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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 78 /N put readonly def /FontBBox{0 -504 2615 1004}readonly def /UniqueID 5032014 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF5B8CABB9FFC6A66A4000A13D5F68BFF326D 1D432B0D064B56C598F4338C319309181D78E1629A31ECA5DD8536379B03C383 D10F04E2CB7C8461B10646CD63AFEB7608468CA0FCFC4D3458FB43D22879B515 27DD9CCF44C2BFCD95A4DE911E4915FBC02335E9999FD9B546134081D6DA3792 EC4A76DEBA77635BE52E09986268A919CB48B5EFB1A1301EE0683CB5709BC8CE D819D799020CBA673BA39C911075501395B1FD20EAD392C9D5A8C9FD1198C737 D1A614CF0C0432F29DDEB4BF9DB026908DBE89EE522B7D55DE9BF64AFBE6248E 2E10466655EB9083E7D23E3F0EE26154F191BEBC9987930CD4B4CABE1275BDF9 8755EF3D531FDF91D54954FC53F15A38D1E8F8D1E36447484FA2C09D34813615 838B6330FEAE536D08376E4A0FDDF58CDF5647C9F1FF3A7D1ACAD376DB3CADB6 9459F7A5D4F1864863B79E9F93A1EDE8B99C3138D26227C01F6FE0AAC800F2E5 94DD81CF7B1355B642CE45CB532FC5B535D66EDFFEA076C009E87406D9772D71 848C3C53B7496A5D6B58679EF11E114C5F457C6A0D3CDE50278E4A89D5393B1C F877CF4E2142A4D045C4AA9138105D748903BACC28FD43DFEDB341E1FCDBE2EA D412498FBB5374D6836CFBEB13D4C2B7B9625C25B037FDA9DCC42F5679C4B3C1 6340E341F73A921013790936801297855EDE27C68907C6C87633FE64CBDCFEC9 DD8EC8784857A09FE395D7FE095A87CC113B930AD09643AC6F9F5A44A1154C89 7951C1CEF380FE489886299A1C5A2E1FB2D475FD3478BEDD0EC21A4CBAD46924 9AF698FCD47B9891629762AAD9E00C0C31B4F54AA5E59A575DB50A8961F05D7B D54237D5CE59FDB5C3E83AFEB532CC4F900F7E85358A528D56A6FBE9F3002E56 EA59E9C2459EEA543F906E74846306E52E324E00D300A78B984ADD86E21B5C08 4E19F5F28704CCA9BC6F5B8E11C74674881613A81A1763E4217B4FC14BD6FF18 B37A14375DF5F7CCD561DC7ABC388F4539424239C618F1D92CD37F507FF94133 927748C386DF1C1EA2F61DC341C76A4E72E64AA9723292B83079A9C3FCEA7355 51666A804736DB26A32A5E44562BF0EEC98870D116148D9E17AFD856254CF45F 25F15F274CD668C048FCC6AD42D003519C706E093B91CD448AE1F879F789D869 B1907F0AE617801BC19C7CBDBA68D819A0CC55652A2E737CAAF8B513CC95B593 004E2D4ACC07362FF705EC944AD11A89322C2B8F22640ACC07DE6247F524ED9B 54E6645A122774A70E1AC3B1CD4EF56DD526DCE88D27742285DE6A956F52AB83 885853C13481CEF4A9C518918D4ADFD9818E9B8F57BE56B5575FA1DA295DFB3B 1F528233265281FD7614B4CDE7D1D0DB66CDB1B7C1A53CEC9CB178CEA88005F0 3E482938AFFDB44E2C31E928F068B35EB7A91B910F2B2FBC769AA38806DC7FA1 973956477669BDE4702ABB9AFF6696247831A9D7212DE60A61A070E4D250F018 670F3354BEADAC44DC7F8CC4E56DF154BA250DAEB7F085FC417BD4F364BCC00B 2AA2E19F3F5B728DE0A42143EFAEA62DF1678A79D25D2E3D69CFEBA6C5844595 AE2D53DE40C091BEDF754155362627581E94EC9009DD04454CE9D9C53DE3F615 E4CB174176BC5479D9 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSBM10 %!PS-AdobeFont-1.1: MSBM10 2.1 %%CreationDate: 1993 Sep 17 11:10:37 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 82 /R put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueID 5000816 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A 221A37D9A807DD01161779DDE7D5FC1B2109839E5B52DFBB2A7C1B5D8E7E8AA0 5B10EA43D6A8ED61AF5B23D49920D8F79DAB6A59062134D84AC0100187A6CD1F 80F5DDD9D222ACB1C23326A7656A635C4A241CCD32CBFDF8363206B8AA36E107 1477F5496111E055C7491002AFF272E46ECC46422F0380D093284870022523FB DA1716CC4F2E2CCAD5F173FCBE6EDDB874AD255CD5E5C0F86214393FCB5F5C20 9C3C2BB5886E36FC3CCC21483C3AC193485A46E9D22BD7201894E4D45ADD9BF1 CC5CF6A5010B5654AC0BE0DA903DB563B13840BA3015F72E51E3BC80156388BA