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[{"key": "dc.contributor.author", "value": "Kangasniemi, Maaria", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2022-06-17T06:48:59Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2022-06-17T06:48:59Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2022", "language": "", "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/81835", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4m\u00e4n tutkielman tarkoituksena on luoda yleiskatsaus peliteoriaan ja sen soveltamiseen biologiassa. Tutkielmassa k\u00e4sitell\u00e4\u00e4n aluksi sellaisia kahden pelaajan pelej\u00e4, joissa toinen voittaa sen mink\u00e4 toinen h\u00e4vi\u00e4\u00e4. T\u00e4llaisissa nollasummapeleiksi kutsutuissa peleiss\u00e4 pelaajien voitot summautuvat siis nollaksi. Nollasummapelien yhteydess\u00e4 m\u00e4\u00e4ritell\u00e4\u00e4n molemmille pelaajille optimaaliset strategiat, jotka ovat parhaan mahdollisen voiton tuottavia strategioita. Optimaalisten strategioiden etsimisen j\u00e4lkeen esitell\u00e4\u00e4n Von Neumannin minimax-lause, jonka mukaan lopputuloksen kannalta ei ole v\u00e4li\u00e4, kumpi pelaaja optimoi ensin strategiansa. Sama voitto saavutetaan molemmissa tapauksissa, jolloin t\u00e4t\u00e4 kyseist\u00e4 voittoa kutsutaan my\u00f6s pelin arvoksi.\n\nNollasummapeleist\u00e4 siirryt\u00e4\u00e4n k\u00e4sittelem\u00e4\u00e4n yleisi\u00e4 summapelej\u00e4, joissa pelaajien voitot eiv\u00e4t nollasummapelien tapaan summaudu nollaan. Yleisten summapelien k\u00e4sittely aloitetaan kahden pelaajan tapauksilla, mink\u00e4 j\u00e4lkeen siirryt\u00e4\u00e4n useamman pelaajan peleihin. Sek\u00e4 kahden pelaajan ett\u00e4 useamman pelaajan summapeleihin tutustutaan aluksi esimerkkien avulla,\nmink\u00e4 j\u00e4lkeen muotoillaan Nashin tasapaino ja todistetaan t\u00e4h\u00e4n liittyv\u00e4 Nashin lause. Nashin tasapaino on sellainen pelaajien strategiayhdistelm\u00e4, josta yhdenk\u00e4\u00e4n pelaajan ei kannata yksipuolisesti poiketa. T\u00e4llainen tasapaino l\u00f6ytyy Nashin lauseen mukaan jokaisesta v\u00e4hint\u00e4\u00e4n kahden pelaajan pelist\u00e4.\n\nTutkielman viimeisess\u00e4 luvussa palataan j\u00e4lleen kahden pelaajan peleihin, joita tutkitaan biologisessa kontekstissa. T\u00e4llaisille peleille m\u00e4\u00e4ritell\u00e4\u00e4n evolutiivisesti tasapainoinen strategia, sek\u00e4 tuodaan esille sen yhteys Nashin tasapainoon. Apuna evolutiivisesti tasapainoisen strategian m\u00e4\u00e4ritelm\u00e4n k\u00e4sittelyss\u00e4 k\u00e4ytet\u00e4\u00e4n kahta yleist\u00e4 pelityyppi\u00e4, joista esitell\u00e4\u00e4n my\u00f6s esimerkit\nluonnonpopulaatioissa.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Miia Hakanen (mihakane@jyu.fi) on 2022-06-17T06:48:59Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2022-06-17T06:48:59Z (GMT). No. of bitstreams: 0\n Previous issue date: 2022", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "54", "language": "", "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "schema": "dc"}, {"key": "dc.language.iso", "value": "fin", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "nollasummapelit", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "yleiset summapelit", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Nashin tasapaino", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Nashin lause", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "evolutiivisesti tasapainoinen strategia", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Peliteorian perusteita ja sovelluksia evoluutioekologiassa", "language": "", "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-202206173444", "language": "", "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "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": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "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": "yvv.contractresearch.funding", "value": "0", "language": "", "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "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.oppiainekoodi", "value": "4041", "language": "", "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matematiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "pelit", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "peliteoria", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.format.content", "value": "fulltext", "language": null, "element": "format", "qualifier": "content", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}, {"key": "dc.type.okm", "value": "G2", "language": null, "element": "type", "qualifier": "okm", "schema": "dc"}]
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