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[{"key": "dc.contributor.author", "value": "Nousiainen, Henri", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2013-09-05T18:05:08Z", "language": "", "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2013-09-05T18:05:08Z", "language": "", "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2013", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.other", "value": "oai:jykdok.linneanet.fi:1279312", "language": null, "element": "identifier", "qualifier": "other", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/42067", "language": "", "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4m\u00e4n tutkielman tarkoituksena on osoittaa, ett\u00e4 jokaisella usean pelaajan yleisell\u00e4 summapelill\u00e4 on olemassa v\u00e4hint\u00e4\u00e4n yksi Nashin tasapaino. Lis\u00e4ksi osoitetaan, ett\u00e4 kahden pelaajan nollasummapeleiss\u00e4 Nashin tasapainojen mukaiset pelaajien voittojen odotusarvojen suuruudet ovat yksik\u00e4sitteiset, ja n\u00e4ytet\u00e4\u00e4n kuinka kyseiset odotusarvot voidaan ratkaista lineaarisen optimoinnin avulla.\r\n\r\nTutkielmassa m\u00e4\u00e4ritell\u00e4\u00e4n yleiset summapelit kolmikkoina, jotka muodostuvat \u00e4\u00e4rellisest\u00e4 m\u00e4\u00e4r\u00e4st\u00e4 pelaajia, joista jokaiseen on liitetty \u00e4\u00e4rellinen joukko. N\u00e4iden joukkojen alkioita kutsutaan pelaajien puhtaiksi strategioiksi. Kolmikon viimeisen j\u00e4senen muodostaa jokaiselle pelaajalle erikseen m\u00e4\u00e4ritelty kuvaus edell\u00e4 mainittujen strategioiden joukosta reaalilukujoukkoon. Kyseinen kuvaus, eli hy\u00f6tyfunktio, mallintaa pelaajan menestyst\u00e4 peliss\u00e4. Nollasummapeliksi peli m\u00e4\u00e4ritell\u00e4\u00e4n silloin, kun h\u00e4vi\u00e4j\u00e4t maksavat voittajille tietyn ennalta m\u00e4\u00e4r\u00e4tyn m\u00e4\u00e4r\u00e4n rahaa.\r\n\r\nPelitapaa, jossa pelaajat valitsevat peliss\u00e4 k\u00e4ytett\u00e4v\u00e4n strategian jollakin kiinnitetyll\u00e4 todenn\u00e4k\u00f6isyydell\u00e4, sanotaan pelaajan sekastrategiaksi. Kaikkien sekastrategioiden muodostama joukko osoitetaan konveksiksi. Konveksisuutta hyv\u00e4ksik\u00e4ytt\u00e4en todistetaan minimax-lause. Lauseen mukaan kahden pelaajan nollasummapeleiss\u00e4 pelaajien voitoilla on olemassa odotusarvoiset alarajat, jotka saavutetaan optimaalisiksi strategioiksi kutsuttujen sekastrategioiden avulla. Minimax-lauseen takaaman voiton alarajan sek\u00e4 optimaalisten strategioiden selvitt\u00e4miseksi k\u00e4ytet\u00e4\u00e4n simplex-algoritmia, jolla voidaan ratkaista lineaarisia optimointiteht\u00e4vi\u00e4.\r\n\r\nYleisiss\u00e4 summapeleiss\u00e4 optimaalisten strategioiden yleistyksien muodostamia pelaajien strategiajoukkoja kutsutaan Nashin tasapainoiksi. Toisin kuin kahden pelaajan nollasummapeleiss\u00e4, yleisiss\u00e4 summapeleiss\u00e4 Nashin tasapainojen mukaiset voittojen odotusarvojen arvot eiv\u00e4t aina ole yksik\u00e4sitteiset. Brouwerin kiintopistelauseen avulla n\u00e4ytet\u00e4\u00e4n, ett\u00e4 jokaisessa yleisess\u00e4 summapeliss\u00e4 on oltava v\u00e4hint\u00e4\u00e4n yksi Nashin tasapaino.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted using Plone Publishing form by Henri Nousiainen (hemiilno) on 2013-09-05 18:05:07.696042. Form: Pro gradu -lomake (1 tekij\u00e4) (https://kirjasto.jyu.fi/julkaisut/julkaisulomakkeet/pro-gradu-lomake-1-tekijae). JyX data:", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by jyx lomake-julkaisija (jyx-julkaisija@noreply.fi) on 2013-09-05T18:05:08Z\r\nNo. of bitstreams: 2\r\nURN:NBN:fi:jyu-201309052229.pdf: 504340 bytes, checksum: 59807918e3475f7e8b1d4e45d79430b4 (MD5)\r\nlicense.html: 107 bytes, checksum: a7d86e598caa500b1b433bbb9dc8ef1c (MD5)", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2013-09-05T18:05:08Z (GMT). No. of bitstreams: 2\r\nURN:NBN:fi:jyu-201309052229.pdf: 504340 bytes, checksum: 59807918e3475f7e8b1d4e45d79430b4 (MD5)\r\nlicense.html: 107 bytes, checksum: a7d86e598caa500b1b433bbb9dc8ef1c (MD5)\r\n Previous issue date: 2013", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "1 verkkoaineisto.", "language": null, "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": "algoritmit", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": 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