F83C7D393392BCBC227771CDCB976E93302535C253C2A7A0D2A39F364428A2F6 E75C522DF7779C207C50458653CFCBB74C28D8FB93C4A505CBCFF64175CE3168 7335D1F5349075B3FD6AB84CBA8513CAA1308A96DB6D10EA70D799A769103385 A17B45DECE34805BEF8C5E3EA1A98378F39BE12FAF47F32F1D2EDC8E2FA74450 CA4D6CEC79938A78D77D19670D63B58072FFB537BBB1C02ABD88184252025035 0CA16CFDFC7054B087641008ADE2E766C36E7AF153BF69990A4E1A7318F7F21F 68A6C1DA96E305C43B336894A7FBE48C1196B3E2631824734053D61E5318DEAC B1D99B725675117C039A80BA59FE078D17564CB7383B763095F1E29F86904D59 C1C093BFE0CB330D82606142AC66F4EA4FB2D49F8F724C3CD5C583A2AECA1D13 28F29191D3F2B42AB2AAAAB4C3EFCF9A394D927D06FCBEA63C106EF2F506E39F DB6E94AE7E8473E80D4A33D88F5EEF36A0EECB0428A3BA52E8BE1D01CAF278E3 92A04889CD88AC1891FEAC5CBCB7E90F06E98EE5999B3EF9FB18DF6E20D64773 C4752C5079A60F36CC784EFEF1CB7DAE82186B93FA1B4594CAD9AD20BCAD87D6 A34A8132611DE3E37625C7F28FC4DBD27D8F786DB1A1FC8239B5A00065B72D79 CE34E506C732FA5B68245D93824AE17EFB8402308B832C61F08CF89E4143AA8B FE5D7992C167C7A5D0A8B13789EA6544F894BB48DA4318C38933EA774D005447 72AA693D35AB41E1A4D616A4328414C50A9D763E2CC730FF4482DC6DD3E84F1A 071C987CF5D6C4D8B55CD7B11E6F05054653454094C984411ACE192CC72387B1 728457605F436FD7B1B56EE8E64C2862336E6EE25042EF65556B50D5D43C6CCB 5E2568D4F967B3F42B806EDB92866C910F7FF1BF5A0B61759AB3253A4933AAFA 5CE15481EC85E888125F1EA92273DD99DF6CF7F4375C1AA05F82159DC8ECB75F 935322B904A9EE6089806A7F0BA101970EC0BB1E9FF66D2B8AA6ACF994C426D5 B2F96275AD20AD0C4F5591FFB7A6E3A52B44CE009BBC2F233658497F9EF815B4 FD5004B5D0695E80F496A9CEFC1615F38B87A2EBCE258E7ACCB2524688AA961F 61935BF37E0BA228D164E6E8253746BF88D0ED26885290E0C245B9CC9016BA29 F95DEA118938F5D2AA800A2979CD5FB49D37A4FBC534E0BFD4F1FC0421CAE5F4 8A6E5C408A65B3F259B4437A4EAACDBB784BA3 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 56 /bracelefttp put dup 58 /braceleftbt put dup 60 /braceleftmid put dup 80 /summationtext put dup 83 /uniontext put dup 91 /uniondisplay put dup 113 /radicalBig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5 5250011D19E9366EB6FD153D3A100CAA6212E3D5D93990737F8D326D347B7EDC 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C 68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueID 5000769 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F0364CD5660F74BEE96790DE35AFA90CCF712 B1805DA88AE375A04D99598EADFC625BDC1F9C315B6CF28C9BD427F32C745C99 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CMMI12 1.100 %%CreationDate: 1996 Jul 27 08:57:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-30 -250 1026 750}readonly def /UniqueID 5087386 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5 5250011D19E9366EB6FD153D3A100CAA6212E3D5D93990737F8D326D347B7EDC 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%%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A 221A37D9A807DD01161779DDE7D31FF2B87F97C73D63EECDDA4C49501773468A 27D1663E0B62F461F6E40A5D6676D1D12B51E641C1D4E8E2771864FC104F8CBF 5B78EC1D88228725F1C453A678F58A7E1B7BD7CA700717D288EB8DA1F57C4F09 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C 68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361 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American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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%%BeginFont: CMR17 %!PS-AdobeFont-1.1: CMR17 1.0 %%CreationDate: 