Spēļu teorijas pamati bipolāru struktūru kontekstā
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Latvijas Universitāte
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Abstract
Bakalaura darbs ir veltīts spēļu teorijas izvēlēto nodaļu analīzei. Darba sakumā tiek apskatīti n- personu spēļu teorijas pamatjēdzieni. To pielietojums tiek ilustrēts ar piemēriem. Tālāk tiek aprakstīta spēļu klasifikācija un pievērsta uzmanība bipolāro struktūru lomai spēļu modelī. Ar piemēru palīdzību ir parādītas galvenās atšķirības no klasiskajām spēlēm. Atsevišķi izdalīts jautājums par spēļu attēlošanas veidiem, izmantojot režģus. Beigās ir aplūkoti vieni no svarīgākajiem spēļu teorijas jēdzieniem – Šepli vektors un kodols.
Atslēgvārdi: matemātiskā spēle, koalīcija, spēles harakteristiskā funkcija, režģis, bipolārā struktūra, Šepli vektors, kodols.
Bachelor's work is devoted to the analysis of selected structures of the game theory. In the beginning of the work main notions of n-person game theory are given and illustrated with examples. After that some generalizations of classical games are described, a special attention is paid to the role of bipolar structures in modeling of games. By using examples the main differences between classic games and generalizations are shown. Especially is analyzed question about lattice role in the game theory. At the end a general survey of such main concepts of the game theory as Shapley vector and a core is given. Key words: mathematical game, coalition, game function, lattice, bipolar structure, Shapley vector, core.
Bachelor's work is devoted to the analysis of selected structures of the game theory. In the beginning of the work main notions of n-person game theory are given and illustrated with examples. After that some generalizations of classical games are described, a special attention is paid to the role of bipolar structures in modeling of games. By using examples the main differences between classic games and generalizations are shown. Especially is analyzed question about lattice role in the game theory. At the end a general survey of such main concepts of the game theory as Shapley vector and a core is given. Key words: mathematical game, coalition, game function, lattice, bipolar structure, Shapley vector, core.