|sh suroh w1 Irupdoo|= j k +w, @ e+gkc| , zkhuh j k lv d suredelolw| glvwulexwlrq ryhu w|sh surohv iru wkh srsxodwlrq +Q> , lqgxfhg iurp wkh xqlyhuvdo eholhiv ixqfwlrq e1 Sod|huv duh dvvxphg wr kdyh frqvlvwhqw eholhiv zlwk uhvshfw wr j k 1 Lw lv lpsruwdqw wr uhdol}h wkh glhuhqfhv ehwzhhq ixqfwlrqv j k dqg e1 Ixqfwlrq j k lv ghqhg uhodwlyh wr d srsxodwlrq +Q> , dqg lwv grpdlq lv W 1 Ixqfwlrq e/ krzhyhu/ lv ghqhg lqghshqghqwo| ri dq| vshflf jdph dqg kdv grpdlq G1< D suhjdph lv jlyhq e| d wxsoh J @ +> D> W > e> k,/ frqvlvwlqj ri d frp0 sdfw phwulf vsdfh / frxqwdeoh vhwv D dqg W / ixqfwlrqv e = G $ ^3> 4` dqg ; < Qrwh wkdw _kc| lv d surmhfwlrq ri kc@c| rqwr l f 9 1 Dovr/ vxpplqj }k ryhu lwv grpdlq jlyhv d ydoxh ri rqh 0 ehfdxvh lw ghvfulehv d xqltxh srsxodwlrq 0 zkloh wkh vxp ri K ryhu lwv grpdlq lv qrq0qlwh 0 ehfdxvh lw ghvfulehv eholhiv iru dq| srsxodwlrq1 43 k = D W Z $ Un 1 Dv glvfxvvhg deryh zh uhihu wr d srsxod0 wlrq +Q> , dv lqgxflqj/ wkurxjk wkh suhjdph/ d Ed|hvldq jdph +Q> , +Q> D> W> jk > xk ,1 516 Vwudwhjlhv dqg h{shfwhg sd|rv Wdnh dv jlyhq d srsxodwlrq +Q> , dqg lqgxfhg Ed|hvldq jdph +Q> D> W> jk > xk ,1 Nqrzlqj klv rzq w|sh/ exw qrw wkrvh ri klv rssrqhqwv d sod|hu fkrrvhv dq dfwlrq1 D sxuh vwudwhj| ghwdlov wkh dfwlrq d sod|hu zloo wdnh iru hdfk w|sh w5 5 W dqg lv jlyhq e| d ixqfwlrq v& = W $ D zkhuh v& +w5 , lv wkh dfwlrq sod|hg e| wkh sod|hu li kh lv ri w|sh w5 1 Ohw V ghqrwh wkh vhw ri vwudwhjlhv1 D +pl{hg, vwudwhj| lv jlyhq e| d suredelolw| glvwulexwlrq ryhu wkh vhw ri sxuh vwudwhjlhv1 Wkh vhw ri vwudwhjlhv lv wkxv +V,1 Jlyhq d vwudwhj| { zh ghqrwh e| {+n, wkh suredelolw| wkdw d sod|hu sod|v sxuh vwudwhj| n 5 V1 Zh ghqrwh e| {+d, mw5 , wkh suredelolw| wkdw d sod|hu sod|v dfwlrq d, jlyhq S wkdw kh lv ri w|sh w5 1 Zh qrwh wkdw @, M {+d, mw5 , @ 4 iru doo w5 5 W 1 Ohw @ +V, ghqrwh wkh vhw ri vwudwhj| yhfwruv1 Zh uhihu wr d vwudwhj| yhfwru p dv d ghjhqhudwh li iru doo l 5 Q dqg w5 5 W wkhuh h{lvwv vrph d, vxfk wkdw p +d, mw5 , @ 41 Zh dvvxph wkdw sod|huv duh prwlydwhg e| h{shfwhg sd|rv143 Jlyhq d vwudwhj| yhfwru / d w|sh w5 5 W dqg eholhiv derxw wkh w|sh suroh sk wkh suredelolw| wkdw sod|hu l sxwv rq wkh dfwlrq suroh0w|sh suroh sdlu d @ +d > ===> d? , dqg w @ +w > ===> w3 > w5 > wn > ===> w? , lv jlyhq e|= _iu Su+d> w3 mw5 , @ sk +w3 mw5 , +d mw ,=== +d mw5 ,=== ? +d? mw? ,1 43 Zh xvh wkh yQP dvvxpswlrq iru frqyhqlhqfh exw rxu uhvxowv gr qrw ghshqg rq lw= Wr ghulyh rxu pdlq uhvxowv zh lpsrvh hlwkhu d odujh jdph surshuw| ru d frqwlqxlw| surshuw| dqg lq grlqj vr lpsrvh doo wkh dvvxpswlrqv qhhghg rq wkh Lk ixqfwlrqv1 Qhlwkhu wkh odujh jdph surshuw| ru frqwlqxlw| surshuw| uhtxluh wkh yQP dvvxpswlrq wr krog1 44 Wkxv/ jlyhq dq| vwudwhj| yhfwru / iru dq| w|sh w5 5 W dqg dq| sod|hu l ri w|sh w5 / wkh h{shfwhg sd|r ri sod|hu l fdq eh fdofxodwhg1 Ohw Xk +mw5 , = $ U ghqrwh wkh h{shfwhg xwlolw| ixqfwlrq ri sod|hu l frqglwlrqdo rq wkh w|sh ri sod|hu l ehlqj w5 zkhuh= _iu [ [ Su+d> w mw5 ,xk +d> w > w ,1 3 5 3 @M |3 MA3 Xk +mw5 , @ 517 Qdvk htxloleulxp dqg sxulfdwlrq Wkh vwdqgdug ghqlwlrq ri d Ed|hvldq Qdvk htxloleulxp dssolhv1 D vwudwhj| yhfwru lv d Ed|hvldq Qdvk %0htxloleulxp +ru lqirupdoo| dq dssur{lpdwh Ed|hvldq Qdvk htxloleulxp, li dqg rqo| li= Xk + > 3 mw5 , Xk +{> 3 mw5 , % iru doo { 5 +V,/ doo w5 5 W dqg iru doo l 5 Q1 Zh vd| wkdw d Ed|hvldq Qdvk % htxloleulxp p lv d Ed|hvldq Qdvk %0htxloleulxp lq sxuh vwudwhjlhv li p lv ghjhqhudwh1 Jlyhq d jdph +Q> , zh vd| wkdw wzr vwudwhj| surohv dqg p duh %0htxlydohqw li/ iru doo l 5 Q dqg w5 5 W = mXk +pmw5 , Xk +mw5 ,m %1 Zh vd| wkdw d vwudwhj| suroh fdq eh %0sxulhg li wkhuh h{lvwv d vwudwhj| suroh p wkdw lv ghjhqhudwh dqg %0htxlydohqw wr 144 44 D uhodwhg qrwlrq ri 00sxulfdwlrq zdv lqwurgxfhg e| Dxpdqq hw1 do1 +4<;6,1 Wkhuh/ wkh qrwlrq ri 00sxulfdwlrq lv uhodwlyh wr vwudwhjlhv dqg qrw vwudwhj| yhfwruv1 Wkxv/ wzr vwudwhjlhv R dqg | duh 00htxlydohqw iru sod|hu li Lk ERc j 3 3 Lk E|c j 3 0 iru dq| j 3 M P .t 1 Wklv ghqlwlrq suryhv xvhixo lq frqvlghulqj jdphv ri lqfrpsohwh lqirupdwlrq exw lv wrr uhvwulfwlyh wr eh ri xvh lq frqvlghulqj jdphv ri frpsohwh lqirupdwlrq1 45 6 Sxulfdwlrq Ehiruh surylglqj rxu pdlq uhvxowv lw pd| eh xvhixo wr surylgh d vlpsoh h{0 dpsoh= H{dpsoh 4= Wkhuh duh wzr furzglqj dwwulexwhv 0 ulfk dqg srru1 Sod|huv pxvw fkrrvh rqh ri wzr sxuh vwudwhjlhv ru orfdwlrqv D dqg E1 D srru sod|hu suhihuv olylqj zlwk ulfk sod|huv dqg wkxv klv sd|r lv htxdo wr wkh sursruwlrq ri ulfk sod|huv zkrvh fkrlfh ri orfdwlrq kh pdwfkhv1 D ulfk sod|hu suhihuv wr qrw olyh zlwk srru sod|huv dqg wkxv klv sd|r lv htxdo wr wkh sursruwlrq ri srru sod|huv zkrvh fkrlfh ri orfdwlrq kh grhv qrw pdwfk1 Dq| jdph lqgxfhg iurp wklv suhjdph kdv d Qdvk htxloleulxp1 Lw lv vlpsoh wr vhh/ krzhyhu/ wkdw li wkhuh h{lvwv dq rgg qxpehu ri hlwkhu ulfk ru srru sod|huv wkhq wkhuh grhv qrw h{lvw d Qdvk htxloleulxp lq sxuh vwudwhjlhv1 Dovr/ li hlwkhu wkh qxpehu ri ulfk sod|huv ru wkh qxpehu ri srru sod|huv lv vpdoo wkhq wkhuh qhhg qrw h{lvw dq dssur{lpdwh Qdvk htxloleulxp lq sxuh vwudwhjlhv/ qr pdwwhu krz odujh wkh wrwdo srsxodwlrq1 Rxu uvw pdlq uhvxow +Wkhruhp 5, ghprqvwudwhv wkdw li d suhjdph vdwlv0 hv d odujh jdph surshuw| wkhq/ lq dq| lqgxfhg jdph zlwk vx!flhqwo| pdq| sod|huv/ dq| Qdvk htxloleulxp fdq eh dssur{lpdwho| sxulhg1 Wkh suhjdph ri H{dpsoh 4 grhv qrw vdwlvi| wkh odujh jdph surshuw|> wkh odujh jdph surs0 huw| uhtxluhv wkdw dq| vpdoo jurxs ri sod|huv kdyh glplqlvklqj lq xhqfh lq srsxodwlrqv zlwk d odujhu sod|hu vhw1 Rxu vhfrqg pdlq uhvxow +Wkhruhp 6, ghprqvwudwhv wkdw li d suhjdph vdwlvhv d plog frqwlqxlw| surshuw| wkhq/ lq dq| jdph czlwk d wklfn glvwul0 exwlrq ri dwwulexwhv*/ wkhuh h{lvwv dq dssur{lpdwh Qdvk htxloleulxp lq sxuh vwudwhjlhv1 Wkh suhjdph ri H{dpsoh 4 vdwlvhv wkh frqwlqxlw| surshuw|> ds0 46 so|lqj Wkhruhp 6 ghprqvwudwhv wkdw li wkhuh duh vx!flhqwo| pdq| sod|huv zkr duh ulfk dqg dovr vx!flhqwo| pdq| zkr duh srru wkhq wkhuh h{lvwv dq dssur{lpdwh Qdvk htxloleulxp lq sxuh vwudwhjlhv1 614 Dssur{lpdwlqj pl{hg vwudwhj| surohv e| sxuh vwudwhj| surohv Wklv vhfwlrq vwdwhv d suholplqdu| uhvxow1 Wkhruhp 4 vkrzv wkdw jlyhq dq| vwudwhj| suroh / wkhuh h{lvwv d ghjhqhudwh vwudwhj| suroh p vxfk wkdw +l, hdfk sod|hu l lv dvvljqhg d sxuh vwudwhj| n lq wkh vxssruw ri / dqg +ll, wkh qxpehu ri sod|huv zkr sod| hdfk sxuh vwudwhj| n lv cforvh* wr wkh h{shfwhg qxpehu zkr zrxog kdyh sod|hg n jlyhq vwudwhj| suroh 1 Zlwk wklv uhvxow lq kdqg rxu pdlq uhvxowv fdq eh hdvlo| suryhg1 Zh qrwh qrz wkdw/ zkhq dsso|lqj Wkhruhp 4 lq wkh surriv ri Wkhruhpv 5 dqg 6/ wkh vwudwhj| suroh lv qrw +qhfhvvdulo|, wr eh wkrxjkw ri dv cwkh vwudwhj| suroh ri wkh srsxodwlrq* exw pruh dv wkh vwudwhj| suroh uhvwulfwhg wr wkrvh sod|huv zkr kdyh wkh vdph furzglqj dwwulexwh1 Wkhruhp 4= Iru dq| vwudwhj| suroh @ + > ===> ? , wkhuh h{lvwv d ghjhq0 hudwh vwudwhj| suroh p @ +p > ===> p? , vxfk wkdw= vxssruw+p , vxssruw+ , +5, iru doo l dqg= ? ? [ [ p +n, +n, 4 iru doo n 5 V1 ' ' +6, Revhuyh wkdw li / lq Wkhruhp 4/ zhuh d Qdvk htxloleulxp/ wkhq Wkhruhp 4 vwdwhv wkdw wkhuh lv dq dssur{lpdwlqj sxuh vwudwhj| suroh p zkhuh hyhu| 47 sod|hu sod|v d sxuh vwudwhj| lq klv ehvw uhvsrqvh vhw iru 1 Wklv lv fuxfldo lq surylqj rxu wzr pdlq wkhruhpv lq wkdw doorzv xv wr cdjjuhjdwh* wkh vwudwhjlhv ri sod|huv zkr kdyh wkh vdph furzglqj dwwulexwh |hw srwhqwldoo| glhuhqw wdvwh dwwulexwhv1 Zh kljkoljkw wkh uhodwlrqvkls ehwzhhq Wkhruhp 4 dqg wkh uhodwhg exw glvwlqfw Vkdsoh|0Ironpdq Wkhruhp dqg qrwh wkdw wkh Vkdsoh|0Ironpdq Wkh0 ruhp zloo qrw vx!fh iru rxu sxusrvhv145 Iru wkh uhdghu*v frqyhqlhqfh zh vwdwh wkh Vkdsoh|0Ironpdq Wkhruhp= Vkdsoh|0Ironpdq Wkhruhp =46 Li D > ===> Da lv d froohfwlrq ri vhwv lq U6 / S M A p/ wkhq iru dq| { 5 frq+ D , wkhuh h{lvwv d uhsuhvhqwdwlrq ri { ri S S wkh irup= { @ a | . a2 } / zkhuh iru hdfk m 5 M / | 5 D dqg iru hdfk m 5 M2 > } 5 frq+D ,/ mM m . mM2 m @ M dqg mM2 m p1 Li zh ohw N ghqrwh wkh qxpehu ri vwudwhjlhv wkhq iurp wkh Vkdsoh|0Ironpdq Wkhruhp zh rewdlq= iru dq| vwudwhj| suroh @ + > ===> ? , wkhuh h{lvwv d gh0 jhqhudwh vwudwhj| suroh p @ +p > ===> p? , vxfk wkdw= vxssruw+p , vxssruw+ , iru doo l dqg= ? ? [ [ pd{ p +n, +n, ? N & M7 ' +7, ' Lq Wkhruhp 4 zh rewdlq d erxqg wkdw lv lqghshqghqw ri wkh qxpehu ri vwudwhjlhv N1 Wklv lv fohduo| fuxfldo lq wuhdwlqj d qrq0qlwh vhw ri vwudwhjlhv/ zklfk lv shuplwwhg e| rxu prgho1 Zh ohdyh wkh ixoo uhodwlrqvkls ehwzhhq wkh Vkdsoh|0Ironpdq Wkhruhp dqg Wkhruhp 4 dv dq rshq txhvwlrq1 45 Dv glvfxvvhg lq Vhfwlrq 7 Udvklg +4<;6, grhv pdnh xvh ri wkh Vkdsoh|0Ironpdq Wkh0 ruhp lq surylqj d vshfldo fdvh ri rxu Wkhruhp 51 46 Vhh/ iru h{dpsoh/ Juhhq dqg Khoohu +4<<4, iru d surri ri wkh Vkdsoh|0Ironpdq Wkhr0 uhp1 48 615 Frqwlqxlw| lq furzglqj dwwulexwhv Wr ghulyh rxu