1991 Aug 20 16:38:24 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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Fj(\016)1969 1694 y Fo(.)257 1954 y Fl(T)-9 b(rigger-Strategie)98 b Fo(Hierb)s(ei)25 b(handelt)h(es)f(sic)m(h)h(um) f(die)h(Strategie,)f(die)g(im)g(T)-8 b(urnier)257 2075 y(v)m(on)29 b(Axelro)s(d)g(als)f(FRIEDMAN)g(b)s(ek)-5 b(ann)m(t)29 b(ist.)f(Es)h(handelt)g(sic)m(h)g(um)g(die)f(primitivste) 257 2195 y(Strategie,)40 b(die)h(das)f(V)-8 b(erhalten)40 b(des)h(anderen)g(Spielers)g(mit)f(b)s(edenkt.)h(Sie)f(b)s(eginn)m(t) 257 2315 y(k)m(o)s(op)s(erativ,)30 b(ab)s(er)f(die)g(erste)h(Defektion) f(zahlt)h(sie)f(mit)h(unerbittlic)m(her)h(V)-8 b(ergeltungs-)257 2436 y(suc)m(h)m(t)40 b(heim,)e(d.h.)g(v)m(on)h(da)e(an)h(defektiert)h (sie)f(st)2125 2440 y(\177)2125 2436 y(andig.)g(Also:)g Fm(s)2721 2400 y Fk(0)2721 2460 y(1)2797 2436 y Fo(=)e Fm(K)7 b Fo(;)38 b Fm(s)3110 2394 y Fj(t)p Fk(+1)3110 2460 y(1)3266 2436 y Fo(=)e Fm(K)7 b Fo(,)257 2556 y(w)m(enn)32 b Fm(s)553 2520 y Fj(t)578 2496 y Fg(0)553 2581 y Fk(2)633 2556 y Fo(=)c Fm(K)37 b Fo(f)890 2560 y(\177)887 2556 y(ur)31 b(0)c Fn(\024)h Fm(t)1226 2520 y Fh(0)1277 2556 y Fn(\024)h Fm(t)p Fo(.)h(Es)i(gilt)e(hingegen)i Fm(s)2233 2515 y Fj(t)p Fk(+1)2233 2580 y(1)2380 2556 y Fo(=)c Fm(D)s Fo(,)i(w)m(enn)i Fm(s)2921 2520 y Fj(t)2946 2496 y Fg(0)2921 2581 y Fk(2)3000 2556 y Fo(=)c Fm(D)33 b Fo(f)3251 2560 y(\177)3248 2556 y(ur)e(ein)257 2676 y(0)d Fn(\024)g Fm(t)474 2640 y Fh(0)525 2676 y Fn(\024)g Fm(t)p Fo(.)33 b(Nat)888 2680 y(\177)885 2676 y(urlic)m(h)h(sind)f(die)g (Rollen)g(v)m(on)g(1)g(und)g(2)f(hierb)s(ei)i(v)m(ertausc)m(h)m(bar.) 257 2936 y Fl(2.)53 b(F)-9 b(all)98 b Fo(2)45 b(w)m(eic)m(h)m(t)j(ab)d (v)m(on)h(der)g(Ko)s(op)s(erationssc)m(hiene,)h(d.h.)j(^)-53 b Fm(s)2803 2900 y Fj(t)2803 2961 y Fk(2)2892 2936 y Fo(=)49 b Fm(K)j Fo(f)3185 2940 y(\177)3182 2936 y(ur)46 b(0)j Fn(\024)257 3057 y Fm(t)31 b Fn(\024)g Fm(m)23 b Fn(\000)h Fo(1,)34 b(ab)s(er)k(^)-53 b Fm(s)1017 3020 y Fj(m)1017 3081 y Fk(2)1114 3057 y Fo(=)30 b Fm(D)s Fo(.)k(Damit)g(sic)m(h)i(das)e(Ab)m(w)m(eic)m(hen)j(ren)m(tiert,)f(hat) e(zu)g(gelten:)257 3177 y Fm(u)313 3192 y Fk(2)352 3177 y Fo(\()p Fm(s)436 3192 y Fk(1)476 3177 y Fm(;)20 b Fo(^)-52 b Fm(s)566 3192 y Fk(2)605 3177 y Fo(\))27 b(=)774 3102 y Fi(P)879 3129 y Fj(m)p Fh(\000)p Fk(1)879 3206 y Fj(j)t Fk(=0)1052 3177 y Fo(7)p Fm(\016)1148 3141 y Fj(j)1198 3177 y Fo(+)13 b(10)p Fm(\016)1432 3141 y Fj(m)1511 3177 y Fo(+)1600 3102 y Fi(P)1705 3129 y Fh(1)1705 3206 y Fj(j)t Fk(=)p Fj(m)p Fk(+1)1966 3177 y Fo(2)p Fm(\016)2062 3141 y Fj(j)2126 3177 y Fn(\025)28 b Fo(7)2334 3138 y Fk(1)p 2290 3154 V 2290 3211 a(1)p Fh(\000)p Fj(\016)2423 3177 y Fo(.)g(Durc)m(h)h(Umformen)g(erh)3381 3181 y(\177)3381 3177 y(alt)257 3309 y(man)37 b Fm(\016)g Fn(\024)679 3270 y Fk(3)p 679 3286 36 4 v 679 3344 a(8)724 3309 y Fo(,)f(d.h.)h(w)m(enn)g(die)g(Zukunft)f(gen)1928 3313 y(\177)1925 3309 y(ugend)h(wic)m(h)m(tig)h(ist)e(\()p Fm(\016)i(>)2933 3270 y Fk(3)p 2933 3286 V 2933 3344 a(8)2978 3309 y Fo(\),)e(lohn)m(t)h(sic)m(h)257 3430 y(ein)d(Ab)m(w)m(eic)m(hen)h(v)m(on)f(der)f(T)-8 b(rigger-Strategie)32 b(nic)m(h)m(t.)257 3689 y Fl(Satz)38 b(1)98 b Fo(Es)33 b(seien)h(die)f(V)-8 b(oraussetzungen)35 b(des)e(unendlic)m(h)i(oft)d (iterierten)i(Gefange-)257 3810 y(nendilemmas)j(erf)959 3814 