Dynamics of Spatial Game Theory Networks with Novel Modifications

Introduction: Advances in biotechnology have shed light on many biological processes. In biological networks, nodes are used to represent the function of individual entities within a system and have historically been studied in isolation. Network structure adds edges that enable communication between nodes. An emerging fieldis to combine node function and network structure to yield network function. One of the most complex networks known in biology is the neural network within the brain. Modeling neural function will require an understanding of networks, dynamics, andneurophysiology. It is with this work that modeling techniques will be developed to work at this complex intersection. Methods: Spatial game theory was developed by Nowak in the context of modeling evolutionary dynamics, or the way in which species evolve over time. Spatial game theory offers a two dimensional view of analyzingthe state of neighbors and updating based on the surroundings. Our work builds upon this foundation by studying evolutionary game theory networks with respect to neural networks. This novel concept is that neurons may adopt a particular strategy that will allow propagation of information. The strategy may therefore act as the mechanism for gating. Furthermore, the strategy of a neuron, as in a real brain, isimpacted by the strategy of its neighbors. The techniques of spatial game theory already established by Nowak are repeated to explain two basic cases and validate the implementation of code. Two novel modifications are introduced in Chapters 3 and 4 that build on this network and may reflect neural networks. Results: The introduction of two novel modifications, mutation and rewiring, in large parametricstudies resulted in dynamics that had an intermediate amount of nodes firing at any given time. Further, even small mutation rates result in different dynamics more representative of the ideal state hypothesized. Conclusions: In both modificationsto Nowak's model, the results demonstrate the network does not become locked into a particular global state of passing all information or blocking all information. It is hypothesized that normal brain function occurs within this intermediate range and that a number of diseases are the result of moving outside of this range.

Design and implementation of a 3D computer game controller using inertial MEMS sensors

Though 3D computer graphics has seen tremendous advancement in the past two decades, most available mechanisms for computer interaction in 3D are high cost and targeted for industry and virtual reality applications. Recent advances in Micro-Electro-Mechanical-System (MEMS) devices have brought forth a variety of new low-cost, low-power, miniature sensors with high accuracy, which are well suited for hand-held devices. In this work a novel design for a 3D computer game controller using inertial sensors is proposed, and a prototype device based on this design is implemented. The design incorporates MEMS accelerometers and gyroscopes from Analog Devices to measure the three components of the acceleration and angular velocity. From these sensor readings, the position and orientation of the hand-held compartment can be calculated using numerical methods. The implemented prototype is utilizes a USB 2.0 compliant interface for power and communication with the host system. A Microchip dsPIC microcontroller is used in the design. This microcontroller integrates the analog to digital converters, the program memory flash, as well as the core processor, on a single integrated circuit. A PC running Microsoft Windows operating system is used as the host machine. Prototype firmware for the microcontroller is developed and tested to establish the communication between the design and the host, and perform the data acquisition and initial filtering of the sensor data. A PC front-end application with a graphical interface is developed to communicate with the device, and allow real-time visualization of the acquired data.

Game-theoretic view on intermediated exchange

Intermediaries permeate modern economic exchange. Most classical models on intermediated exchange are driven by information asymmetry and inventory management. These two factors are of reduced significance in modern economies. This makes it necessary to develop models that correspond more closely to modern financial marketplaces. The goal of this dissertation is to propose and examine such models in a game theoretical context. The proposed models are driven by asymmetries in the goals of different market participants. Hedging pressure as one of the most critical aspects in the behavior of commercial entities plays a crucial role. The first market model shows that no equilibrium solution can exist in a market consisting of a commercial buyer, a commercial seller and a non-commercial intermediary. This indicates a clear economic need for non-commercial trading intermediaries: a direct trade from seller to buyer does not result in an equilibrium solution. The second market model has two distinct intermediaries between buyer and seller: a spread trader/market maker and a risk-neutral intermediary. In this model a unique, natural equilibrium solution is identified in which the supply-demand surplus is traded by the risk-neutral intermediary, whilst the market maker trades the remainder from seller to buyer. Since the market maker’s payoff for trading at the identified equilibrium price is zero, this second model does not provide any motivation for the market maker to enter the market. The third market model introduces an explicit transaction fee that enables the market maker to secure a positive payoff. Under certain assumptions on this transaction fee the equilibrium solution of the previous model applies and now also provides a financial motivation for the market maker to enter the market. If the transaction fee violates an upper bound that depends on supply, demand and riskaversity of buyer and seller, the market will be in disequilibrium.

Optimal game theoretic distributed control methodologies in small scale power systems

This dissertation presents the competitive control methodologies for small-scale power system (SSPS). A SSPS is a collection of sources and loads that shares a common network which can be isolated during terrestrial disturbances. Micro-grids, naval ship electric power systems (NSEPS), aircraft power systems and telecommunication system power systems are typical examples of SSPS. The analysis and development of control systems for small-scale power systems (SSPS) lacks a defined slack bus. In addition, a change of a load or source will influence the real time system parameters of the system. Therefore, the control system should provide the required flexibility, to ensure operation as a single aggregated system. In most of the cases of a SSPS the sources and loads must be equipped with power electronic interfaces which can be modeled as a dynamic controllable quantity. The mathematical formulation of the micro-grid is carried out with the help of game theory, optimal control and fundamental theory of electrical power systems. Then the micro-grid can be viewed as a dynamical multi-objective optimization problem with nonlinear objectives and variables. Basically detailed analysis was done with optimal solutions with regards to start up transient modeling, bus selection modeling and level of communication within the micro-grids. In each approach a detail mathematical model is formed to observe the system response. The differential game theoretic approach was also used for modeling and optimization of startup transients. The startup transient controller was implemented with open loop, PI and feedback control methodologies. Then the hardware implementation was carried out to validate the theoretical results. The proposed game theoretic controller shows higher performances over traditional the PI controller during startup. In addition, the optimal transient surface is necessary while implementing the feedback controller for startup transient. Further, the experimental results are in agreement with the theoretical simulation. The bus selection and team communication was modeled with discrete and continuous game theory models. Although players have multiple choices, this controller is capable of choosing the optimum bus. Next the team communication structures are able to optimize the players’ Nash equilibrium point. All mathematical models are based on the local information of the load or source. As a result, these models are the keys to developing accurate distributed controllers.