sxulfdwlrq uhvxowv zh pdnh xvh ri d qdwxudo dqg plog frqwlqx0 lw| dvvxpswlrq rq furzglqj dwwulexwhv/ lqwurgxfhg lq Zrrghuv/ Fduwzuljkw dqg Vhowhq +5334,/ wkdw zloo eh dvvxphg wkurxjkrxw1 Jlyhq wkh vwudwhj| fkrlfhv ri rwkhu sod|huv/ lw lv dvvxphg wkdw hdfk sod|hu lv qhduo| lqglhuhqw wr d plqru shuwxuedwlrq ri wkh furzglqj dwwulexwhv ri rwkhu sod|huv +surylghg klv rzq furzglqj dwwulexwh lv xqfkdqjhg,1 Irupdoo|= Frqwlqxlw| lq furzglqj dwwulexwhv= Zh vd| wkdw d suhjdph J vdwlvhv frqwlqxlw| lq furzglqj dwwulexwhv li= iru dq| % A 3/ dq| wzr srsxodwlrqv +Q> , dqg +Q> , dqg dq| vwudwhj| suroh 5 li= pd{ glvw++m,> +m,, ? % M wkhq iru dq| l 5 Q zkhuh +l, @ +l,= k X + > 3 mw5 , Xk + > 3 mw5 , ? % doo w5 5 W 1 Zkhuh cglvw* lv wkh phwulf rq wkh vsdfh ri furzglqj dwwulexwhv F= Qrwh wkdw lq wkh ghqlwlrq ri frqwlqxlw| lq furzglqj dwwulexwhv wkh vwudw0 hj| suroh lv khog frqvwdqw1 Wkxv/ wkh dwwulexwhv ri sod|huv pd| fkdqjh exw wkhlu vwudwhjlhv gr qrw1 616 Odujh jdph surshuw| Wr ghqh wkh odujh jdph surshuw|/ vrph dgglwlrqdo qrwdwlrq dqg ghqlwlrqv duh uhtxluhg1 Ghqrwh e| HZ wkh vhw ri ixqfwlrqv pdsslqj F D W lqwr Un / wkh vhw ri qrq0qhjdwlyh uhdov1 Zh uhihu wr hz 5 HZ dv dq h{shfwhg 49 zhljkw ixqfwlrq1 Jlyhq d srsxodwlrq +Q> , zh vd| wkdw dq h{shfwhg zhljkw ixqfwlrq hzkcj lv uhodwlyh wr vwudwhj| suroh li dqg rqo| li= hzkcj +f> d, > w5 , @ [[ M M zkc@c| +f> d, > w5 , Su+d> w, @ | A iru doo $> d, dqg w5 1 Wkxv/ hzkcj +$> d, > w5 , ghqrwhv wkh h{shfwhg qxpehu ri sod|huv ri furzglqj0dwwulexwh f zkr zloo kdyh w|sh w5 dqg sod| dfwlrq d, 1 Qrwh wkdw wklv h{shfwdwlrq lv wdnhq ehiruh dq| sod|hu lv dzduh ri klv w|sh1 Il{ d srsxodwlrq +Q> ,1 Ohw HZk ghqrwh wkh vhw ri h{shfwhg zhljkw ixqfwlrqv wkdw pd| eh uhdol}hg jlyhq srsxodwlrq +Q> ,1 Zh ghqh d phwulf rq wkh vsdfh HZk = glvw4+hz> hj, @ 4 [ [ [ , 5 , 5 d > w , hj+f> d > w , hz+f> mQm , @ M |5 M9 SM iru dq| hz> hj 5 HZk 1 Wkxv/ wzr h{shfwhg zhljkw ixqfwlrqv duh cforvh* li wkh h{shfwhg sursruwlrq ri sod|huv zlwk hdfk furzglqj dwwulexwh dqg hdfk w|sh sod|lqj hdfk dfwlrq duh forvh1 Zh fdq qrz vwdwh rxu pdlq dvvxpswlrq= Odujh jdph surshuw|= Zh vd| wkdw d suhjdph J vdwlvhv wkh odujh jdph surshuw| li= iru dq| % A 3/ dq| srsxodwlrq +Q> , dqg dq| wzr vwudwhj| surohv > 5 zlwk h{shfwhg zhljkw ixqfwlrqv hzkcj > hzkcj vdwlvi|lqj= glvw4+hzkcj > hzkcj , ? % li @ wkhq= mXk + > 3 mw5 , Xk + > 3 mw5 ,m ? % iru doo w5 5 W 1 Li d suhjdph vdwlvhv wkh odujh jdph surshuw| wkhq zh fdq wklqn ri jdphv lqgxfhg iurp wkh suhjdph dv vdwlvi|lqj wzr frqglwlrqv rq sd|r ixqfwlrqv= 4: 41 D sod|hu lv qhduo| lqglhuhqw wr d fkdqjh lq wkh sursruwlrq ri sod|huv ri hdfk dwwulexwh sod|lqj hdfk sxuh vwudwhj| +surylghg klv rzq vwudwhj| lv xqfkdqjhg,> wkxv/ dq| rqh lqglylgxdo kdv qhdu0qhjoljleoh lq xhqfh ryhu wkh sd|rv ri rwkhu sod|huv1 51 D sod|hu lv culvn qhxwudo* lq wkh vhqvh wkdw wkh h{shfwhg zhljkw ixqfwlrq odujho| ghwhuplqhv klv sd|r> wkxv wzr vwudwhj| surohv wkdw lqgxfh wkh vdph h{shfwhg zhljkw ixqfwlrq jlyh d vlplodu sd|r1 Wkh uvw frqglwlrq lv uh hfwlyh ri wkh dwwulexwh ri jdph xqghu frqvlghudwlrq dqg lv fuxfldo wr rewdlqlqj rxu pdlq uhvxow> H{dpsoh 4/ iru lqvwdqfh/ grhv qrw vdwlvi| wkh odujh jdph surshuw| lq wklv uhvshfw1 Wkh vhfrqg frqglwlrq lv uhodwlyho| plog jlyhq wkdw zh frqvlghu jdphv zlwk pdq| sod|huv> lw iroorzv/ iru h{dpsoh/ iurp wkh odz ri odujh qxpehuv wkdw lq wkh fdvh ri d qlwh vwudwhj| vhw/ zlwk kljk suredelolw|/ lq d jdph zlwk pdq| sod|huv wkh uhdol}hg zhljkw ixqfwlrq zloo eh forvh wr wkh h{shfwhg zhljkw ixqfwlrq +Ndodl 5335,147 Qrwh wkdw wkh odujh jdph surshuw| uhodwhv wr fkdqjhv lq wkh vwudwhjlhv ri sod|huv zkloh wkhlu dwwulexwhv gr qrw fkdqjh> wklv frqwudvwv zlwk wkh dv0 vxpswlrq ri frqwlqxlw| lq furzglqj dwwulexwhv wkdw uhodwhv wr fkdqjhv lq dwwulexwhv zkloh vwudwhjlhv gr qrw fkdqjh1 Dv d frqvhtxhqfh d suhjdph pd| vdwlvi| wkh odujh jdph surshuw| dqg |hw wkhuh qrw eh frqwlqxlw| lq dwwulexwhv dqg ylfh0yhuvd1 617 Pdlq Uhvxow> Dssur{lpdwh sxulfdwlrq Rxu pdlq uhvxow ghprqvwudwhv wkdw lq vx!flhqwo| odujh jdphv zlwk pdq| sod|huv dq| Qdvk htxloleulxp fdq eh dssur{lpdwho| sxulhg1 47 Wkxv/ lw lv qrw vr pxfk wkdw sod|huv duh ulvn qhxwudo exw udwkhu wkdw wkhuh lv olwwoh ulvn1 4; Wkhruhp 5= Frqvlghu d suhjdph J @ +> D> W > e> k, vdwlvi|lqj frqwlqxlw| lq furzglqj dwwulexwhv dqg wkh odujh jdph surshuw|1 Jlyhq dq| uhdo qxpehu % A 3 wkhuh lv dq lqwhjhu +%, zlwk wkh surshuw| wkdw/ iru dq| lqgxfhg jdph +Q> , zkhuh mQm A +%, dqg iru dq| Qdvk htxloleulxp ri jdph +Q> ,> wkhuh h{lvwv d Ed|hvldq Qdvk %0htxloleulxp lq sxuh vwudwhjlhv p wkdw lv dq %0sxulfdwlrq ri 1 Surri= Vxssrvh qrw1 Wkhq wkhuh lv vrph % A 3 vxfk wkdw iru hdfk lqwhjhu wkhuh lv dq lqgxfhg jdph +Q D > D , zlwk mQ D m A dqg d Qdvk htxloleulxp zlwk wkh surshuw| wkdw wkhuh h{lvwv qr Qdvk %0htxloleulxp lq sxuh vwudwhjlhv surylglqj dq %0sxulfdwlrq ri 1 Jlyhq wkdw D lv d Qdvk htxloleulxp/ iru dq| l 5 Q D dqg iru dq| vwudwhj| pD zkhuh vxssruw+pD , vxssruw+D , zh kdyh= D D Xk +pD > D3 mw5 , Xk +v> D3 mw5 , +8, iru doo w5 5 W dqg v 5 1 Xvh frpsdfwqhvv ri F wr zulwh F dv wkh glvmrlqw xqlrq ri d qlwh qxpehu ri qrq0hpsw| vxevhwv F > ===> F / hdfk ri gldphwhu ohvv wkdq S %1 Iru hdfk d @ 4> ===> D/ fkrrvh dqg { d srlqw f@ 5 F@ 1 Iru hdfk / zlwkrxw fkdqjlqj wdvwh dwwulexwhv ri sod|huv/ zh ghqh wkh furzglqj dwwulexwh ixqfwlrq D e| lwv frruglqdwhv D +, dv iroorzv= iru hdfk m 5 Q/ D +m, @ f@ li dqg rqo| li +m, 5 F@ = Ghqh qhz dwwulexwh ixqfwlrqv D e| D +m, @ ++m,> D +m,, zkhq D +m, @ ++m,> D +m,, iru hdfk m 5 Q D 1 E| dsso|lqj Wkhruhp 4 wr hdfk f 5 D +Q,/ l1h1 f > ===> f lw iroorzv wkdw wkhuh h{lvwv d vhtxhqfh ipD j ri ghjhqhudwh vwudwhj| surohv vxfk wkdw= 4< 41 iru doo f 5 F/ d, 5 D dqg w5 5 W olp D <" hjkD D c6D +f> d, > w5 , hzkD D cjD +f> d, > w5 , @ olp > dqg D <" mQ D m mQ D m +9, 51 iru doo dqg l 5 Q D / vxssruw+pD , vxssruw+D ,= +:, Slfn dq duelwudu| dqg sod|hu l 5 Q D 1 Frqvlghu wkh dwwulexwh ixqfwlrq D D D zkhuh +l, @ D +l, dqg +m, @ D +m, iru doo m 5 @ l1 E| frqwlqxlw| lq furzglqj dwwulexwhv= D % D k D 5 k D 5 X +v> 3 mw , X +v> 3 mw , ? 9 iru doo w5 5 W dqg v 5 / dqg= % D D k X +v> pD3 mw5 , Xk +v> pD3 mw5 , ? 9 iru dq| w5 5 W dqg v 5 1 Lq ylhz ri +9, dqg wkh odujh jdph surshuw| lw lv fohdu li zdv vx!flhqwo| odujh= % D D k X +v> D3 mw5 , Xk +v> pD3 mw5 , ? 9 iru dq| w5 5 W dqg v 5 1 Wkxv/ iru vx!flhqwo| odujh dqg iru dq| l 5 Q D = kD X +v> pD3 mw5 , XkD +v> D3 mw5 , ? % 5 iru dq| w5 5 W dqg v 5 1 Ilqdoo|/ jlyhq +:, dqg +8, iru vx!flhqwo| odujh= D D Xk +pD > pD3 mw5 , Xk +v> pD3 mw5 , A % iru doo w5 5 W dqg v 5 1 Wklv jlyhv wkh ghvluhg frqwudglfwlrq1 53 618 Pdq| sod|huv ri hdfk furzglqj dwwulexwh Rxu wklug uhvxow ghprqvwudwhv wkdw/ zkhq iru hdfk sod|hu lq dq lqgxfhg jdph wkhuh duh vx!flhqwo| pdq| sod|huv zlwk vlplodu dwwulexwhv/ zhdnhu frqglwlrqv duh vx!flhqw wr dssur{lpdwho| sxuli| Qdvk htxloleulxp1 Il{ d srsxodwlrq +Q> ,1 Dv ehiruh ohw HZk ghqrwh wkh vhw ri h{shfwhg zhljkw ixqfwlrqv wkdw pd| eh uhdol}hg jlyhq srsxodwlrq +Q> ,1 Iru hdfk f 5 F zlwk f 5 +Q,/ ohw +f, 3 +f, eh wkh qxpehu ri sod|huv zlwk furzglqj dwwulexwh f1 Zh ghqh d vhfrqg phwulf rq wkh vsdfh HZk = 3 4 [ [ [ 4 C glvw5+hz> hj, @ hz+f> d, > w5 , hj+f> d, > w5 ,D +f, , SMVE @ M |5 M9 iru dq| hz> hj 5 HZk 1 Wkxv/ wzr h{shfwhg zhljkw ixqfwlrqv duh cforvh* li wkh h{shfwhg sursruwlrqv ri sod|huv zlwk hdfk furzglqj dwwulexwh sod|lqj hdfk sxuh vwudwhj| duh forvh1 Wklv glhuv vljqlfdqwo| iurp wkh hduolhu glvw4 zkhuh forvhqhvv lv mxgjhg rq wkh sursruwlrqv uhodwlyh wr wkh wrwdo srsxodwlrq sod|lqj hdfk sxuh vwudwhj|1 Lw lv lpphgldwh wkdw glvw5+hz> hj, glvw4+hz> hj,1 Zh vwdwh d vhfrqg dvvxpswlrq wkdw zhdnhqv wkh odujh jdph surshuw|= Frqwlqxlw| surshuw|= Zh vd| wkdw d suhjdph J vdwlvhv wkh frqwlqxlw| surshuw| li= iru dq| % A 3/ dq| srsxodwlrq +Q> , dqg dq| wzr vwudwhj| surohv > 5 zkhuh= glvw5+hzkcj > hzkcj , ? % li @ wkhq= mXk + > 3 mw5 , Xk + > 3 mw5 ,m ? % iru doo w5 5 W 1 54 Wkh frqwlqxlw| surshuw| dsshduv plog1 Lq sduwlfxodu/ rqh sod|hu fdq kdyh d odujh lq xhqfh hyhq lq odujh srsxodwlrqv li kh lv wkh rqo| sod|hu zlwk klv furzglqj dwwulexwh1 Wkxv/ iru h{dpsoh/ wkh suhjdph ri H{dpsoh 4 vdwlvhv wkh frqwlqxlw| surshuw| exw qrw wkh odujh jdph surshuw|1 Wklv looxvwudwhv wkdw wkh frqwlqxlw| surshuw| lv qrw vx!flhqw wr rewdlq d uhvxow vxfk dv Wkhruhp 51 Ohw E +f, ghqrwh d edoo lq furzglqj dwwulexwh vsdfh F fhqwhuhg rq f ri udglxv 1 Zh ghqrwh e| I +> , wkh vhw ri srsxodwlrqv zkhuh +Q> , 5 I +> , li dqg rqo| li [ M +f , A S ES iru doo f 5 +Q,1 Wkxv/ srsxodwlrq +Q> , 5 I +> , rqo| li wkhuh lv d fhuwdlq cwklfnqhvv* wr wkh glvwulexwlrq ri sod|huv ryhu furzglqj dwwulexwhv1 Qrwh/ krzhyhu/ wkdw d srsxodwlrq +Q> , 5 I +> , pd| kdyh wkh surshuw| wkdw wkhuh lv d codujh* vxevhw ri dwwulexwh vsdfh dqg qr sod|hu