y(\177)956 3810 y(ullt.)e(F)-8 b(erner)35 b(gelte)g(f)1739 3814 y(\177)1736 3810 y(ur)f(den)i(Disk)m(on)m(tfaktor)f Fm(\016)g(>)2860 3771 y Fk(3)p 2860 3787 V 2860 3844 a(8)2905 3810 y Fo(.)f(Dann)h(ist)g(die)257 3930 y(\(b)s(eidseitige\))f (T)-8 b(rigger-Strategie)33 b(ein)g(teilspielp)s(erfektes)j(Nash-Gleic) m(hgewic)m(h)m(t.)257 4190 y Fl(Satz)c(2)98 b Fo(Sei)28 b(\000)g(ein)g(Spiel)h(in)f(Normalform)f(mit)h(genau)g(einem)h (Nash-Gleic)m(hgewic)m(h)m(t)257 4310 y Fm(s)303 4274 y Fj(N)408 4310 y Fo(in)38 b(reinen)h(Strategien.)f(Dann)g(hat)f(das)h (endlic)m(h)i(oft)d(iterierte)i(Spiel)f(\(mit)g(\000)g(als)257 4431 y(Basisspiel\))d(genau)e(ein)g(Nash-Gleic)m(hgewic)m(h)m(t,)i(und) e(zw)m(ar)h(immer)f Fm(s)2849 4395 y Fj(N)2916 4431 y Fo(.)404 4691 y Fl(Bew)m(eis)97 b Fo(R)911 4695 y(\177)908 4691 y(uc)m(kw)1123 4695 y(\177)1123 4691 y(artsinduktion:)42 b(Da)37 b(durc)m(h)j(das)e(letzte)i(Spiel)f(k)m(eine)h(Zukunft)257 4811 y(b)s(eein\015usst)33 b(wird,)e(ist)g Fm(s)1163 4775 y Fj(N)1261 4811 y Fo(das)g(einzige)h(Nash-Gleic)m(hgewic)m(h)m(t) h(in)e(dieser)h(Runde.)f(Da-)257 4931 y(mit)42 b(stehen)h(die)f (Strategien)g(in)f(der)h(letzten)g(Runde)g(ab)s(er)g(sc)m(hon)g(fest.)g (Nun)g(k)-5 b(ann)257 5052 y(dieselb)s(e)636 5030 y(\177)624 5052 y(Ub)s(erlegung)33 b(auc)m(h)g(f)1407 5056 y(\177)1404 5052 y(ur)g(das)g(v)m(orletzte)h(Spiel)f(durc)m(hgef)2707 5056 y(\177)2704 5052 y(uhrt)h(w)m(erden)g(usw.)1852 5637 y(2)p eop end %%Page: 3 3 TeXDict begin 3 2 bop 257 573 a Fp(2)161 b(Unendlic)l(h)73 b(oft)i(wiederholte)d(Spiele)h(aus)i(for-)499 756 y(maler)55 b(Sic)l(h)l(t)257 975 y Fl(De\014nition)99 b Fo(Gegeb)s(en)34 b(sei)i(\000\()p Fm(n;)17 b(S;)g(u)p Fo(\))33 b(ein)i(Spiel)g(in)g (Normalform)f(mit)g Fm(n)h Fo(Spielern)257 1095 y Fn(f)p Fo(1)p Fm(;)17 b(:::;)g(n)p Fn(g)p Fo(,)26 b Fm(S)34 b Fo(=)27 b Fm(S)943 1110 y Fk(1)993 1095 y Fn(\002)10 b Fm(:::)g Fn(\002)g Fm(S)1318 1110 y Fj(n)1367 1095 y Fo(,)27 b Fm(u)g Fo(=)g(\()p Fm(u)1701 1110 y Fk(1)1740 1095 y Fm(;)17 b(:::;)g(u)1965 1110 y Fj(n)2011 1095 y Fo(\))28 b(:)g Fm(S)33 b Fn(!)28 b Ff(R)2425 1059 y Fj(n)2498 1095 y Fo(\(Basisspiel,)h(stage)e(game,)257 1215 y(base)34 b(game\).)e({)h(Das)f(unendlic)m(h)j(iterierte)e(Spiel)h (\(zu)f(\000\))f(hat)g(die)2749 1275 y(")2794 1215 y(F)-8 b(orm)h(\\)1382 1511 y Fm(H)35 b Fo(=)27 b Fn(f;g)22 b([)1891 1387 y Fh(1)1871 1417 y Fi([)1862 1629 y Fj(k)r Fk(=1)2007 1511 y Fm(S)2073 1470 y Fj(k)2137 1511 y Fn([)h Fm(S)2292 1470 y Fe(N)2344 1511 y Fm(:)257 1829 y(H)42 b Fo(ist)34 b(die)h(Menge)g(der)1159 1888 y(")1204 1829 y(Historien)-7 b(\\)41 b(des)36 b(Spiels:)f Fn(;)f Fo(ist)h(die)f (leere)h(Historie,)3154 1754 y Fi(S)3237 1780 y Fh(1)3237 1858 y Fj(k)r Fk(=1)3387 1829 y Fm(S)3453 1793 y Fj(k)257 1949 y Fo(sind)f(die)f(endlic)m(hen)i(Historien,)e(und)h Fm(S)1761 1913 y Fe(N)1845 1949 y Fo(ist)f(die)g(unendlic)m(he)i(Gesc)m (hic)m(h)m(te.)404 2070 y(Beginn)e(b)s(ei)g Fn(;)p Fo(:)f(Jeder)i Fm(j)f Fn(2)28 b Fm(n)p 1431 2086 59 4 v 33 w Fo(w)1592 2074 y(\177)1592 2070 y(ahlt)33 b Fm(s)1839 2034 y Fk(0)1839 2094 y Fj(j)1906 2070 y Fn(2)28 b Fm(S)2060 2085 y Fj(j)2097 2070 y Fo(,)k(dh.)h Fm(s)2370 2034 y Fk(0)2437 2070 y Fo(=)28 b(\()p Fm(s)2625 2034 y Fk(0)2625 2094 y(1)2664 2070 y Fm(;)17 b(:::;)g(s)2879 2034 y Fk(0)2879 2094 y Fj(n)2926 2070 y Fo(\))28 b Fn(2)g Fm(S)404 2190 y