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The objective of this research is to develop the framework of empirical-evidence equilibria (EEEs) in stochastic games. This framework was developed while attempting to design decentralized controllers using learning in stochastic games. The overarching goal is to enable a set of agents to control a dynamical system in a decentralized fashion. To do so, the agents play a stochastic game crafted such that its equilibria are decentralized controllers for the dynamical system. Unfortunately, there exists no algorithm to compute equilibria in stochastic games. One explanation for this lack of results is the full-rationality requirement of game theory. In the case of stochastic games, full rationality imposes that two requirements be met at equilibrium. First, each agent has a perfect model of the game and of its opponents strategies. Second, each agent plays an optimal strategy for the POMDP induced by its opponents strategies. Both requirements are unrealistic. An agent cannot know the strategies of its opponents; it can only observe the combined effect of its own strategy interacting with its opponents. Furthermore, POMDPs are intractable; an agent cannot compute an optimal strategy in a reasonable time. In addition to these two requirements, engineered agents cannot carry perfect analytical reasoning and have limited memory; they naturally exhibit bounded rationality. In this research, bounded rationality is not seen as a limitation and is instead used to relax the two requirements. In the EEE framework, agents formulate low-order empirical models of observed quantities called mockups. Mockups have unmodeled states and dynamic effects, but they are statistically consistent; the empirical evidence observed by an agent does not contradict its mockup. Each agent uses its mockup to derive an optimal strategy. 1Since agents are interconnected through the system, these mockups are sensitive to the specific strategies employed by other agents. In an EEE, the two requirements are weakened. First, each agent has a consistent mockup of the game and the strategies of its opponents. Second, each agent plays an optimal strategy for the MDP induced by its mockup. The main contribution of this dissertation is the use of modeling to study stochastic games. This approach, while common in engineering, had not been applied to stochastic games.

Pairs trading has been a popular statistical arbitrage strategy among hedge funds. One important research field in pairs trading is to maximize the return under differential constraints and assumptions. In this thesis, we develop two models to optimize the performance of pairs trading. In the static model, we find the analytic solution of optimal thresholds for pairs trading to maximize the long run profit per unit time. Comparison is made between the optimal rules we developed and the common practice. To overcome limitations of the static model, we extend our research to dynamic pairs trading, where a continuous time Markov chain is used to model the change of parameters. Our objective is to maximize the expected return in the finite horizon under the Constant Relative Risk Aversion (CRRA) utility. Numerical examples are presented to illustrate the impact of price limits, risk aversion rate and regime switching on consumers' investment decision.

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Bibliography: leaves 110-115. / iv, 115 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics, 1999

This dissertation presents the calibration-free image sensor modelling process applicable for localisation, such that these are robust to changes in environment and in sensor properties. The modelling process consists of two distinct parts, which are deterministic and stochastic techniques, and is achieved using mechanistic deconvolution, where the sensor???s mechanical and electrical properties are utilised. In the deterministic technique, the sensor???s effective focal length is first estimated by known lens properties, and is used to approximate the lens system by a thick lens and its properties. The aperture stop position offset???which is one of the thick lens properties???then derives a new factor, namely calibration-free distortion effects factor, to characterise distortion effects inherent in the sensor. Using this factor and the given pan and tilt angles of an arbitrary plane of view, the corrected image data is generated. The corrected data complies with the image sensor constraints modified by the pan and tilt angles. In the stochastic technique, the stochastic focal length and distortion effects factor are first approximated, using tolerances of the mechanical and electrical properties. These are then utilised to develop the observation likelihood necessary in recursive Bayesian estimation. The proposed modelling process reduces dependency on image data, and, as a result, do not require experimental setup or calibration. An experimental setup was constructed to conduct extensive analysis on accuracy of the proposed modelling process and its robustness to changes in sensor properties and in pan and tilt angles without recalibration. This was compared with a conventional modelling process using three sensors with different specifications and achieved similar accuracy with one-seventh the number of iterations. The developed model has also shown itself to be robust and, in comparison to the conventional modelling process, reduced the errors by a factor of five. Using area coverage method and one-step lookahead as control strategies, the stochastic sensor model was applied into a recursive Bayesian estimation application and was also compared with a conventional approach. The proposed model provided better target estimation state, and also achieved higher efficiency and reliability when compared with the conventional approach.

Thesis (Ph.D.)--York University, 2005. Graduate Programme in Mathematics and Statistics. / Typescript. Includes bibliographical references (leaves 69-75). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:NR11585

Thesis (Ph. D.)--University of Washington. / Bibliography: l. 111-123.

Thesis (Ph.D.) -- University of Adelaide, Dept. of Pure Mathematics, 1999. / Bibliography: leaves 110-115.

Thesis (Ph. D.)--University of North Texas, May, 2008. / Title from title page display. Includes bibliographical references.