l 5 Q zlwk dwwulexwhv lq 1 Zh rewdlq wkh iroorzlqj uhvxow= Wkhruhp 6= Frqvlghu d suhjdph J @ +> D> W > e> k, wkdw vdwlvhv frqwlqxlw| lq furzglqj dwwulexwhv dqg wkh frqwlqxlw| surshuw|1 Jlyhq dq| uhdo qxpehu % A 3 wkhuh lv dq lqwhjhu +%, dqg d uhdo qxpehu +%, A 3 vxfk wkdw iru dq| srsxodwlrq +Q> , 5 I ++%,> +%,, dqg dq| Qdvk htxloleulxp ri wkh lqgxfhg jdph +Q> , wkhuh h{lvwv d Ed|hvldq Qdvk %0htxloleulxp lq sxuh vwudwhjlhv p wkdw lv dq %0sxulfdwlrq ri 1 Surri= Vxssrvh qrw1 Wkhq wkhuh lv vrph % A 3 vxfk wkdw iru hdfk lqwhjhu % dqg d Qdvk htxloleulxp ri wkhuh lv d srsxodwlrq +Q D > D , 5 I > S wkh lqgxfhg jdph +Q D > D , zlwk wkh surshuw| wkdw wkhuh h{lvwv qr Qdvk 55 %0htxloleulxp lq sxuh vwudwhjlhv wkdw lv dq %0sxulfdwlrq ri 1 Wr vlpsoli| qrwdwlrq iru dq| vhw D F ohw D +D, D +D, eh wkh 3 qxpehu ri sod|huv lq srsxodwlrq +Q D > D , zlwk furzglqj dwwulexwh f 5 D1 Zh frqmhfwxuh +-, wkdw/ e| sdvvlqj wr d vxevhtxhqfh li qhfhvvdu|/ wkhuh h{lvwv d sduwlwlrq ri F lqwr d qlwh qxpehu ri qrq0hpsw| vxevhwv F > ===> F' / hdfk ri gldphwhu ohvv wkdq 0 S zkhuh wkh vhtxhqfh iD +F^ ,jD:f hlwkhu whqgv wr lqqlw| ru frqyhujhv wr }hur1 Dvvxph wkdw frqmhfwxuh +-, lv fruuhfw1 Jlyhq wkh frqwlqxlw| surshuw| lw lv vlpsoh wr vhh wkdw d frqwudglfwlrq fdq eh re0 wdlqhg lq d vlplodu pdqqhu wr wkh frqwudglfwlrq lq wkh surri ri Wkhruhp 51 Lw wkxv uhpdlqv wr suryh frqmhfwxuh +-,1 Ghqh S %1 Xvh frpsdfwqhvv ri F wr zulwh F dv wkh glvmrlqw xqlrq ri d qlwh qxpehu ri qrq0hpsw| vxevhwv F > ===> F- / hdfk ri gldphwhu ohvv wkdq 1 Wklv lqlwldo sduwlwlrq lv xqolnho| wr vdwlvi| wkh ghvluhg surshuwlhv> wkh ghvluhg sduwlwlrq zloo eh ciruphg* e| phujlqj vxevhwv wrjhwkhu1 E| sdvvlqj wr d vxe0vhtxhqfh li qhfhvvdu|/ zh fdq dvvxph/ iru hdfk Fo / wkdw wkh vhtxhqfh \ iD +F ,j" hlwkhu whqgv wr lqqlw| ru frqyhujhv wr d qlwh olplw1 Ghqh o o D ' vxevhwv D" dqg Dn ri iF > ===> F- j e| Fo 5 D" li dqg rqo| li \o whqgv wr lqqlw| dqg Fo 5 Dn li dqg rqo| li \o whqgv wr d srvlwlyh uhdo qxpehu1 +Qrwh wkdw D" dqg Dn gr qrw qhfhvvdulo| frpsulvh d sduwlwlrq ri iF > ===> F j vlqfh - \o pd| eh }hur iru vrph Fo 1, Frqvlghu dq| Fo 5 Dn 1 Wkhuh pxvw h{lvw d uhdo qxpehu o vxfk wkdw iru dq| srsxodwlrq +Q D > D , zkhuh A o wkhuh lv dw ohdvw rqh sod|hu lD 5 Q D zlwk D +lD , 5 Fo 1 Ohw fD D +lD , iru doo 1 E| dvvxpswlrq= [ M D +f , A S ESD iru doo 1 Il{ dq duelwudu| srlqw fo 5 Fo 1 Jlyhq wkdw wkh gldphwhu ri Fo lv 56 lw krogv wkdw= [ M D +f , A S 2 ESo iru doo 1 Sduwlwlrqlqj F lqwr vhwv F > ===> F- dovr sduwlwlrqv wkh edoo E2 +fo , lqwr d qlwh qxpehu ri vhwv E2 +fo , > ==> E2- +fo , zkhuh= f 5 E2@ +fo , li dqg rqo| li f 5 E2@ +fo , dqg f 5 F@ 1 Wklv lpsolhv wkdw wkhuh pxvw h{lvw vrph E2@ +fo , 5 D" 1 Ixuwkhupruh/ glvw+fo > f@ , ? 6 iru doo f@ 5 F@ dqg doo fo 5 Fo 1 Iurp wkh deryh/ lw iroorzv/ wkdw e| dq dssursuldwh phujlqj ri wkh vxevhwv F > ===> F- +dqg/ lq sduwlfxodu/ phujlqj d vhw Fo 5 Dn zlwk d vhw F@ 5 D" , wkhuh pxvw h{lvw d sduwlwlrq ri F lqwr d qlwh qxpehu ri qrq0hpsw| vxevhwv F > ===> F' / hdfk ri gldphwhu ohvv wkdq 9 @ 0 S zkhuh wkh vhtxhqfh iD +Fo ,jD:f hlwkhu whqgv wr lqqlw| ru frqyhujhv wr }hur1 Wklv suryhv frqmhfwxuh +-, dqg wkxv Wkhruhp 61 619 D uhpdun rq h{lvwhqfh ri htxloleulxp Zlwk d frxqwdeoh vhw ri vwudwhjlhv/ d Qdvk htxloleulxp/ hyhq rqh lq pl{hg vwudwhjlhv/ pd| qrw h{lvw1 Wklv lv hdv| wr vhh1 Vxssrvh/ iru h{dpsoh/ wkh jdph lv rqh zkhuh wkh sul}h jrhv wr wkh sod|hu zkr dqqrxqfhv wkh kljkhvw lqwhjhu1 Li zh dgg wkh uhtxluhphqw ri frpsdfwqhvv ri wkh vhwv ri dfwlrqv dqg ri w|shv/ krzhyhu/ wkhq h{lvwhqfh ri d Ed|hvldq0Qdvk htxloleulxp lq pl{hg vwudwhjlhv fdq eh rewdlqhg xvlqj/ iru h{dpsoh/ wkh {hg srlqw wkhruhp ri Jolfnvehuj +4<85,1 57 7 Vrph ixuwkhu uhodwlrqvklsv wr wkh olwhudwxuh Wzr dxwkruv wkdw surylgh uhvxowv rq sxulfdwlrq zlwk odujh exw qlwh sod|hu vhwv duh Udvklg +4<;6, dqg Ndodl +5335,1 Ndodl +5335, surylghv vx!flhqw frqglwlrqv iru wkh h{lvwhqfh ri dq dssur{lpdwh Ed|hvldq h{0srvw Qdvk htxl0 oleulxp1 Rqh lpsolfdwlrq ri Ndodl*v uhvxowv lv wkdw hyhu| Qdvk htxloleulxp fdq eh dssur{lpdwho| sxulhg148 Lq frqwudvw wr wklv sdshu dqg Zrrghuv/ Fduwzuljkw dqg Vhowhq +5334,/ Ndodl uhtxluhv erwk d qlwh qxpehu ri dfwlrqv dqg d qlwh qxpehu ri furzglqj w|shv1 Zh frqmhfwxuh/ exw kdyh qrw ghprq0 vwudwhg/ wkdw Ndodl*v vruw ri sxulfdwlrq uhvxow zloo krog lq wkh frqwh{w ri rxu sdshu1 Zlwk d qlwh vhw ri vwudwhjlhv dqg qlwh w|shv ri sod|huv/ Udvklg +4<;6, pdnhv xvh ri wkh Vkdsoh|0Ironpdq Wkhruhp wr suryh klv uhvxow rq h{lvwhqfh ri dssur{lpdwh htxloleulxp lq sxuh vwudwhjlhv1 E| dvvxplqj d olqhdulw| ri sd|r ixqfwlrqv Udvklg ghprqvwudwhv wkdw cqhdu* wr dq| Qdvk htxloleulxp wkhuh lv dq dssur{lpdwh Qdvk htxloleulxp lq zklfk mQm N sod|huv xvh sxuh vwudwhjlhv +zkhuh N lv wkh qxpehu ri vwudwhjlhv, dqg N sod|huv pd| sod| pl{hg vwudwhjlhv1 +Vhh dovr Fduprqd 5336 zkr dujxhv wkdw dq dgglwlrqdo frqglwlrq/ htxlfrqwlqxlw| ri sd|r ixqfwlrqv iru h{dpsoh/ lv uhtxluhg,1 Pdq| dxwkruv kdyh frqwulexwhg wr wkh olwhudwxuh rq wkh h{lvwhqfh ri d sxuh vwudwhj| qrq0frrshudwlyh htxloleuld lq jdphv zlwk d frqwlqxxp ri sod|0 huv +lqfoxglqj Vfkphlgohu 4<:6/ Pdv0Frohoo 4<;7/ Nkdq 4<;</ 4<<;/ Nkdq hw do1 4<<:/ Sdvfrd 4<<6d/ 4<<; dqg Nkdq dqg Vxq 4<<<,1 Wklv olwhudwxuh/ jlyhq ydulrxv dvvxpswlrqv rq wkh vwudwhj| vsdfh/ kdv ghprqvwudwhg wkh h{lv0 48 Lqghhg/ Ndodl ghprqvwudwhv wkdw qrw rqo| fdq d Qdvk htxloleulxp eh sxulhg exw zkhq d Qdvk htxloleulxp lv sod|hg doprvw dq| uhdol}hg vhw ri vwudwhj| surohv pxvw eh dq dssur{lpdwh Qdvk htxloleulxp wkdw lv/ zlwk suredelolw| duelwudulo| forvh wr rqh/ hyhu| Qdvk htxloleulxp vhoi sxulhv1 Vhh dovr irrwqrwh 71 58 whqfh ri d qrq0frrshudwlyh htxloleulxp zkhq sd|rv ghshqg rq rssrqhqw*v vwudwhjlhv wkurxjk wkh glvwulexwlrq ryhu sxuh vwudwhjlhv1 Rxu Wkhruhp 5 fdq eh vhhq dv surylglqj d qlwh dqdorjxh wr vrph ri wkhvh frqwlqxxp uhvxowv149 Zlwklq wkh olwhudwxuh rq qrq0dwrplf jdphv/ wkh dssurdfk ri Sdvfrd +4<<6d, dsshduv prvw vlplodu wr rxu rzq1 Sdvfrd +4<<6d, ghdov zlwk qrq0 dqrq|prxv jdphv dv lqwurgxfhg e| Juhhq +4<;7,1 D sod|hu lq d qrq0 dqrq|prxv jdph kdv d w|sh +zklfk frxog eh wkrxjkw dv dq dwwulexwh lq rxu iudphzrun, dqg d sod|hu*v sd|r ghshqgv rq klv rssrqhqw*v vwudwhjlhv wkurxjk wkh glvwulexwlrq ryhu w|shv dqg sxuh vwudwhjlhv1 Pruh irupdoo|/ ohw W ghqrwh d vhw ri w|shv dqg G wkh vhw ri Eruho suredelolw| phdvxuhv ryhu W V14: Wkh sd|r wr d sod|hu ri w|sh w iurp sod|lqj vwudwhj| v zkhq wkh vwudwhjlhv ri rssrqhqwv lv 5 G lv jlyhq e| y+w> v> ,1 Wr rewdlq klv uh0 vxowv Sdvfrd dvvxphv wkdw y+w> > , lv mrlqwo| frqwlqxrxv/ zlwk uhvshfw wr wkh zhdn- wrsrorj| rq G14; Wklv fruuhvsrqgv wr rxu dvvxpswlrq ri d suhjdph wkdw vdwlvhv wkh odujh jdph surshuw| dqg frqwlqxlw| lq furzglqj dwwulexwhv1 Sdvfrd +4<<6d/4<<;, dovr rewdlqv h{lvwhqfh uhvxowv xvlqj frqglwlrqv vlplodu wr wkrvh ri rxu Wkhruhp 61 8 Frqfoxvlrqv Wklv sdshu lqwurgxfhv d iudphzrun iru vwxg|lqj dv|pswrwlf surshuwlhv ri vwudwhjlf jdphv zlwk jurzlqj qxpehuv ri sod|huv1 Rxu iudphzrun h{whqgv wkrvh douhdg| lq wkh olwhudwxuh1 Wkh pdmru lqqrydwlrqv duh +d, rxu pdwk0 49 Qrwh wkdw wklv olwhudwxuh lv w|slfdoo| frqfhuqhg zlwk wkh h{lvwhqfh ri d qrq0frrshudwlyh htxloleulxp dqg qrw +dv lq wklv sdshu, wkh sxulfdwlrq ri d qrq0frrshudwlyh htxloleulxp wkdw lv dvvxphg wr h{lvw +h{fhswlrqv lqfoxgh Sdvfrd 4<<;,1 4: Zkhuh 7 ghqrwhv dv suhylrxvo| wkh vhw ri vwudwhjlhv1 4; Sdvfrd +4<<6d, dvvxphv d frpsdfw phwulf vsdfh ri vwudwhjlhv1 59 hpdwlfdo uhvxow +Wkhruhp 4,/ +e, doorzlqj frxqwdeoh vhwv ri dfwlrqv dqg w|shv/ dqg +f, wkh irupdol}dwlrq ri wkh vhsdudwlrq ri furzglqj dqg wdvwh dwwulexwhv ri sod|huv1 Wklv vhsdudwlrq sod|v d uroh lq rwkhu uhvhdufk rq qrq0 frrshudwlyh jdphv/ sduwlfxoduo| rq jdphv zlwk pdq| sod|huv zkhuh vlplodu sod|huv frqirup +vhh Zrrghuv/ Fduwzuljkw dqg Vhowhq 5334 dqg Fduwzuljkw dqg Zrrghuv 5336,1 Wr uhodwh wklv vhsdudwlrq wr rwkhu olqhv ri uhvhdufk/ lq prghov ri sulydwh jrrgv hfrqrplhv zkhuh wkh wdvwhv ri dq lqglylgxdo dhfw rwkhu lqglylgxdov rqo| wkurxjk klv ghpdqg iru sulydwh jrrgv/ d vhsdudwlrq ri wdvwhv iurp rwkhu dwwulexwhv ri d sod|hu/ lq sduwlfxodu/ hqgrzphqw/ lv lp0 solflw1 Lq wkh olwhudwxuh ri orfdo sxeolf jrrgv hfrqrplhv dqg hfrqrplhv zlwk foxev/ zkhuh wkh xwlolw| ri dq lqglylgxdo ghshqgv rq wkh dwwulexwhv ri rwkhu lqglylgxdov lq wkh vdph foxev/ d glvwlqfwlrq vlplodu wr wkdw ri wklv sdshu lv pdgh14< Zkloh vxfk d glvwlqfwlrq pd| eh lpsolflw lq qxphurxv h{dpsohv dqg frxog dovr kdyh ehhq exlow lqwr vrph ri wkh sulru olwhudwxuh/ h{fhsw iru rxu uhvhdufk/ zh duh xqdzduh ri dq| irupdol}dwlrq dqg xvh ri wklv glvwlqf0 wlrq lq wkh sulru olwhudwxuh ri qrqfrrshudwlyh jdph wkhru|1 Lq uhvhdufk lq surjuhvv rq qrqfrrshudwlyh jdphv/ exw iroorzlqj Frqoh| dqg Zrrghuv +4<<9/ 5334, uhvhdufk rq frrshudwlyh dqg sulfh wdnlqj htxloleulxp/ zh hqgrjhqlvh fkrlfh ri furzglqj dwwulexwhv dqg frqvlghu hyroxwlrq ri revhuyhg sdwwhuqv ri furzglqj dwwulexwhv1 9 Dsshqgl{ Zh lqwurgxfh vrph dgglwlrqdo qrwdwlrq1 Ohw d @ +d > ===> d? ,> e @ +e > ===> e? , 5 U? 1 Zh zulwh d e li dqg rqo| li d e iru doo l @ 4> ===> q1 Jlyhq dq| vwudw0 4< Zh uhihu wkh uhdghu wr Zrrghuv/ Fduwzuljkw dqg Vhowhq +5336, dqg Frqoh| dqg Zrrg0 huv +5334, dqg uhihuhqfhv wkhuh iru ixuwkhu prwlydwlrq dqg glvfxvvlrq ri furzglqj w|shv1 5: hj| suroh ohw P+, ghqrwh wkh vhw ri vwudwhj| surohv vxfk wkdw p 5 P+, li dqg rqo| li +4, p lv ghjhqhudwh dqg +5, vxssruw+p , vxssruw+ , iru doo l 5 Q1 Lw lv lpphgldwh wkdw P +, lv qrq0hpsw| iru dq| 1 Ohppd 4= Ohw Q @ i4> ===> qj eh d qlwh vhw1 Iru dq| vwudwhj| suroh S @ + > ===> ? , dqg iru dq| ixqfwlrq j = V $ ]n vxfk wkdw j/ wkhuh h{lvwv p 5 P+, vxfk wkdw [ p j= Surri= Vxssrvh wkh vwdwhphqw ri wkh ohppd lv idovh1 Wkhq wkhuh h{lvwv d S vwudwhj| suroh @ + > ===> ? , dqg d ixqfwlrq j zkhuh M j/ vxfk wkdw/ iru dq| yhfwru p @ +p > ===> p? , 5 P+, wkhuh pxvw h{lvw dw ohdvw rqh S e n, ? j+e n,1 Iru hdfk yhfwru p 5 P+, ohw O eh n zkhuh e n 5 V dqg p +e ghqhg dv iroorzv= O+p, @ # [ M & 7G S 6 E&} j+n, & [ $ p +n, Zh qrwh wkdw O+p, pxvw eh qlwh dqg srvlwlyh iru doo p153 Vhohfw pf 5 P+, iru zklfk O+p, dwwdlqv lwv plqlpxp ydoxh ryhu doo p 5 P+,1 Lqwxlwlyho| wkh yhfwru pf lv cdv forvh* dv zh fdq jhw wr vdwlvi|lqj wkh ohppd1 Zh uhpdun wkdw wkh phwkrg ri surri zloo eh rqh ri cvkx"lqj* wkh sxuh vwudwhjlhv wkdw sod|huv xvh vr dv wr ghprqvwudwh wkh h{lvwhqfh ri d vwudwhj| suroh pW zkhuh O+pW , @ O+pf , 41 Surylglqj wkh ghvluhg frqwudglfwlrq1 S n, pf +e n, A 31 Iru dq| vxevhw L ri Q Slfn d vwudwhj| e n vxfk wkdw j+e ohw wkh vhw V+L, V eh vxfk wkdw= q r V+L, @ e n ^ n 5 V = pf +n, @ 4 iru vrph l 5 L S Qrwh wkdw wkh vhw ri & vxfk wkdw 6 E& }& qhhg qrw eh qlwh1 Jlyhq/ krzhyhu/ S S S wkdw & j E& ' lw pxvw eh wkdw & }E& $ dqg wkxv uE6 lv qlwh1 53 5; Zh fdq qrz ghqh vhwv Q | iru w @ 3> 4> === dv iroorzv= q r l 5 Q = pf +e n, @ 4 dqg iru doo w A 3 Qf @ ; < ? m 5 Q = +n, A 3 dqg pf +n, @ 3 @ Q | @ Q |3 ^ |3 = > iru vrph n 5 V Q W W Xowlpdwho|/ iru vrph wW 4 zh pxvw kdyh wkdw Q | n @ Q | Q1 Wklv lv dq lpphgldwh frqvhtxhqfh ri wkh qlwhqhvv ri wkh sod|hu vhw1 Ohw V+Q, V1 Frqvlghu dq| sxuh vwudwhj| nW 5 V1 Wkh frqvwuxfwlrq ri Q dqg V lpso| wkdw wkhuh pxvw h{lvw d fkdlq ri sod|huv il > ===> l| j Q zkhuh +4, pf| +n| , @ 4 iru w @ 4> ===> w 4/ +5, p| +nW , @ 4/ +6, | +n|3 , A 3 iru w @ 5> ===> w dqg +7, n, A 31 Wkxv/ wkhuh h{lvwv d yhfwru pW 5 P +, vxfk wkdw= +e n, @ 4/ pW +n , @ 3 dqg pW +e pW| +nW , @ 3 dqg pW| +n| 3 , @ 4 pW| +n| , @ 3 dqg pW| +n|3 , @ 4/ iru doo w @ 5> ===> w 4/dqg pW +n, @ pf +n, iru doo rwkhu l dqg n= Vxssrvh wkdw= [ M pf +n W , A j+nW ,= Wklv lpsolhv wkdw= [ M W f dqg wkxv O+p , @ O+p , 41 pf +nW , j+nW , . 4 Wr dyrlg d frqwudglfwlrq zh qhhg= [ pf +n, j+n,= M +;, iru doo n 5 V1 Xvlqj wkh ghqlwlrq ri V wkhuh fdq h{lvw qr sod|hu m 5 QqQ vxfk wkdw +n, A 3 iru vrph n 5 V xqohvv pf +n, @ 41 Wklv lpsolhv wkdw= [ [ pf +n, +n, +<, M . M . 5< iru doo n 5 V1 Xvlqj wkh ghqlwlrq ri V zh kdyh wkdw= [[ M M [[ pf +n, & 7 M M +n,= +43, & 7 Frpelqlqj +<, dqg +43, dqg xvlqj wkh vwdwhphqw ri wkh ohppd/ zh vhh wkdw= [[ M M pf +n, & 7 [[ M M +n, & 7 [ M j+n, & 7 Krzhyhu/ e| dvvxpswlrq= [ j+e n, A M pf +e n, dqg dovr e| dvvxpswlrq/ e n 5 V1 Wkxv/ wkhuh pxvw h{lvw dw ohdvw rqh n 5 V vxfk wkdw= j+n, ? [ M pf +n,= Wklv frqwudglfwv +;, dqg frpsohwhv wkh surri1 Zh lqwurgxfh vrph dgglwlrqdo qrwdwlrq1 Jlyhq uhdo qxpehu k ohw ekf ghqrwh wkh qhduhvw lqwhjhu ohvv wkdq ru htxdo wr k dqg gkh wkh qhduhvw lqwhjhu juhdwhu wkdq k +l1h1 e<=8f @ < dqg g<=8h @ 431 Dovr qrwh wkdw e<f @ < dqg g<h @ 43,1 Wkhruhp 4= Iru dq| vwudwhj| suroh @ + > ===> ? , wkhuh h{lvwv d d gh0 jhqhudwh vwudwhj| suroh p @ +p > ===> p? , vxfk wkdw= vxssruw+p , vxssruw+ , +44, iru doo l dqg= ) ? [ ' * +n, ? [ p +n, ' ' ? [ ' 63 ( +n, iru doo n 5 V1 Surri= Ghqrwh e| P W +, wkh vhw ri yhfwruv p @ +p > ===> p? , 5 P+, vxfk S S wkdw p +n, e +n,f iru doo n1 E| Ohppd 4 wklv vhw lv qrq0hpsw|1 Surylqj wkh Ohppd wkxv dprxqwv wr vkrzlqj wkdw wkhuh h{lvwv d yhfwru S S p 5 P W +, vxfk wkdw g +n,h p +n, iru doo v& 5 V1 Vxssrvh qrw1 Wkhq/ iru hyhu| yhfwru p 5 P W +, wkhuh h{lvwv vrph vwudwhj| n 5 V vxfk S S wkdw p +n, A g +n,h1 Iru dq| vwudwhj| suroh p 5 P W +, ghqh O+p, e|= O+p, & S G # ? [ [ 6 E& : S g j E& h ) p +n, ' ? [ *$ +n, 1 ' Zh qrwh wkdw O+p, lv dozd|v srvlwlyh dqg qlwh1 Slfn vwudwhj| suroh pf 5 P W +, zkhuh wkh ydoxh ri O+p, lv plqlpl}hg1 Zh qrwh wkdw pf frphv dv forvh dv dq| suroh wr vdwlvi|lqj wkh vwdwhphqw ri wkh Ohppd1 Ghqrwh e| e n d sxuh vwudwhj| vxfk wkdw= ) ? * ? [ [ f e p +n, A +e n, = ' ' Zh lqwurgxfh vhwv V | dqg Q | / w @ 3> 4> 5> ===/ zkhuh= n, @ 4j dqg iru w A 3 Q f @ il = pf +e dqg iru w A 3/ V | @ in = +n, A 3 iru vrph l 5 Q |3 j Q | @ il = pf +n, @ 4 iru vrph n 5 V | j1 W W W W Iru vrph wW / Q | @ Q | n Q dqg V | @ V | n V1 Wkh frqvwuxfwlrq ri V | dqg Q | lpso| wkdw iru dq| n W 5 V wkhuh pxvw h{lvw d vhw ri sod|huv 64 ilf > l > ===> l| j 5 Q vxfk wkdw= n, @ 4 dqg f +n , A 3/ pff +e pfo +no , @ 4 dqg o +non , A 3 iru doo u @ 4> ==> w 4/ pf| +n| , @ 4 dqg | +nW , A 3/ Vxssrvh wkhuh h{lvwv nW 5 V vxfk wkdw= ? [ pf +n W , ' ? [ +nW ,1 ' Jlyhq wkh fkdlq ri sod|huv ilf > l > ===> l| j 5 Q dv lqwurgxfhg deryh/ frqvlghu wkh yhfwru pW frqvwuxfwhg dv iroorzv= pWf +e n, @ 3 dqg pWf +n , @ 4/ pWo +no , @ 3 dqg pWo +non , @ 4 iru doo u @ 4> ===> w 4/ pW| +n| , @ 3 dqg pW| +nW , @ 4/ pW +n, @ pf +n, iru doo rwkhu n 5 V dqg l 5 Q1 Lw lv hdvlo| fkhfnhg wkdw wkh yhfwru pW 5 P+, ohdgv wr wkh ghvluhg frqwud0 glfwlrq jlyhq wkdw O+P W , @ O+pf , 41 Zh qrwh/ krzhyhu/ wkdw= ? [ [ M [[ pf +n, @ Q @ +n,= M ' & 7 Wkxv/ li= ? [ pf +e n, A ' ? [ +e n, ' wkhuh pxvw h{lvw vrph nW 5 V vxfk wkdw= ? [ ' p +n W , M & 7 [ M +nW , [ M ? [ ' jlylqj wkh ghvluhg frqwudglfwlrq1 65 +e n, +nW , Uhihuhqfhv ^4` Dxpdqq/ U1M1/ \1 Ndw}qhovrq/ U1 Udgqhu/ U1Z1 Urvhqwkdo/ dqg E1 Zhlvv +4<;6, Dssur{lpdwh sxulfdwlrq ri pl{hg vwudwhjlhv/ Pdwkh0 pdwlfv ri Rshudwlrqv Uhvhdufk ;/ 65:06741 ^5` Fduwzuljkw/ H1 dqg P1 Zrrghuv +5335, Vrfldo frqiruplw| lq duelwudu| jdphv zlwk lqfrpsohwh lqirupdwlrq/ Xqlyhuvlw| ri Zduzlfn Zrunlqj Sdshu qr1 9:51 ^6` Frqoh|/ M1 dqg P1K1 Zrrghuv +5334, Wlherxw hfrqrplfv zlwk glhuhq0 wldo jhqhwlf w|shv dqg hqgrjhqrxvo| fkrvhq furzglqj fkdudfwhulvwlfv/ Mrxuqdo ri Hfrqrplf Wkhru| <;= 59405<71 ^7` Frqoh|/ M1 dqg P1K1 Zrrghuv +4<<:, Htxlydohqfh ri wkh fruh dqg frp0 shwlwlyh htxloleulxp lq d Wlherxw hfrqrp| zlwk furzglqj w|shv/ Mrxu0 qdo ri Xuedq Hfrqrplfv 74 +4<<:, 75407731 ^8` Frqoh|/ lw| ri furzglqj fkrlfhv/ M1 dqg rswlpdo P1K1 Zrrghuv mxulvglfwlrqv w|shv Ulfkhufkh dqg lq +4<<9, d hqgrjhqrxv Hfrqrplfkh 83/ Wdvwh Wlherxw krprjhqh0 hfrqrp| hgxfdwlrqdo 69:06;:1 zlwk lqyhvwphqw Rq0olqh dw kwws=22zzz51zduzlfn1df1xn2idf2vrf2hfrqrplfv2vwd2idfxow|2zrrghuv21 ^9` Fulssv/ P1Z/ J1 Nhoohu/ dqg V1 Udg| +5335, Vwudwhjlf h{shulphq0 wdwlrq= Wkh fdvh ri srlvvrq edqglwv/ Pd| 5335 FHV Zrunlqj Sdshu &:6:1 ^:` Jolfnvehuj/ L1 +4<85, D ixuwkhu jhqhudol}dwlrq ri wkh Ndnxwdql Il{hg Srlqw Wkhruhp/ zlwk dssolfdwlrq wr Qdvk htxloleulxp srlqwv/ Surfhhg0 lqjv ri wkh Dphulfdq Pdwkhpdwlfdo Vrflhw|/ 6= 4:304:7/ 66 ^;` Juhhq/ H1M1 +4<;7, Frqwlqxxp dqg qlwh0sod|hu qrqfrrshudwlyh prg0 hov ri frpshwlwlrq/ Hfrqrphwulfd yro185/ qr1 7= <:80<<61 ^<` Juhhq/ M1 dqg Z1S1 Khoohu +4<<4, Pdwkhpdwlfdo dqdo|vlv dqg frqyh{0 lw| zlwk dssolfdwlrqv wr hfrqrplfv/ lq Kdqgerrn ri Pdwkhpdwlfdo Hfr0 qrplfv/ Yro14/ N1M1 Duurz dqg Z1 Lqwuloljdwru/ hgv1 Qruwk Kroodqg= Dpvwhugdp/ Qhz \run/ R{irug1 ^43` Jurvv/ U1 +4<<9, Sv|fkrorj|1 Wkh Vflhqfh ri Plqg dqg Ehkdylrxu/ Krg0 ghu dqg Vwrxjkwrq1 ^44` Kduvdq|l/ M1F1 +4<:6, Jdphv zlwk udqgrpo| glvwxuehg sd|rv= d qhz udwlrqdoh iru pl{hg vwudwhj| htxloleulxp srlqwv/ Lqwhuqdwlrqdo Mrxuqdo ri Jdph Wkhru| 5= 40561 ^45` Ndodl/ H1 +5335, H{0srvw vwdelolw| lq odujh jdphv/ Qruwkzhvwhuq Xql0 yhuvlw| Glvfxvvlrq Sdshu 46841 ^46` Nkdq/ D1 +4<;<, Rq Frxuqrw0Qdvk htxloleulxp glvwulexwlrqv iru jdphv zlwk d qrqphwul}deoh dfwlrq vsdfh dqg xsshu vhpl frqwlqxrxv sd|rv/ Wudqvdfwlrqv ri wkh Dphulfdq Pdwkhpdwlfdo vrflhw| 5<6= :6:0:7<1 ^47` Nkdq/ D1 dqg \1 Vxq +5335, Qrqfrrshudwlyh jdphv zlwk pdq| sod|0 huv/ Kdqgerrn ri Jdph Wkhru|/ U1 Dxpdq dqg V1 Kduw/ hgv1 Qruwk Kroodqg1 ^48` Nkdq/ D1 dqg \1 Vxq +4<<<, Qrq0frrshudwlyh jdphv rq k|shuqlwh Orhe vsdfhv/ Mrxuqdo ri Pdwkhpdwlfdo Hfrqrplfv 64/ 78807<51 ^49` Nkdq/ D1/ N1S1 Udwk dqg \1Q1 Vxq +4<<:, Rq wkh h{lvwhqfh ri sxuh vwudwhj| htxloleuld zlwk d frqwlqxxp ri sod|huv/ Mrxuqdo ri Hfrqrplf Wkhru| :9=460791 67 ^4:` Pdv0Frohoo/ D1 +4<;7, Rq d wkhruhp ri Vfkphlgohu/ Mrxuqdo ri Pdwk0 hpdwlfdo Hfrqrplfv 46= 53905431 ^4;` Rhupdq/ W1/ M1 Srwwhuv dqg M1 Vrqqhpdqv/ 5335/ Lplwdwlrq dqg eholhi ohduqlqj lq dq roljrsro| h{shulphqw/ Uhylhz ri Hfrqrplf Vwxglhv/ 9<= <:60<<:1 ^4<` Sdvfrd/ P1 +4<<;, Qdvk htxloleulxp dqg wkh odz ri odujh qxpehuv/ Lqwhuqdwlrqdo Mrxuqdo ri Jdph Wkhru| 5:= ;60<51 ^53` Sdvfrd/ P1 +4<<6d, Dssur{lpdwh htxoleulxp lq sxuh vwudwhjlhv iru qrqdwrplf jdphv/ Mrxuqdo ri Pdwkhpdwlfdo Hfrqrplfv 55= 55605741 ^54` Sdvfrd/ P1 +4<<6e, Qrqfrrshudwlyh htxloleulxp dqg Fkdpehuolqldq prqrsrolvwlf frpshwlwlrq/ Mrxuqdo ri Hfrqrplf Wkhru|/ 9<= 66806861 ^55` Udgqhu/ U dqg U1Z1 Urvhqwkdo +4<;5, Sulydwh lqirupdwlrq dqg sxuh0 vwudwhj| htxloleuld/ Pdwkhpdwlfv ri Rshudwlrqv Uhvhdufk := 734073< ^56` Udvklg/ V1 +4<;6, Htxloleulxp srlqwv ri qrqdwrplf jdphv> Dv|pswrwlf uhvxowv/ Hfrqrplfv Ohwwhuv 45= :0431 ^57` Udwk/ N1S1/ \1 Vxq/ V1 \dpdvkljh +4<<8, Wkh qrqh{lvwhqfh ri v|p0 phwulf htxloleuld lq dqrq|prxv jdphv zlwk frpsdfw dfwlrq vsdfhv/ Mrxuqdo ri Pdwkhpdwlfdo Hfrqrplfv 57= 66406791 ^58` Urvhqwkdo/ U1Z +4<:6, D fodvv ri jdphv srvvhvvlqj sxuh0vwudwhj| Qdvk htxloleuld/ Lqwhuqdwlrqdo Mrxuqdo ri Jdph Wkhru|/ 5=989:/ 4<:61 ^59` Vfkphlgohu/ G1 +4<:6, Htxloleulxp srlqwv ri qrqdwrplf jdphv/ Mrxu0 qdo ri Vwdwlvwlfdo Sk|vlfv := 5<806331 68 ^5:` Zrrghuv/ P1/ H1 Fduwzuljkw dqg U1 Vhowhq +5334, Vrfldo frqiruplw| dqg vrfldo frqiruplw| lq jdphv zlwk pdq| sod|huv/ Xqlyhuvlw| ri Zdu0 zlfn Ghsduwphqw ri Hfrqrplfv Zrunlqj Sdshu 8;< +uhylvhg dv 969,1 69 NOTE DI LAVORO DELLA FONDAZIONE ENI ENRICO MATTEI Fondazione Eni Enrico Mattei Working Paper Series Our working papers are available on the Internet at the following addresses: http://www.feem.it/Feem/Pub/Publications/WPapers/default.html http://papers.ssrn.com SUST 1.2002 ETA 2.2002 WAT 3.2002 CLIM 4.2002 VOL CLIM 5.2002 6.2002 ETA 7.2002 KNOW 8.2002 NRM KNOW 9.2002 10.2002 ETA 11.2002 KNOW 12.2002 NRM CLIM CLIM 13.2002 14.2002 15.2002 CLIM ETA 16.2002 17.2002 Coalition Theory Network Coalition Theory Network Coalition Theory Network NRM 18.2002 CLIM 22.2002 CLIM 23.2002 ETA CLIM 24.2002 25.2002 ETA 26.2002 SUST 27.2002 SUST KNOW ETA 28.2002 29.2002 30.2002 19.2002 K. TANO, M.D. FAMINOW, M. KAMUANGA and B. SWALLOW: Using Conjoint Analysis to Estimate Farmers’ Preferences for Cattle Traits in West Africa Efrem CASTELNUOVO and Paolo SURICO: What Does Monetary Policy Reveal about Central Bank’s Preferences? Duncan KNOWLER and Edward BARBIER: The Economics of a “Mixed Blessing” Effect: A Case Study of the Black Sea Andreas LöSCHEL: Technological Change in Economic Models of Environmental Policy: A Survey Carlo CARRARO and Carmen MARCHIORI: Stable Coalitions Marzio GALEOTTI, Alessandro LANZA and Matteo MANERA: Rockets and Feathers Revisited: An International Comparison on European Gasoline Markets Effrosyni DIAMANTOUDI and Eftichios S. SARTZETAKIS: Stable International Environmental Agreements: An Analytical Approach Alain DESDOIGTS: Neoclassical Convergence Versus Technological Catch-up: A Contribution for Reaching a Consensus Giuseppe DI VITA: Renewable Resources and Waste Recycling Giorgio BRUNELLO: Is Training More Frequent when Wage Compression is Higher? Evidence from 11 European Countries Mordecai KURZ, Hehui JIN and Maurizio MOTOLESE: Endogenous Fluctuations and the Role of Monetary Policy Reyer GERLAGH and Marjan W. HOFKES: Escaping Lock-in: The Scope for a Transition towards Sustainable Growth? Michele MORETTO and Paolo ROSATO: The Use of Common Property Resources: A Dynamic Model Philippe QUIRION: Macroeconomic Effects of an Energy Saving Policy in the Public Sector Roberto ROSON: Dynamic and Distributional Effects of Environmental Revenue Recycling Schemes: Simulations with a General Equilibrium Model of the Italian Economy Francesco RICCI (l): Environmental Policy Growth when Inputs are Differentiated in Pollution Intensity Alberto PETRUCCI: Devaluation (Levels versus Rates) and Balance of Payments in a Cash-in-Advance Economy László Á. KÓCZY (liv): The Core in the Presence of Externalities Steven J. BRAMS, Michael A. JONES and D. Marc KILGOUR (liv): Single-Peakedness and Disconnected Coalitions 20.2002 Guillaume HAERINGER (liv): On the Stability of Cooperation Structures 21.2002 Fausto CAVALLARO and Luigi CIRAOLO: Economic and Environmental Sustainability: A Dynamic Approach in Insular Systems Barbara BUCHNER, Carlo CARRARO, Igor CERSOSIMO and Carmen MARCHIORI: Back to Kyoto? US Participation and the Linkage between R&D and Climate Cooperation Andreas LÖSCHEL and ZhongXIANG ZHANG: The Economic and Environmental Implications of the US Repudiation of the Kyoto Protocol and the Subsequent Deals in Bonn and Marrakech Marzio GALEOTTI, Louis J. MACCINI and Fabio SCHIANTARELLI: Inventories, Employment and Hours Hannes EGLI: Are Cross-Country Studies of the Environmental Kuznets Curve Misleading? New Evidence from Time Series Data for Germany Adam B. JAFFE, Richard G. NEWELL and Robert N. STAVINS: Environmental Policy and Technological Change Joseph C. COOPER and Giovanni SIGNORELLO: Farmer Premiums for the Voluntary Adoption of Conservation Plans The ANSEA Network: Towards An Analytical Strategic Environmental Assessment Paolo SURICO: Geographic Concentration and Increasing Returns: a Survey of Evidence Robert N. STAVINS: Lessons from the American Experiment with Market-Based Environmental Policies NRM 31.2002 NRM KNOW 32.2002 33.2002 KNOW 34.2002 CLIM 35.2002 CLIM CLIM CLIM SUST 36.2002 37.2002 38.2002 39.2002 NRM 40.2002 NRM 41.2002 CLIM CLIM 42.2002 43.2002 CLIM 44.2002 ETA 45.2002 ETA SUST SUST KNOW Coalition Theory Network Coalition Theory Network ETA ETA 46.2002 47.2002 48.2002 49.2002 50.2002 Carlo GIUPPONI and Paolo ROSATO: Multi-Criteria Analysis and Decision-Support for Water Management at the Catchment Scale: An Application to Diffuse Pollution Control in the Venice Lagoon Robert N. STAVINS: National Environmental Policy During the Clinton Years A. SOUBEYRAN and H. STAHN : Do Investments in Specialized Knowledge Lead to Composite Good Industries? G. BRUNELLO, M.L. PARISI and Daniela SONEDDA: Labor Taxes, Wage Setting and the Relative Wage Effect C. BOEMARE and P. QUIRION (lv): Implementing Greenhouse Gas Trading in Europe: Lessons from Economic Theory and International Experiences T.TIETENBERG (lv): The Tradable Permits Approach to Protecting the Commons: What Have We Learned? K. REHDANZ and R.J.S. TOL (lv): On National and International Trade in Greenhouse Gas Emission Permits C. FISCHER (lv): Multinational Taxation and International Emissions Trading G. SIGNORELLO and G. PAPPALARDO: Farm Animal Biodiversity Conservation Activities in Europe under the Framework of Agenda 2000 S .M. CAVANAGH, W. M. HANEMANN and R. N. STAVINS: Muffled Price Signals: Household Water Demand under Increasing-Block Prices A. J. PLANTINGA, R. N. LUBOWSKI and R. N. STAVINS: The Effects of Potential Land Development on Agricultural Land Prices C. OHL (lvi): Inducing Environmental Co-operation by the Design of Emission Permits J. EYCKMANS, D. VAN REGEMORTER and V. VAN STEENBERGHE (lvi): Is Kyoto Fatally Flawed? An Analysis with MacGEM A. ANTOCI and S. BORGHESI (lvi): Working Too Much in a Polluted World: A North-South Evolutionary Model P. G. FREDRIKSSON, Johan A. LIST and Daniel MILLIMET (lvi): Chasing the Smokestack: Strategic Policymaking with Multiple Instruments Z. YU (lvi): A Theory of Strategic Vertical DFI and the Missing Pollution-Haven Effect Y. H. FARZIN: Can an Exhaustible Resource Economy Be Sustainable? Y. H. FARZIN: Sustainability and Hamiltonian Value C. PIGA and M. VIVARELLI: Cooperation in R&D and Sample Selection M. SERTEL and A. SLINKO (liv): Ranking Committees, Words or Multisets 51.2002 Sergio CURRARINI (liv): Stable Organizations with Externalities 52.2002 53.2002 CLIM ETA 54.2002 55.2002 SUST SUST 56.2002 57.2002 SUST SUST 58.2002 59.2002 VOL 60.2002 ETA 61.2002 PRIV PRIV 62.2002 63.2002 PRIV 64.2002 SUST 65.2002 ETA PRIV 66.2002 67.2002 CLIM CLIM SUST 68.2002 69.2002 70.2002 SUST 71.2002 Robert N. STAVINS: Experience with Market-Based Policy Instruments C.C. JAEGER, M. LEIMBACH, C. CARRARO, K. HASSELMANN, J.C. HOURCADE, A. KEELER and R. KLEIN (liii): Integrated Assessment Modeling: Modules for Cooperation Scott BARRETT (liii): Towards a Better Climate Treaty Richard G. NEWELL and Robert N. STAVINS: Cost Heterogeneity and the Potential Savings from MarketBased Policies Paolo ROSATO and Edi DEFRANCESCO: Individual Travel Cost Method and Flow Fixed Costs Vladimir KOTOV and Elena NIKITINA (lvii): Reorganisation of Environmental Policy in Russia: The Decade of Success and Failures in Implementation of Perspective Quests Vladimir KOTOV (lvii): Policy in Transition: New