Fo(W)-8 b(eiter)36 b(b)s(ei)g Fm(s)930 2154 y Fk(0)1002 2190 y Fn(2)d Fm(S)1167 2154 y Fk(1)1238 2190 y Fo(:Jeder)k Fm(j)h Fn(2)33 b Fm(n)p 1707 2206 V 36 w Fo(w)1871 2194 y(\177)1871 2190 y(ahlt)j Fm(s)2121 2154 y Fk(1)2121 2215 y Fj(j)2193 2190 y Fn(2)d Fm(S)2352 2205 y Fj(j)2388 2190 y Fo(,)j(dh.)g Fm(s)2668 2154 y Fk(1)2739 2190 y Fo(=)d(\()p Fm(s)2932 2154 y Fk(1)2932 2215 y(1)2971 2190 y Fm(;)17 b(:::;)g(s)3186 2154 y Fk(1)3186 2215 y Fj(n)3233 2190 y Fo(\))32 b Fn(2)h Fm(S)6 b Fo(,)257 2310 y(\()p Fm(s)341 2274 y Fk(0)381 2310 y Fm(;)17 b(s)471 2274 y Fk(1)510 2310 y Fo(\))27 b Fn(2)h Fm(S)735 2274 y Fk(2)802 2310 y Fo(=)g Fm(S)g Fn(\002)22 b Fm(S)6 b Fo(.)404 2431 y(...)404 2551 y Fm(Z)34 b Fo(:=)28 b Fm(S)702 2515 y Fe(N)754 2551 y Fo(,)k Fm(E)i Fo(=)28 b Fm(H)8 b Fn(n)p Fm(Z)f Fo(.)404 2672 y(Spielv)m(erlauf:)46 b Fm(h)i Fn(2)g Fm(E)6 b Fo(:)45 b Fm(h)j Fo(=)f(\()p Fm(s)1650 2635 y Fk(0)1690 2672 y Fm(;)17 b(:::;)g(s)1905 2635 y Fj(m)p Fh(\000)p Fk(1)2061 2672 y Fo(\))48 b Fn(2)g Fm(S)2327 2635 y Fj(m)2438 2672 y Fo(und)c(jeder)h(Spieler)h Fm(j)54 b Fn(2)48 b Fm(n)257 2792 y Fo(w)327 2796 y(\177)327 2792 y(ahlt)36 b Fm(s)577 2756 y Fj(m)577 2817 y(j)677 2792 y Fn(2)d Fm(S)836 2807 y Fj(j)908 2792 y Fo(:)j Fm(s)1017 2756 y Fj(m)1116 2792 y Fo(=)d(\()p Fm(s)1309 2756 y Fj(m)1309 2817 y Fk(1)1375 2792 y Fm(;)17 b(:::;)g(s)1590 2756 y Fj(m)1590 2817 y(n)1656 2792 y Fo(\))36 b(mit:)g(Ergebnis)h(der) f(Runde)g(Nr.)g(m+1)f(:)h Fm(h)3363 2756 y Fh(0)3419 2792 y Fo(=)257 2912 y(\()p Fm(s)341 2876 y Fk(0)381 2912 y Fm(;)17 b(:)g(:)g(:)e(;)i(s)645 2876 y Fj(m)712 2912 y Fo(\))404 3033 y(Spiel?)38 b(Gehalt:)f(Pr)1149 3037 y(\177)1149 3033 y(aferenzen)i(auf)e(Z:)h(Jeder)g(Spieler)g Fm(j)k Fn(2)37 b Fm(n)g Fo(sollte)h(pr)3102 3037 y(\177)3102 3033 y(aferieren:)257 3153 y Fm(z)t(;)17 b(z)399 3117 y Fh(0)452 3153 y Fn(2)28 b Fm(Z)34 b Fo(:)45 b Fm(z)32 b Fn(\025)873 3168 y Fj(j)938 3153 y Fm(z)987 3117 y Fh(0)404 3274 y Fo(Hier)h(b)s(ek)-5 b(ann)m(t:)33 b Fm(z)f Fo(=)c(\()p Fm(z)1284 3237 y Fj(t)1314 3274 y Fo(\))g Fn(2)g Fm(S)1540 3237 y Fe(N)404 3394 y Fm(\016)447 3409 y Fk(1)486 3394 y Fm(;)17 b(\016)573 3409 y Fj(s)638 3394 y Fn(2)p Fo(]0)p Fm(;)g Fo(1[:)27 b Fm(z)33 b Fn(\025)28 b Fm(z)1186 3358 y Fh(0)1265 3394 y Fn(\()-17 b(\))1503 3319 y Fi(P)1608 3345 y Fh(1)1608 3423 y Fj(t)p Fk(=0)1745 3394 y Fm(u)1801 3409 y Fj(j)1837 3394 y Fo(\()p Fm(z)1924 3358 y Fj(t)1954 3394 y Fo(\))p Fm(\016)2039 3358 y Fj(t)2035 3419 y(j)2100 3394 y Fn(\025)2205 3319 y Fi(P)2310 3345 y Fh(1)2310 3423 y Fj(t)p Fk(=0)2446 3394 y Fm(u)2502 3409 y Fj(j)2538 3394 y Fo(\()p Fm(z)2625 3358 y Fh(0)p Fj(t)2675 3394 y Fo(\))p Fm(\016)2760 3358 y Fj(t)2756 3419 y(j)404 3534 y Fo(lim)17 b(inf)690 3459 y Fi(P)796 3485 y Fj(T)796 3563 y(t)p Fk(=0)995 3494 y(1)p 942 3511 142 4 v 942 3568 a Fj(T)10 b Fk(+1)1093 3534 y Fo(\()p Fm(u)1187 3549 y Fj(j)1223 3534 y Fo(\()p Fm(z)1310 3497 y Fj(t)1340 3534 y Fo(\))22 b Fn(\000)h Fm(u)1556 3549 y Fj(j)1592 3534 y Fo(\()p Fm(z)1679 3497 y Fh(0)p Fj(t)1728 3534 y Fo(\))404 3654 y(Strategie:)33 b Fm(s)889 3669 y Fj(j)953 3654 y Fo(:)28 b Fm(E)33 b Fn(!)28 b Fm(S)1301 3669 y Fj(j)1370 3654 y Fm(s)1416 3669 y Fj(j)1452 3654 y Fo(\()p Fm(u)p Fo(\))f Fn(2)h Fm(S)1765 3669 y Fj(j)404 3774 y Fo(Strategiepro\014el:)33 b Fm(s)28 b Fo(=)f(\()p Fm(s)1369 3789 y Fk(1)1409 3774 