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[{"key": "dc.contributor.advisor", "value": "Laukkarinen, Eija", "language": null, "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Tuoresj\u00e4rvi, Tapani", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2025-06-16T10:20:33Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2025-06-16T10:20:33Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2025", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/103564", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4m\u00e4n tutkielman aiheena ovat nollasumma- ja yleisummapelit. Nollasummapelien perusideana on se, ett\u00e4 toisen pelaajan h\u00e4vi\u00f6 on toisen pelaajan\n voitto. Nollasummapelej\u00e4 ovat esimerkiksi pokeri ja hex-peli. Nollasummapeliss\u00e4 pelaajat tekev\u00e4t vuoronsa samanaikaisesti, vaikka toisen pelaajan siirtoa ei voida ennalta tiet\u00e4\u00e4. T\u00e4st\u00e4 huolimatta pelaaja voi kuitenkin varmistaa\n itselleen tietyn voiton tai h\u00e4vi\u00f6n. T\u00e4t\u00e4 varmistettua tulosta kutsutaan nollasummapelin arvoksi. Nollasummapelin tapahtumia voidaan kuvata voittomatriisin avulla, jossa esitet\u00e4\u00e4n pelaajien mahdolliset siirrot ja siirroista\n aiheutuvat tulokset.\n T\u00e4ss\u00e4 tutkielmassa tarkastellaan ensin erilaisia ratkaisutapoja kahden pelaajan nollasummapeleille. Tutkielmassa nollasummapelien ratkaisutavoista\n k\u00e4sitell\u00e4\u00e4n min-max-teoria, satulapisteteoria ja matriisilaskentaan pohjautuva teoria. minimax-teorissa pelin arvo lasketaan todenn\u00e4k\u00f6isyyksien avulla.\n Oletetaan, ett\u00e4 pelaaja pelaa tapahtuman A todenn\u00e4k\u00f6isyydell\u00e4 x ja tapahtuman B todenn\u00e4k\u00f6isyydell\u00e4 1 \u2212 x. Satulapisteteoriassa pelin arvo voidaan\n ratkaista suoraan voittomatriisista, jos kyseinen peli sis\u00e4lt\u00e4\u00e4 niin sanotun\n satulapisteen. Matriisilaskentaan perustuva menetelm\u00e4 on puolestaan nopea\n tapa ratkaista yksinkertainen nollasummapeli.\n T\u00e4m\u00e4n j\u00e4lkeen tutkielmassa k\u00e4sitell\u00e4\u00e4n yleissummapelej\u00e4. Yleissumma\npeleiss\u00e4 ei ole en\u00e4\u00e4 optimistrategioita. Molemmille pelaajille l\u00f6ytyy kuitenkin\n niin sanottua turvastrategioita, mutta ne eiv\u00e4t vastaa pelin tasapainoa. Yleissummapeleiss\u00e4 pelaajilta l\u00f6ytyy paras vaste toisen strategialle. Tutkielman\n lopussa Nashin tasapaino todistetaan Browerin kiintopistelauseen avulla.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.abstract", "value": "", "language": "en", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2025-06-16T10:20:33Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2025-06-16T10:20:33Z (GMT). No. of bitstreams: 0\n Previous issue date: 2025", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "37", "language": null, "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.language.iso", "value": "fin", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": null, "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "summapelit", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Nollasumma- ja yleissummapelit", "language": null, "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-202506165376", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Matematiikan ja tilastotieteen laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Mathematics and Statistics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": null, "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": null, "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Matematiikan opettajankoulutus", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Teacher education programme in Mathematics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.copyright", "value": "\u00a9 The Author(s)", "language": "fi", "element": "rights", "qualifier": "copyright", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "restrictedAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.yso", "value": "pelit", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matematiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "peliteoria", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "strategiat", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "strateginen suunnittelu", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "teoriat", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}, {"key": "dc.rights.accessrights", "value": "Tekij\u00e4 ei ole antanut lupaa avoimeen julkaisuun, joten aineisto on luettavissa vain Jyv\u00e4skyl\u00e4n yliopiston kirjaston arkistoty\u00f6semalta. Ks. https://kirjasto.jyu.fi/fi/tyoskentelytilat/laitteet-ja-tilat#autotoc-item-autotoc-2", "language": "fi", "element": "rights", "qualifier": "accessrights", "schema": "dc"}, {"key": "dc.rights.accessrights", "value": "The author has not given permission to make the work publicly available electronically. Therefore the material can be read only at the archival workstation at Jyv\u00e4skyl\u00e4 University Library (https://kirjasto.jyu.fi/fi/tyoskentelytilat/laitteet-ja-tilat#autotoc-item-autotoc-2.", "language": "en", "element": "rights", "qualifier": "accessrights", "schema": "dc"}]
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