Framework for Russia’s Climate Policy Fanny MISSFELDT and Arturo VILLAVICENCO (lvii): How Can Economies in Transition Pursue Emissions Trading or Joint Implementation? Giovanni DI BARTOLOMEO, Jacob ENGWERDA, Joseph PLASMANS and Bas VAN AARLE: Staying Together or Breaking Apart: Policy-Makers’ Endogenous Coalitions Formation in the European Economic and Monetary Union Robert N. STAVINS, Alexander F.WAGNER and Gernot WAGNER: Interpreting Sustainability in Economic Terms: Dynamic Efficiency Plus Intergenerational Equity Carlo CAPUANO: Demand Growth, Entry and Collusion Sustainability Federico MUNARI and Raffaele ORIANI: Privatization and R&D Performance: An Empirical Analysis Based on Tobin’s Q Federico MUNARI and Maurizio SOBRERO: The Effects of Privatization on R&D Investments and Patent Productivity Orley ASHENFELTER and Michael GREENSTONE: Using Mandated Speed Limits to Measure the Value of a Statistical Life Paolo SURICO: US Monetary Policy Rules: the Case for Asymmetric Preferences Rinaldo BRAU and Massimo FLORIO: Privatisations as Price Reforms: Evaluating Consumers’ Welfare Changes in the U.K. Barbara K. BUCHNER and Roberto ROSON: Conflicting Perspectives in Trade and Environmental Negotiations Philippe QUIRION: Complying with the Kyoto Protocol under Uncertainty: Taxes or Tradable Permits? Anna ALBERINI, Patrizia RIGANTI and Alberto LONGO: Can People Value the Aesthetic and Use Services of Urban Sites? Evidence from a Survey of Belfast Residents Marco PERCOCO: Discounting Environmental Effects in Project Appraisal NRM 72.2002 PRIV 73.2002 PRIV PRIV 74.2002 75.2002 PRIV 76.2002 PRIV PRIV 77.2002 78.2002 PRIV 79.2002 PRIV 80.2002 CLIM 81.2002 PRIV 82.2002 PRIV 83.2002 NRM 84.2002 CLIM 85.2002 CLIM ETA ETA ETA 86.2002 87.2002 88.2002 89.2002 ETA ETA CLIM ETA 90.2002 91.2002 92.2002 93.2002 VOL 94.2002 CLIM 95.2002 CLIM KNOW 96.2002 97.2002 ETA 98.2002 ETA ETA 99.2002 100.2002 ETA VOL ETA 101.2002 102.2002 103.2002 ETA 104.2002 PRIV 105.2002 ETA PRIV 106.2002 107.2002 PRIV 108.2002 PRIV 109.2002 PRIV PRIV 110.2002 111.2002 Philippe BONTEMS and Pascal FAVARD: Input Use and Capacity Constraint under Uncertainty: The Case of Irrigation Mohammed OMRAN: The Performance of State-Owned Enterprises and Newly Privatized Firms: Empirical Evidence from Egypt Mike BURKART, Fausto PANUNZI and Andrei SHLEIFER: Family Firms Emmanuelle AURIOL, Pierre M. PICARD: Privatizations in Developing Countries and the Government Budget Constraint Nichole M. CASTATER: Privatization as a Means to Societal Transformation: An Empirical Study of Privatization in Central and Eastern Europe and the Former Soviet Union Christoph LÜLSFESMANN: Benevolent Government, Managerial Incentives, and the Virtues of Privatization Kate BISHOP, Igor FILATOTCHEV and Tomasz MICKIEWICZ: Endogenous Ownership Structure: Factors Affecting the Post-Privatisation Equity in Largest Hungarian Firms Theodora WELCH and Rick MOLZ: How Does Trade Sale Privatization Work? Evidence from the Fixed-Line Telecommunications Sector in Developing Economies Alberto R. PETRUCCI: Government Debt, Agent Heterogeneity and Wealth Displacement in a Small Open Economy Timothy SWANSON and Robin MASON (lvi): The Impact of International Environmental Agreements: The Case of the Montreal Protocol George R.G. CLARKE and Lixin Colin XU: Privatization, Competition and Corruption: How Characteristics of Bribe Takers and Payers Affect Bribe Payments to Utilities Massimo FLORIO and Katiuscia MANZONI: The Abnormal Returns of UK Privatisations: From Underpricing to Outperformance Nelson LOURENÇO, Carlos RUSSO MACHADO, Maria do ROSÁRIO JORGE and Luís RODRIGUES: An Integrated Approach to Understand Territory Dynamics. The Coastal Alentejo (Portugal) Peter ZAPFEL and Matti VAINIO (lv): Pathways to European Greenhouse Gas Emissions Trading History and Misconceptions Pierre COURTOIS: Influence Processes in Climate Change Negotiations: Modelling the Rounds Vito FRAGNELLI and Maria Erminia MARINA (lviii): Environmental Pollution Risk and Insurance Laurent FRANCKX (lviii): Environmental Enforcement with Endogenous Ambient Monitoring Timo GOESCHL and Timothy M. SWANSON (lviii): Lost Horizons. The noncooperative management of an evolutionary biological system. Hans KEIDING (lviii): Environmental Effects of Consumption: An Approach Using DEA and Cost Sharing Wietze LISE (lviii): A Game Model of People’s Participation in Forest Management in Northern India Jens HORBACH: Structural Change and Environmental Kuznets Curves Martin P. GROSSKOPF: Towards a More Appropriate Method for Determining the Optimal Scale of Production Units Scott BARRETT and Robert STAVINS: Increasing Participation and Compliance in International Climate Change Agreements Banu BAYRAMOGLU LISE and Wietze LISE: Climate Change, Environmental NGOs and Public Awareness in the Netherlands: Perceptions and Reality Matthieu GLACHANT: The Political Economy of Emission Tax Design in Environmental Policy Kenn ARIGA and Giorgio BRUNELLO: Are the More Educated Receiving More Training? Evidence from Thailand Gianfranco FORTE and Matteo MANERA: Forecasting Volatility in European Stock Markets with Non-linear GARCH Models Geoffrey HEAL: Bundling Biodiversity Geoffrey HEAL, Brian WALKER, Simon LEVIN, Kenneth ARROW, Partha DASGUPTA, Gretchen DAILY, Paul EHRLICH, Karl-Goran MALER, Nils KAUTSKY, Jane LUBCHENCO, Steve SCHNEIDER and David STARRETT: Genetic Diversity and Interdependent Crop Choices in Agriculture Geoffrey HEAL: Biodiversity and Globalization Andreas LANGE: Heterogeneous International Agreements – If per capita emission levels matter Pierre-André JOUVET and Walid OUESLATI: Tax Reform and Public Spending Trade-offs in an Endogenous Growth Model with Environmental Externality Anna BOTTASSO and Alessandro SEMBENELLI: Does Ownership Affect Firms’ Efficiency? Panel Data Evidence on Italy Bernardo BORTOLOTTI, Frank DE JONG, Giovanna NICODANO and Ibolya SCHINDELE: Privatization and Stock Market Liquidity Haruo IMAI and Mayumi HORIE (lviii): Pre-Negotiation for an International Emission Reduction Game Sudeshna GHOSH BANERJEE and Michael C. MUNGER: Move to Markets? An Empirical Analysis of Privatisation in Developing Countries Guillaume GIRMENS and Michel GUILLARD: Privatization and Investment: Crowding-Out Effect vs Financial Diversification Alberto CHONG and Florencio LÓPEZ-DE-SILANES: Privatization and Labor Force Restructuring Around the World Nandini GUPTA: Partial Privatization and Firm Performance François DEGEORGE, Dirk JENTER, Alberto MOEL and Peter TUFANO: Selling Company Shares to Reluctant Employees: France Telecom’s Experience PRIV 112.2002 PRIV PRIV PRIV PRIV 113.2002 114.2002 115.2002 116.2002 PRIV 1.2003 PRIV PRIV 2.2003 3.2003 CLIM 4.2003 KNOW ETA SIEV 5.2003 6.2003 7.2003 NRM CLIM 8.2003 9.2003 KNOW CLIM 10.2003 11.2003 KNOW 12.2003 KNOW 13.2003 KNOW 14.2003 KNOW 15.2003 KNOW 16.2003 KNOW KNOW Coalition Theory Network PRIV PRIV 17.2003 18.2003 19.2003 20.2003 21.2003 PRIV 22.2003 PRIV PRIV PRIV 23.2003 24.2003 25.2003 PRIV PRIV PRIV 26.2003 27.2003 28.2003 PRIV PRIV ETA 29.2003 30.2003 31.2003 KNOW PRIV KNOW 32.2003 33.2003 34.2003 ETA 35.2003 GG PRIV 36.2003 37.2003 CLIM 38.2003 Isaac OTCHERE: Intra-Industry Effects of Privatization Announcements: Evidence from Developed and Developing Countries Yannis KATSOULAKOS and Elissavet LIKOYANNI: Fiscal and Other Macroeconomic Effects of Privatization Guillaume GIRMENS: Privatization, International Asset Trade and Financial Markets D. Teja FLOTHO: A Note on Consumption Correlations and European Financial Integration Ibolya SCHINDELE and Enrico C. PEROTTI: Pricing Initial Public Offerings in Premature Capital Markets: The Case of Hungary Gabriella CHIESA and Giovanna NICODANO: Privatization and Financial Market Development: Theoretical Issues Ibolya SCHINDELE: Theory of Privatization in Eastern Europe: Literature Review Wietze LISE, Claudia KEMFERT and Richard S.J. TOL: Strategic Action in the Liberalised German Electricity Market Laura MARSILIANI and Thomas I. RENSTRÖM: Environmental Policy and Capital Movements: The Role of Government Commitment Reyer GERLAGH: Induced Technological Change under Technological Competition Efrem CASTELNUOVO: Squeezing the Interest Rate Smoothing Weight with a Hybrid Expectations Model Anna ALBERINI, Alberto LONGO, Stefania TONIN, Francesco TROMBETTA and Margherita TURVANI: The Role of Liability, Regulation and Economic Incentives in Brownfield Remediation and Redevelopment: Evidence from Surveys of Developers Elissaios PAPYRAKIS and Reyer GERLAGH: Natural Resources: A Blessing or a Curse? A. CAPARRÓS, J.