y Fm(;)17 b(:)g(:)g(:)f(;)h(s)1674 3789 y Fj(n)1720 3774 y Fo(\))28 b(:)g Fm(E)33 b Fn(!)28 b Fm(S)404 3895 y(s)p Fo(\()p Fm(h)p Fo(\))f Fn(2)h Fm(S)404 4015 y(S)470 3979 y Fj(m)564 4015 y Fn(3)g Fm(h)g Fn(7!)f Fo(\()p Fm(h;)17 b(s)p Fo(\))27 b Fn(2)h Fm(S)1278 3979 y Fj(m)p Fk(+1)404 4135 y Fo(Def:)k(Dominanz,)h(Nash-GG,)f(b)s(este)h (An)m(t)m(w)m(ort)257 4468 y Fp(3)161 b(F)-13 b(olk-Theorem)53 b(und)g Fd(Ber)-10 b(trand)p Fp(-Spiel)257 4687 y Fl(Satz)34 b(3)f(\(F)-9 b(olk-Theorem\))98 b Fo(Zu)29 b(einem)h(endlic)m(hen)h (Spiel)f(in)f(Normalform)g(existie-)257 4808 y(ren)425 4867 y(")470 4808 y(b)s(eliebig)34 b(viele)-7 b(\\)7 b(Nash-Gleic)m(hgewic)m(h)m(te)36 b(im)d(zugeh)2367 4812 y(\177)2367 4808 y(origen)h(unendlic)m(hen)h(Spiel.)404 5067 y Fl(In)m(terpretation)97 b Fo(Bei)50 b(un)m(b)s(esc)m(hr)1757 5071 y(\177)1757 5067 y(anktem)j(Zeithorizon)m(t)e(k)-5 b(ann)50 b(b)s(einahe)h(jede)257 5188 y(individuell)40 b(rationale)d(Strategie)h(als)g(Nash-Gleic)m(hgewic)m(h)m(t)i(durc)m (hgesetzt)g(w)m(erden,)257 5308 y(d.h.)45 b(es)f(b)s(ereitet)g(k)m (eine)i(Sc)m(h)m(wierigk)m(eiten)h(mehr,)d(Ko)s(op)s(eration)f(zu)h (erkl)3082 5312 y(\177)3082 5308 y(aren)h(-)e(im)1852 5637 y(3)p eop end %%Page: 4 4 TeXDict begin 4 3 bop 257 573 a Fo(Gegen)m(teil:)43 b(Nahezu)g(jedes)f (Ergebnis)h(l)1773 577 y(\177)1773 573 y(asst)g(sic)m(h)g(als)f(Gleic)m (hgewic)m(h)m(tv)m(erhalten)j(b)s(e-)257 693 y(gr)347 697 y(\177)344 693 y(unden.)38 b({)d(W)-8 b(eil)37 b(die)g(Urheb)s (ersc)m(haft)h(dieses)g(seit)f(fast)f(50)g(Jahren)h(b)s(ek)-5 b(ann)m(ten)37 b(Er-)257 814 y(gebnisses)e(nic)m(h)m(t)f(gekl)1090 818 y(\177)1090 814 y(art)f(ist,)g(spric)m(h)m(t)h(man)f(v)m(om)2160 873 y(")2204 814 y(folk)g(theorem)-7 b(\\)7 b(.)404 1073 y Fl(Generisc)m(h)98 b Fo(Sei)37 b Fm(K)43 b Fn(\032)35 b Ff(R)1455 1037 y Fj(n)1539 1073 y Fo(eine)j(k)m(ompakte)g(Menge)g (und)f Fm(K)46 b Fn(6)p Fo(=)35 b Fn(;)p Fo(.)i(Zu)g Fm(k)h Fn(2)d Fm(K)257 1194 y Fo(gibt)e(es)g(dann)g(ein)g(Nash-GLeic)m (hgewic)m(h)m(t)i(mit)e Fm(k)j Fo(als)d(Ergebnis.)257 1454 y Fl(Beispiel)111 b Fc(Ber)-7 b(trand)p Fo(-Oligop)s(ol)21 b(\(Preisk)-5 b(ampf)7 b(\);)23 b(Erg)2411 1458 y(\177)2411 1454 y(anzung)f(zu)g Fc(Cournot-St)-7 b(a)n(ckelber)n(g)p Fo(.)373 1640 y Fn(\017)49 b Fo(zw)m(ei)34 b(Spieler)g(1)p Fm(;)17 b Fo(2)373 1802 y Fn(\017)49 b Fo(Kosten)33 b Fm(cs)891 1817 y Fj(i)919 1802 y Fo(,)g Fm(s)1025 1817 y Fj(i)1085 1802 y Fo(v)m(erk)-5 b(aufte)34 b(Pro)s(duktion)373 1964 y Fn(\017)49 b Fm(N)10 b Fo(\()p Fm(p)p Fo(\))48 b(Nac)m(hfrage)g(zum)g(Preis)h Fm(p)k Fn(\025)h Fm(c)p Fo(,)47 b Fm(N)2130 1928 y Fh(0)2154 1964 y Fo(\()p Fm(p)p Fo(\))53 b Fm(<)g Fo(0;)48 b(eine)g(\(fast)g(zu\))g(simple)472 2085 y(M)561 2089 y(\177)561 2085 y(oglic)m(hk)m(eit)35 b(ist)e Fm(N)10 b Fo(\()p Fm(p)p Fo(\))28 b(=)f Fm(M)33 b Fn(\000)23 b Fm(p)32 b Fo(mit)h Fm(M)39 b Fo(=)32 b(maximale)i(Nac)m (hfrage)373 2246 y Fn(\017)49 b Fm(u)528 2261 y Fj(i)556 2246 y Fo(\()p Fm(p)643 2261 y Fk(1)682 2246 y Fm(;)17 b(p)775 2261 y Fk(2)814 2246 y Fo(\))28 b(=)f(\()p Fm(p)1070 2261 y Fj(i)1120 2246 y Fn(\000)c Fm(c)p Fo(\))p Fm(d)1351 2261 y Fj(i)1379 2246 y Fo(\()p Fm(p)1466 2261 y Fk(1)1505 2246 y Fm(;)17 b(p)1598 2261 y Fk(2)1637 2246 y Fo(\))33 b(mit)1179 2606 y Fm(d)1230 2621 y Fk(1)1269 2606 y Fo(\()p Fm(p)1356 2621 y Fk(1)1395 2606 y Fm(;)17 b(p)1488 