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This thesis is about game theory, its general application to different games, and its different notions. We are going to focus on how different solutions can be found depending on how we view the game in question. We will particularly focus on games where the information is incomplete. In order to do so, we will use a game named ”The battle of sexes” as a guide throughout the entire thesis. We will adapt that game to the different kinds of games we will talk about. The importance with game theory and why it is an interesting field of study is that it gives a way to mathematically understand and analyse various situations in different other fields and real life areas. In this thesis we will not go deeper into the applications of game theory, but will mostly focus on the mathematical part of the field, and understanding how to find different desired outcomes for a given game. We will primarily lay out the fundamentals of game theory, in order for the reader to understand the basic notions of a game, a equilibria, and have the necessary knowledge to explore the field. Guillermo Owen’s book Game theory covers the field in a wider sense than this thesis, and is an interesting lecture to broaden ones knowledge on game theory.

We study a stochastic game of hiring and firing in which the employee has a random capacity which is not directly observable for the employer, and only par- tially observable for the employee. In this setting, we derive a Nash Equilibrium of strategies.

The purpose of this paper is to present a new nonparametric test statistic for testing against ordered alternatives in a Balanced Incomplete Block Design (BIBD). This test will then be compared with the Durbin test which tests for differences between treatments in a BIBD but without regard to order. For the comparison, Monte Carlo simulations were used to generate the BIBD. Random samples were simulated from: Normal Distribution; Exponential Distribution; T distribution with three degrees of freedom. The number of treatments considered was three, four and five with all the possible combinations necessary for a BIBD. Small sample sizes were 20 or less and large sample sizes were 30 or more. The powers and alpha values were then estimated after 10,000 repetitions.The results of the study show that the new test proposed is more powerful than the Durbin test. Regardless of the distribution, sample size or number of treatments, the new test tended to have higher powers than the Durbin test.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第22984号 / 理博第4661号 / 新制||理||1669(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 藤 定義, 教授 佐々 真一, 教授 早川 尚男 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Ph. D.

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No description available.

This research was conducted to analyze the genetics of soybean mosaic virus (SMV) resistance in soybean [Glycine max (L.) Merr.] and to determine allelic relationships of SMV resistance genes and their interactions with SMV strain groups. In the first part of this study, the inheritance of SMV resistance in OX670 and 'Harosoy' was studied to determine the source and identity of the resistance gene/genes in OX670. Other researchers reported that OX670 possesses a single gene at a locus independent of Rsv1 and assigned the gene symbol Rsv2. Rsv2 was presumably derived from the cultivar 'Raiden'. However, later work showed that Raiden contains a single resistance gene at the Rsv1 locus, raising the possibility that the resistance gene in OX670 was not from Raiden. Harosoy and its derivatives make up much of the remaining pedigree of OX670. Results from crosses of OX670 with susceptible cultivars indicate that it contains two independent genes for SMV resistance. One is allelic to the Rsv1 locus, expresses resistance to SMV-G1 and G7 and is derived from Raiden. The other is allelic to the Rsv3 locus, expresses resistance to SMV-G7 but susceptibility to SMV-G1 and is derived from Harosoy. Therefore the Rsv2 locus does not appear to exist in OX670 or its ancestors. The presence of Rsv1 and Rsv3 makes OX670 resistant to all SMV strains from G1 through G7. The second study was conducted to investigate the inheritance and allelomorphic relationships of resistance gene(s) in 'Tousan 140' and 'Hourei', which were reported to carry single independent resistance genes when inoculated with the Japanese SMV strain C. Both of these lines exhibit resistance to strains SMV-G1 through G7. This inheritance study shows that Tousan 140 and Hourei each possess two resistance genes. One of the genes in Hourei confers resistance to SMV-G1 and G7 strains; the other gene confers susceptibility to SMV-G1 but resistance to SMV-G7. Allelism tests indicate that one of the genes in both Hourei and Tousan 140 is allelic to Rsv1, and the other is allelic to Rsv3. The two genes in Tousan 140 were separated into individual lines, R1 and R2. R1, most probably containing Rsv1, exhibited resistance to SMV-G1 through G3 but was susceptible to SMV-G5 through G7. Line R2, most likely possesses Rsv3 gene, was susceptible to SMV-G1 through G3 but resistant to SMV-G5 through G7. Therefore, presence of these two genes makes Tousan 140 resistant to SMV-G1 through G7. The objective of the third study was to investigate inheritance and allelomorphic relationships of SMV resistance in PI88788. PI88788 exhibits resistance to SMV-G1 through G7. Genetic analysis of our data reveals that SMV resistance in PI88788 is conferred by a single gene at a locus tentatively labeled 'Rsv4'. Expression of this gene in the homozygous state decreased accumulation rate and prevented vascular movement of SMV. In the heterozygous state vascular movement of the SMV was delayed but not prevented. / Ph. D.

M.S.