-C. PEREAU and T. TAZDAÏT: North-South Climate Change Negotiations: a Sequential Game with Asymmetric Information Giorgio BRUNELLO and Daniele CHECCHI: School Quality and Family Background in Italy Efrem CASTELNUOVO and Marzio GALEOTTI: Learning By Doing vs Learning By Researching in a Model of Climate Change Policy Analysis Carole MAIGNAN, Gianmarco OTTAVIANO and Dino PINELLI (eds.): Economic Growth, Innovation, Cultural Diversity: What are we all talking about? A critical survey of the state-of-the-art Carole MAIGNAN, Gianmarco OTTAVIANO, Dino PINELLI and Francesco RULLANI (lix): Bio-Ecological Diversity vs. Socio-Economic Diversity. A Comparison of Existing Measures Maddy JANSSENS and Chris STEYAERT (lix): Theories of Diversity within Organisation Studies: Debates and Future Trajectories Tuzin BAYCAN LEVENT, Enno MASUREL and Peter NIJKAMP (lix): Diversity in Entrepreneurship: Ethnic and Female Roles in Urban Economic Life Alexandra BITUSIKOVA (lix): Post-Communist City on its Way from Grey to Colourful: The Case Study from Slovakia Billy E. VAUGHN and Katarina MLEKOV (lix): A Stage Model of Developing an Inclusive Community Selma van LONDEN and Arie de RUIJTER (lix): Managing Diversity in a Glocalizing World Sergio CURRARINI: On the Stability of Hierarchies in Games with Externalities Giacomo CALZOLARI and Alessandro PAVAN (lx): Monopoly with Resale Claudio MEZZETTI (lx): Auction Design with Interdependent Valuations: The Generalized Revelation Principle, Efficiency, Full Surplus Extraction and Information Acquisition Marco LiCalzi and Alessandro PAVAN (lx): Tilting the Supply Schedule to Enhance Competition in UniformPrice Auctions David ETTINGER (lx): Bidding among Friends and Enemies Hannu VARTIAINEN (lx): Auction Design without Commitment Matti KELOHARJU, Kjell G. NYBORG and Kristian RYDQVIST (lx): Strategic Behavior and Underpricing in Uniform Price Auctions: Evidence from Finnish Treasury Auctions Christine A. PARLOUR and Uday RAJAN (lx): Rationing in IPOs Kjell G. NYBORG and Ilya A. STREBULAEV (lx): Multiple Unit Auctions and Short Squeezes Anders LUNANDER and Jan-Eric NILSSON (lx): Taking the Lab to the Field: Experimental Tests of Alternative Mechanisms to Procure Multiple Contracts TangaMcDANIEL and Karsten NEUHOFF (lx): Use of Long-term Auctions for Network Investment Emiel MAASLAND and Sander ONDERSTAL (lx): Auctions with Financial Externalities Michael FINUS and Bianca RUNDSHAGEN: A Non-cooperative Foundation of Core-Stability in Positive Externality NTU-Coalition Games Michele MORETTO: Competition and Irreversible Investments under Uncertainty_ Philippe QUIRION: Relative Quotas: Correct Answer to Uncertainty or Case of Regulatory Capture? Giuseppe MEDA, Claudio PIGA and Donald SIEGEL: On the Relationship between R&D and Productivity: A Treatment Effect Analysis Alessandra DEL BOCA, Marzio GALEOTTI and Paola ROTA: Non-convexities in the Adjustment of Different Capital Inputs: A Firm-level Investigation Matthieu GLACHANT: Voluntary Agreements under Endogenous Legislative Threats Narjess BOUBAKRI, Jean-Claude COSSET and Omrane GUEDHAMI: Postprivatization Corporate Governance: the Role of Ownership Structure and Investor Protection Rolf GOLOMBEK and Michael HOEL: Climate Policy under Technology Spillovers KNOW CTN KNOW KNOW 39.2003 40.2003 41.2003 42.2003 ETA 43.2003 CLIM 44.2003 PRIV SIEV 45.2003 46.2003 ETA 47.2003 CLIM 48.2003 CLIM 49.2003 CTN 50.2003 CTN CTN CTN CTN CTN CTN CTN 51.2003 52.2003 53.2003 54.2003 55.2003 56.2003 57.2003 KNOW 58.2003 KNOW ETA CLIM 59.2003 60.2003 61.2003 GG 62.2003 SIEV CLIM 63.2003 64.2003 SIEV SIEV SIEV 65.2003 66.2003 67.2003 CLIM 68.2003 KNOW KNOW KNOW KNOW 69.2003 70.2003 71.2003 72.2003 KNOW 73.2003 KNOW KNOW 74.2003 75.2003 KNOW KNOW KNOW 76.2003 77.2003 78.2003 KNOW 79.2003 ETA 80.2003 IEM 81.2003 CLIM 82.2003 Slim BEN YOUSSEF: Transboundary Pollution, R&D Spillovers and International Trade Carlo CARRARO and Carmen MARCHIORI: Endogenous Strategic Issue Linkage in International Negotiations Sonia OREFFICE: Abortion and Female Power in the Household: Evidence from Labor Supply Timo GOESCHL and Timothy SWANSON: On Biology and Technology: The Economics of Managing Biotechnologies Giorgio BUSETTI and Matteo MANERA: STAR-GARCH Models for Stock Market Interactions in the Pacific Basin Region, Japan and US Katrin MILLOCK and Céline NAUGES: The French Tax on Air Pollution: Some Preliminary Results on its Effectiveness Bernardo BORTOLOTTI and Paolo PINOTTI: The Political Economy of Privatization Elbert DIJKGRAAF and Herman R.J. VOLLEBERGH: Burn or Bury? A Social Cost Comparison of Final Waste Disposal Methods Jens HORBACH: Employment and Innovations in the Environmental Sector: Determinants and Econometrical Results for Germany Lori SNYDER, Nolan MILLER and Robert STAVINS: The Effects of Environmental Regulation on Technology Diffusion: The Case of Chlorine Manufacturing Lori SNYDER, Robert STAVINS and Alexander F. WAGNER: Private Options to Use Public Goods. Exploiting Revealed Preferences to Estimate Environmental Benefits László Á. KÓCZY and Luc LAUWERS (lxi): The Minimal Dominant Set is a Non-Empty Core-Extension Matthew O. JACKSON (lxi):Allocation Rules for Network Games Ana MAULEON and Vincent VANNETELBOSCH (lxi): Farsightedness and Cautiousness in Coalition Formation Fernando VEGA-REDONDO (lxi): Building Up Social Capital in a Changing World: a network approach Matthew HAAG and Roger LAGUNOFF (lxi): On the Size and Structure of Group Cooperation Taiji FURUSAWA and Hideo KONISHI (lxi): Free Trade Networks Halis Murat YILDIZ (lxi): National Versus International Mergers and Trade Liberalization Santiago RUBIO and Alistair ULPH (lxi): An Infinite-Horizon Model of Dynamic Membership of International Environmental Agreements Carole MAIGNAN, Dino PINELLI and Gianmarco I.P. OTTAVIANO: ICT, Clusters and Regional Cohesion: A Summary of Theoretical and Empirical Research Giorgio BELLETTINI and Gianmarco I.P. OTTAVIANO: Special Interests and Technological Change Ronnie SCHÖB: The Double Dividend Hypothesis of Environmental Taxes: A Survey Michael FINUS, Ekko van IERLAND and Robert DELLINK: Stability of Climate Coalitions in a Cartel Formation Game Michael FINUS and Bianca RUNDSHAGEN: How the Rules of Coalition Formation Affect Stability of International Environmental Agreements Alberto PETRUCCI: Taxing Land Rent in an Open Economy Joseph E. ALDY, Scott BARRETT and Robert N. STAVINS: Thirteen Plus One: A Comparison of Global Climate Policy Architectures Edi DEFRANCESCO: The Beginning of Organic Fish Farming in Italy Klaus CONRAD: Price Competition and Product Differentiation when Consumers Care for the Environment Paulo A.L.D. NUNES, Luca ROSSETTO, Arianne DE BLAEIJ: Monetary Value Assessment of Clam Fishing Management Practices in the Venice Lagoon: Results from a Stated Choice Exercise ZhongXiang ZHANG: Open Trade with the U.S. Without Compromising Canada’s Ability to Comply with its Kyoto Target David FRANTZ (lix): Lorenzo Market between Diversity and Mutation Ercole SORI (lix): Mapping Diversity in Social History Ljiljana DERU SIMIC (lxii): What is Specific about Art/Cultural Projects? Natalya V. TARANOVA (lxii):The Role of the City in Fostering Intergroup Communication in a Multicultural Environment: Saint-Petersburg’s Case Kristine CRANE (lxii): The City as an Arena for the Expression of Multiple Identities in the Age of Globalisation and Migration Kazuma MATOBA (lxii): Glocal Dialogue- Transformation through Transcultural Communication Catarina REIS OLIVEIRA (lxii): Immigrants’ Entrepreneurial Opportunities: The Case of the Chinese in Portugal Sandra WALLMAN (lxii): The Diversity of Diversity - towards a typology of urban systems Richard PEARCE (lxii): A Biologist’s View of Individual Cultural Identity for the Study of Cities Vincent MERK (lxii): Communication Across Cultures: from Cultural Awareness to Reconciliation of the Dilemmas Giorgio BELLETTINI, Carlotta BERTI CERONI and Gianmarco I.P.OTTAVIANO: Child Labor and Resistance to Change Michele MORETTO, Paolo M. PANTEGHINI and Carlo SCARPA: Investment Size and Firm’s Value under Profit Sharing Regulation Alessandro LANZA, Matteo MANERA and Massimo GIOVANNINI: Oil and Product Dynamics in International Petroleum Markets Y. Hossein FARZIN and Jinhua ZHAO: Pollution Abatement Investment When Firms Lobby Against Environmental Regulation CLIM CLIM NRM 83.2003 84.2003 85.2003 KNOW 86.2003 SIEV 87.2003 CLIM 88.2003 CLIM CLIM CLIM IEM 89.2003 90.2003 91.2003 92.2003 ETA CTN IEM 93.2003 94.2003 95.2003 IEM 96.2003 CTN 97.2003 KNOW 98.2003 KNOW KNOW KNOW KNOW 99.2003 100.2003 101.2003 102.2003 CLIM CLIM 103.2003 104.2003 