2621 y Fk(2)1527 2606 y Fo(\))28 b(=)1696 2401 y Fi(8)1696 2491 y(<)1696 2670 y(:)1826 2484 y Fm(N)10 b Fo(\()p Fm(p)2001 2499 y Fk(1)2041 2484 y Fo(\))138 b(f)10 b(\177)-52 b(ur)83 b Fm(p)2478 2499 y Fk(1)2545 2484 y Fm(<)28 b(p)2698 2499 y Fk(2)1836 2565 y(1)p 1836 2582 36 4 v 1836 2639 a(2)1881 2605 y Fm(N)10 b Fo(\()p Fm(p)2056 2620 y Fk(1)2096 2605 y Fo(\))83 b(f)10 b(\177)-52 b(ur)83 b Fm(p)2478 2620 y Fk(1)2545 2605 y Fo(=)28 b Fm(p)2698 2620 y Fk(2)1826 2725 y Fo(0)342 b(f)10 b(\177)-52 b(ur)83 b Fm(p)2478 2740 y Fk(1)2545 2725 y Fm(>)28 b(p)2698 2740 y Fk(2)257 2978 y Fl(Satz)45 b(4)98 b Fm(p)715 2942 y Fh(\003)715 3003 y Fk(1)793 2978 y Fo(=)39 b Fm(p)957 2942 y Fh(\003)957 3003 y Fk(2)1035 2978 y Fo(=)g Fm(c)g Fo(ist)h(das)f(einzige)i (Nash-Gleic)m(hgewic)m(h)m(t)h(v)m(om)e Fc(Ber)-7 b(trand)p Fo(-)257 3098 y(Duop)s(ol.)404 3358 y Fl(Bew)m(eis)97 b Fo(\()p Fm(p)923 3373 y Fk(1)963 3358 y Fm(;)17 b(p)1056 3373 y Fk(2)1095 3358 y Fo(\))27 b Fn(6)p Fo(=)h(\()p Fm(c;)17 b(c)p Fo(\),)32 b(d.h.)g(wir)h(m)1973 3362 y(\177)1970 3358 y(ussen)h(v)m(ersc)m(hiedene)i(F)2856 3362 y(\177)2856 3358 y(alle)c(un)m(tersc)m(hei-)257 3479 y(den:)373 3665 y Fn(\017)49 b Fm(p)521 3680 y Fk(1)588 3665 y Fm(>)28 b(p)741 3680 y Fk(2)808 3665 y Fm(>)f(c)p Fo(:)g Fm(p)1056 3680 y Fk(1)1123 3665 y Fn(!)g Fm(p)1299 3629 y Fh(0)1350 3665 y Fn(2)p Fo(])p Fm(c;)17 b(p)1578 3680 y Fk(2)1618 3665 y Fo([,)27 b Fm(u)1755 3680 y Fk(1)1794 3665 y Fo(\()p Fm(p)1881 3680 y Fk(1)1920 3665 y Fm(;)17 b(p)2013 3680 y Fk(2)2052 3665 y Fo(\))28 b(=)f(0,)g Fm(u)2380 3680 y Fj(i)2407 3665 y Fo(\()p Fm(p)2494 3629 y Fh(0)2494 3690 y Fk(1)2534 3665 y Fm(;)17 b(p)2627 3680 y Fk(2)2666 3665 y Fo(\))27 b(=)h(\()p Fm(p)2922 3629 y Fh(0)2922 3690 y Fk(1)2971 3665 y Fn(\000)10 b Fm(c)p Fo(\))p Fm(N)g Fo(\()p Fm(p)3313 3629 y Fh(0)3313 3690 y Fk(1)3354 3665 y Fo(\))27 b Fm(>)472 3786 y Fo(0)373 3948 y Fn(\017)49 b Fo(etc.)33 b(\(4-5)f(F)921 3952 y(\177)921 3948 y(alle)g(erg)1229 3952 y(\177)1229 3948 y(anzen!\))257 4207 y Fl(Satz)f(5)97 b Fo(Sei)27 b Fm(M)37 b Fo(der)26 b(Monop)s(olpreis.)h(Zu)f Fm(p)i Fn(2)g Fo([)p Fm(c;)17 b(M)10 b Fo(])27 b(existiert)h(die)e(T)-8 b(riggerstrategie)257 4328 y(als)49 b(Nash-Gleic)m(hgewic)m(h)m(t)i (des)f(unendlic)m(h)h(oft)d(wiederholten)i Fc(Ber)-7 b(trand)p Fo(-Spiels,)257 4448 y(w)m(enn)41 b Fm(\016)h(>)725 4409 y Fk(1)p 725 4425 V 725 4483 a(2)771 4448 y Fo(.)d(Dab)s(ei)f(ist) i Fm(M)49 b Fo(so)39 b(gew)1700 4452 y(\177)1700 4448 y(ahlt,)h(dass)g Fm(g)t Fo(\()p Fm(p)p Fo(\))d(=)i(\()p Fm(p)26 b Fn(\000)h Fm(c)p Fo(\))p Fm(N)10 b Fo(\()p Fm(p)p Fo(\),)39 b Fm(p)g Fn(2)g Fo([)p Fm(c;)17 b(M)10 b Fo(])257 4569 y(steigend)34 b(\(mit)f(maximalem)h Fm(M)10 b Fo(\).)404 4828 y Fl(Bew)m(eis)97 b Fm(p)885 4792 y Fk(0)885 4853 y(1)952 4828 y Fo(=)28 b Fm(p)k Fo(und)404 4949 y Fm(p)453 4908 y Fj(t)p Fk(+1)453 4973 y(1)600 4949 y Fo(=)c Fm(p)k Fo(w)m(enn)i Fm(p)1086 4913 y Fj(t)1111 4889 y Fg(0)1086 4973 y Fk(2)1166 4949 y Fn(\025)28 b Fm(p)k Fo(f)1385 4953 y(\177)1382 4949 y(ur)h(0)27 b Fn(\024)h Fm(t)1723 4913 y Fh(0)1775 4949 y Fn(\024)g Fm(t)404 5069 y(p)453 5028 y Fj(t)p Fk(+1)453 5094 y(1)600 5069 y Fo(=)g Fm(c)k Fo(w)m(enn)i Fm(p)1079 5033 y Fj(t)1104 5010 y Fg(0)1079 5094 y Fk(2)1159 5069 y Fn(\025)28 b Fm(p)k Fo(f)1378 5073 y(\177)1375 5069 y(ur)h(0)27 b Fn(\024)i