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dc.contributor.advisorSzidarovszky, Ferencen_US
dc.contributor.authorEngel, Andrew
dc.creatorEngel, Andrewen_US
dc.date.accessioned2013-04-11T08:41:44Z
dc.date.available2013-04-11T08:41:44Z
dc.date.issued2002en_US
dc.identifier.urihttp://hdl.handle.net/10150/279955
dc.description.abstractInternational fishing as a special dynamic game will be analyzed, which is a combination of classical population dynamics and oligopoly theory. The interaction of the countries or firms is through market rules assuming that all markets are open to all participants. In addition, all fishing parties base their activity on the existing common fish stock. The available fish stock and the beliefs of the participants on the fish stock are the state variables. Depending on the possible symmetry of the fishing parties and on their behavior several alternative models will be formed. The classical competitive model will be first formulated and examined, and two special cases will be introduced. First, when the countries, or firms, are identical, second, when one country, or firm, is significantly different than the others. Next, we will assume that a grand coalition is formed, and the total profit of the industry is maximized. Finally, the partially cooperative case will be examined, in which each participant's objective function contains a certain proportion of the profits of the others in addition to its own profits. In all cases, a detailed mathematical model will be constructed, the equilibrium will be computed and the modified population dynamics rule will be formulated. For each case, I will determine the number of positive equilibria, the stability of which will be analyzed first based on the assumption that each participant has instantaneous information on the fish stock. However, there is always a time lag due to information collection and implementation. Since the delay is uncertain, continuously distributed time lags will be assumed. Under this assumption, the dynamic system will be described by Volterra-type integro-differential equations. The asymptotical behavior of the state trajectory will be analyzed by using linearization. Conditions for the local asymptotical stability will be first derived, and in the case of instability, special bifurcations, especially the birth of limit cycles, will be studied. In illustrating the theoretical, analytic results, simple computer studies will be presented.
dc.language.isoen_USen_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.subjectMathematics.en_US
dc.subjectEconomics, Theory.en_US
dc.subjectOperations Research.en_US
dc.titleDynamic market games with time delays and their application to international fishingen_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
thesis.degree.grantorUniversity of Arizonaen_US
thesis.degree.leveldoctoralen_US
dc.identifier.proquest3050316en_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineSystems and Industrial Engineeringen_US
thesis.degree.namePh.D.en_US
dc.identifier.bibrecord.b42724089en_US
refterms.dateFOA2018-06-15T05:25:19Z
html.description.abstractInternational fishing as a special dynamic game will be analyzed, which is a combination of classical population dynamics and oligopoly theory. The interaction of the countries or firms is through market rules assuming that all markets are open to all participants. In addition, all fishing parties base their activity on the existing common fish stock. The available fish stock and the beliefs of the participants on the fish stock are the state variables. Depending on the possible symmetry of the fishing parties and on their behavior several alternative models will be formed. The classical competitive model will be first formulated and examined, and two special cases will be introduced. First, when the countries, or firms, are identical, second, when one country, or firm, is significantly different than the others. Next, we will assume that a grand coalition is formed, and the total profit of the industry is maximized. Finally, the partially cooperative case will be examined, in which each participant's objective function contains a certain proportion of the profits of the others in addition to its own profits. In all cases, a detailed mathematical model will be constructed, the equilibrium will be computed and the modified population dynamics rule will be formulated. For each case, I will determine the number of positive equilibria, the stability of which will be analyzed first based on the assumption that each participant has instantaneous information on the fish stock. However, there is always a time lag due to information collection and implementation. Since the delay is uncertain, continuously distributed time lags will be assumed. Under this assumption, the dynamic system will be described by Volterra-type integro-differential equations. The asymptotical behavior of the state trajectory will be analyzed by using linearization. Conditions for the local asymptotical stability will be first derived, and in the case of instability, special bifurcations, especially the birth of limit cycles, will be studied. In illustrating the theoretical, analytic results, simple computer studies will be presented.


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