CLIM NRM NRM SIEV SIEV 105.2003 106.2003 107.2003 108.2003 109.2003 NRM NRM ETA CTN 110.2003 111.2003 112.2003 113.2003 CTN CTN CTN CTN CTN CTN 114.2003 115.2003 116.2003 117.2003 118.2003 119.2003 CTN CTN 120.2003 121.2003 CTN 122.2003 1000 Giuseppe DI VITA: Is the Discount Rate Relevant in Explaining the Environmental Kuznets Curve? Reyer GERLAGH and Wietze LISE: Induced Technological Change Under Carbon Taxes Rinaldo BRAU, Alessandro LANZA and Francesco PIGLIARU: How Fast are the Tourism Countries Growing? The cross-country evidence Elena BELLINI, Gianmarco I.P. OTTAVIANO and Dino PINELLI: The ICT Revolution: opportunities and risks for the Mezzogiorno Lucas BRETSCGHER and Sjak SMULDERS: Sustainability and Substitution of Exhaustible Natural Resources. How resource prices affect long-term R&D investments Johan EYCKMANS and Michael FINUS: New Roads to International Environmental Agreements: The Case of Global Warming Marzio GALEOTTI: Economic Development and Environmental Protection Marzio GALEOTTI: Environment and Economic Growth: Is Technical Change the Key to Decoupling? Marzio GALEOTTI and Barbara BUCHNER: Climate Policy and Economic Growth in Developing Countries A. MARKANDYA, A. GOLUB and E. STRUKOVA: The Influence of Climate Change Considerations on Energy Policy: The Case of Russia Andrea BELTRATTI: Socially Responsible Investment in General Equilibrium Parkash CHANDER: The γ-Core and Coalition Formation Matteo MANERA and Angelo MARZULLO: Modelling the Load Curve of Aggregate Electricity Consumption Using Principal Components Alessandro LANZA, Matteo MANERA, Margherita GRASSO and Massimo GIOVANNINI: Long-run Models of Oil Stock Prices Steven J. BRAMS, Michael A. JONES, and D. Marc KILGOUR: Forming Stable Coalitions: The Process Matters John CROWLEY, Marie-Cecile NAVES (lxiii): Anti-Racist Policies in France. From Ideological and Historical Schemes to Socio-Political Realities Richard THOMPSON FORD (lxiii): Cultural Rights and Civic Virtue Alaknanda PATEL (lxiii): Cultural Diversity and Conflict in Multicultural Cities David MAY (lxiii): The Struggle of Becoming Established in a Deprived Inner-City Neighbourhood Sébastien ARCAND, Danielle JUTEAU, Sirma BILGE, and Francine LEMIRE (lxiii) : Municipal Reform on the Island of Montreal: Tensions Between Two Majority Groups in a Multicultural City Barbara BUCHNER and Carlo CARRARO: China and the Evolution of the Present Climate Regime Barbara BUCHNER and Carlo CARRARO: Emissions Trading Regimes and Incentives to Participate in International Climate Agreements Anil MARKANDYA and Dirk T.G. RÜBBELKE: Ancillary Benefits of Climate Policy Anne Sophie CRÉPIN(lxiv): Management Challenges for Multiple-Species Boreal Forests Anne Sophie CRÉPIN (lxiv): Threshold Effects in Coral Reef Fisheries Sara ANIYAR ( lxiv): Estimating the Value of Oil Capital in a Small Open Economy: The Venezuela’s Example Kenneth ARROW, Partha DASGUPTA and Karl-Göran MÄLER(lxiv): Evaluating Projects and Assessing Sustainable Development in Imperfect Economies Anastasios XEPAPADEAS and Catarina ROSETA-PALMA(lxiv): Instabilities and Robust Control in Fisheries Charles PERRINGS and Brian WALKER (lxiv): Conservation and Optimal Use of Rangelands Jack GOODY (lxiv): Globalisation, Population and Ecology Carlo CARRARO, Carmen MARCHIORI and Sonia OREFFICE: Endogenous Minimum Participation in International Environmental Treaties Guillaume HAERINGER and Myrna WOODERS: Decentralized Job Matching Hideo KONISHI and M. Utku UNVER: Credible Group Stability in Multi-Partner Matching Problems Somdeb LAHIRI: Stable Matchings for the Room-Mates Problem Somdeb LAHIRI: Stable Matchings for a Generalized Marriage Problem Marita LAUKKANEN: Transboundary Fisheries Management under Implementation Uncertainty Edward CARTWRIGHT and Myrna WOODERS: Social Conformity and Bounded Rationality in Arbitrary Games with Incomplete Information: Some First Results Gianluigi VERNASCA: Dynamic Price Competition with Price Adjustment Costs and Product Differentiation Myrna WOODERS, Edward CARTWRIGHT and Reinhard SELTEN: Social Conformity in Games with Many Players Edward CARTWRIGHT and Myrna WOODERS: On Equilibrium in Pure Strategies in Games with Many Players Carlo CARRARO, Alessandro LANZA and Valeria PAPPONETTI: One Thousand Working Papers (l) This paper was presented at the Workshop “Growth, Environmental Policies and Sustainability” organised by the Fondazione Eni Enrico Mattei, Venice, June 1, 2001 (li) This paper was presented at the Fourth Toulouse Conference on Environment and Resource Economics on “Property Rights, Institutions and Management of Environmental and Natural Resources”, organised by Fondazione Eni Enrico Mattei, IDEI and INRA and sponsored by MATE, Toulouse, May 3-4, 2001 (lii) This paper was presented at the International Conference on “Economic Valuation of Environmental Goods”, organised by Fondazione Eni Enrico Mattei in cooperation with CORILA, Venice, May 11, 2001 (liii) This paper was circulated at the International Conference on “Climate Policy – Do We Need a New Approach?”, jointly organised by Fondazione Eni Enrico Mattei, Stanford University and Venice International University, Isola di San Servolo, Venice, September 6-8, 2001 (liv) This paper was presented at the Seventh Meeting of the Coalition Theory Network organised by the Fondazione Eni Enrico Mattei and the CORE, Université Catholique de Louvain, Venice, Italy, January 11-12, 2002 (lv) This paper was presented at the First Workshop of the Concerted Action on Tradable Emission Permits (CATEP) organised by the Fondazione Eni Enrico Mattei, Venice, Italy, December 3-4, 2001 (lvi) This paper was presented at the ESF EURESCO Conference on Environmental Policy in a Global Economy “The International Dimension of Environmental Policy”, organised with the collaboration of the Fondazione Eni Enrico Mattei , Acquafredda di Maratea, October 6-11, 2001 (lvii) This paper was presented at the First Workshop of “CFEWE – Carbon Flows between Eastern and Western Europe”, organised by the Fondazione Eni Enrico Mattei and Zentrum fur Europaische Integrationsforschung (ZEI), Milan, July 5-6, 2001 (lviii) This paper was presented at the Workshop on “Game Practice and the Environment”, jointly organised by Università del Piemonte Orientale and Fondazione Eni Enrico Mattei, Alessandria, April 12-13, 2002 (lix) This paper was presented at the ENGIME Workshop on “Mapping Diversity”, Leuven, May 1617, 2002 (lx) This paper was presented at the EuroConference on “Auctions and Market Design: Theory, Evidence and Applications”, organised by the Fondazione Eni Enrico Mattei, Milan, September 2628, 2002 (lxi) This paper was presented at the Eighth Meeting of the Coalition Theory Network organised by the GREQAM, Aix-en-Provence, France, January 24-25, 2003 (lxii) This paper was presented at the ENGIME Workshop on “Communication across Cultures in Multicultural Cities”, The Hague, November 7-8, 2002 (lxiii) This paper was presented at the ENGIME Workshop on “Social dynamics and conflicts in multicultural cities”, Milan, March 20-21, 2003 (lxiv) This paper was presented at the International Conference on "Theoretical Topics in Ecological Economics", organised by the Abdus Salam International Centre for Theoretical Physics ICTP, the Beijer International Institute of Ecological Economics, and Fondazione Eni Enrico Mattei – FEEM Trieste, February 10-21, 2003 2002 SERIES CLIM Climate Change Modelling and Policy (Editor: Marzio Galeotti ) VOL Voluntary and International Agreements (Editor: Carlo Carraro) SUST Sustainability Indicators and Environmental Valuation (Editor: Carlo Carraro) NRM Natural Resources Management (Editor: Carlo Giupponi) KNOW Knowledge, Technology, Human Capital (Editor: Dino Pinelli) MGMT Corporate Sustainable Management (Editor: Andrea Marsanich) PRIV Privatisation, Regulation, Antitrust (Editor: Bernardo Bortolotti) ETA Economic Theory and Applications (Editor: Carlo Carraro) 2003 SERIES CLIM Climate Change Modelling and Policy (Editor: Marzio Galeotti ) GG Global Governance (Editor: Carlo Carraro) SIEV Sustainability Indicators and Environmental Valuation (Editor: Anna Alberini) NRM Natural Resources Management (Editor: Carlo Giupponi) KNOW Knowledge, Technology, Human Capital (Editor: Gianmarco Ottaviano) IEM International Energy Markets (Editor: Anil Markandya) CSRM Corporate Social Responsibility and Management (Editor: Sabina Ratti) PRIV Privatisation, Regulation, Antitrust (Editor: Bernardo Bortolotti) ETA Economic Theory and Applications (Editor: Carlo Carraro) CTN Coalition Theory Network
© Copyright 2026 Paperzz