Fm(t)1717 5033 y Fh(0)1768 5069 y Fn(\024)f Fm(t)404 5190 y Fo(Analog)k Fm(p)786 5205 y Fk(2)825 5190 y Fo(.)404 5310 y(Bew:)h(Annahme)h(:)e(2)h(w)m(eic)m(h)m(t)i(ab)d (mit)53 b(^)-69 b Fm(p)1893 5325 y Fk(2)1960 5310 y Fo(=)27 b(\()20 b(^)-69 b Fm(p)2150 5325 y Fk(2)2190 5267 y Fj(t)2219 5310 y Fo(\))2257 5325 y Fj(t)p Fh(2)p Fe(N)1852 5637 y Fo(4)p eop end %%Page: 5 5 TeXDict begin 5 4 bop 424 573 a Fo(^)-69 b Fm(p)453 588 y Fk(2)492 530 y Fj(t)549 573 y Fo(=)28 b Fm(p)k Fo(f)767 577 y(\177)764 573 y(ur)h(0)27 b Fn(\024)h Fm(t)g Fn(\024)h Fm(m)22 b Fn(\000)h Fo(1)32 b(und)53 b(^)-69 b Fm(p)1771 588 y Fk(2)1810 530 y Fj(m)1905 573 y Fo(=)27 b Fm(p)22 b Fn(\000)h Fm(\017;)17 b(\017)28 b(>)g Fo(0)404 693 y Fm(u)460 708 y Fk(2)499 693 y Fo(\()p Fm(p)586 708 y Fk(1)625 693 y Fm(;)17 b(p)718 708 y Fk(2)757 693 y Fo(\))28 b(=)f(1)p Fm(=)p Fo(2)17 b Fm(N)10 b Fo(\()p Fm(p)p Fo(\))17 b(\()p Fm(p)k Fn(\000)i Fm(c)p Fo(\)\(1)f(+)g Fm(\016)k Fo(+)c Fm(:)17 b(:)g(:)k Fo(+)h Fm(\016)2263 657 y Fj(n)2327 693 y Fm(:)17 b(:)g(:)o Fo(\))28 b(=)2664 646 y Fj(g)r Fk(\()p Fj(p)p Fk(\))p 2620 670 215 4 v 2620 728 a(2\(1)p Fh(\000)p Fj(\016)r Fk(\))404 831 y Fm(u)460 846 y Fk(2)499 831 y Fo(\()p Fm(p)586 846 y Fk(1)625 831 y Fm(;)36 b Fo(^)-68 b Fm(p)718 846 y Fk(2)757 831 y Fo(\))28 b(=)f(1)p Fm(=)p Fo(2)17 b Fm(N)10 b Fo(\()p Fm(p)p Fo(\))17 b(\()p Fm(p)k Fn(\000)i Fm(c)p Fo(\)\(1)f(+)g Fm(\016)k Fo(+)c Fm(:)17 b(:)g(:)k Fo(+)h Fm(\016)2263 795 y Fj(m)p Fh(\000)p Fk(1)2420 831 y Fo(\))g(+)g Fm(\016)2625 795 y Fj(m)2692 831 y Fm(g)t Fo(\()p Fm(p)f Fn(\000)i Fm(\017)p Fo(\))f(+)g(0)404 952 y Fm(u)460 967 y Fk(2)499 952 y Fo(\()p Fm(p)586 967 y Fk(1)625 952 y Fm(;)17 b(p)718 967 y Fk(2)757 952 y Fo(\))28 b Fm(>)f(u)982 967 y Fk(2)1021 952 y Fo(\()p Fm(p)1108 967 y Fk(1)1148 952 y Fm(;)36 b Fo(^)-68 b Fm(p)1241 967 y Fk(2)1280 952 y Fo(\))27 b Fn(\()-17 b Fo(=)28 b Fm(\016)j(>)1720 913 y Fk(1)p 1720 929 36 4 v 1720 986 a(2)257 1212 y Fl(Satz)53 b(6)97 b Fo(Sei)46 b(die)g(Situation)g(v)m(on)g(Satz)f(5)g(gegeb)s(en,)i(mit)e (der)h(einzigen)h(Ausnah-)257 1332 y(me,)37 b(dass)g(nic)m(h)m(t)g(2,)f (sondern)h(allgemein)f Fm(n)g Fo(Firmen)h(b)s(eteiligt)f(sind.)h(Dann)f (existiert)257 1452 y(die)f(T)-8 b(rigger-Strategie)35 b(als)g(Nash-Gleic)m(hgewic)m(h)m(t)i(des)f(unendlic)m(h)g(oft)e (wiederholten)257 1573 y Fc(Ber)-7 b(trand)p Fo(-Spiels,)40 b(w)m(enn)f Fm(\016)i(>)c Fo(1)26 b Fn(\000)1735 1534 y Fk(1)p 1731 1550 43 4 v 1731 1607 a Fj(n)1784 1573 y Fo(.)38 b({)g(Je)h(mehr)f(Firmen)h(k)m(onkurrieren,)h(desto)257 1693 y(wic)m(h)m(tiger)35 b(m)m(uss)f(also)f(die)g(Zukunft)g(eingesc)m (h)1992 1697 y(\177)1992 1693 y(atzt)h(w)m(erden.)404 1953 y Fl(Bew)m(eis)849 1932 y Fo(\177)836 1953 y(Ubungsaufgab)s(e.)257 2213 y Fl(Satz)39 b(7)98 b Fo(Un)m(ter)34 b(der)h(Annahme,)g(dass)f (die)h(T)-8 b(riggerstrategie)34 b(erst)h(nac)m(h)f Fm(k)j Fo(Runden)257 2362 y(wirksam)d(w)m(erden)h(k)-5 b(ann)32 b(\()p Fm(k)f Fn(6)p Fo(=)d(0\),)k(gilt)g(f)1790 2366 y(\177)1787 2362 y(ur)h(den)g(Disk)m(on)m(tfaktor)g Fm(\016)f(>)2916 2326 y Fb(k)q Fa(+1)2972 2248 y Fi(q)p 3072 2248 234 4 v 114 x Fo(1)21 b Fn(\000)3256 2323 y Fk(1)p 3252 2339 43 4 v 3252 2397 a Fj(n)3305 2362 y Fo(.)404 2659 y Fl(Bew)m(eis)849 2638 y Fo(\177)836 2659 y(Ubungsaufgab)s(e.)1852 5637 y(5)p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF