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Chandrasekar, SwathiAn Engage or Retreat differential game with Mobile Agents
Master of Science in Electrical Engineering (MSEE), Wright State University, 2017, Electrical Engineering
The thesis is aimed at developing optimal defensive strategies that dissuade an attacker from engaging a defender while simultaneously persuading the attacker to retreat. A two-player Engage or Retreat differential game is developed in which one player represents a mobile attacker and the other player represents a mobile defender. Both players are modeled as massless particles moving with constant velocity. The choice to terminate the game in engagement or retreat lies with the attacker. The defender indirectly influences the choice of the attacker by manipulating the latter's utility function. In other words, the defender co-operates with the attacker so that retreat appears to be the best option available. The solution to the differential game is obtained by solving two related optimization problems namely the Game Of Engagement and Optimal Constrained Retreat. In the Game of Engagement, the attacker terminates the game by capturing the defender.In the Optimal Constrained Retreat, a value function constraint is imposed which deters the attacker's retreat trajectory from entering into a region where it may lead to engagement. Such regions where constrained retreat occurs are known as escort regions. The solutions to these two problems are used to construct the global equilibrium solutions to the Engage or Retreat differential game.The global equilibrium solution divides the admissible state space into two regions that contain qualitatively different equilibrium control strategies. Numerical solutions are included to support the theory presented.

Committee:

Zachariah E. Fuchs, Ph.D. (Advisor); Luther Palmer, Ph.D. (Committee Member); Xiadong (Frank) Zhang, Ph.D. (Committee Member)

Subjects:

Electrical Engineering

Keywords:

Differential game theory; Optimal control; Game theory; Nash equilibrium;

Bichescu, Bogdan CristianPerformance Analysis of Decentralized Supply Chains: Considerations of Channel Power and Subcontracting
PhD, University of Cincinnati, 2006, Business Administration : Quantitative Analysis
Our work, comprising three essays, examines supply chain agent performance in a variety of decentralized systems under both stochastic and deterministic customer demand. In the first two essays, we develop models for both periodic and continuous review inventory policies when the decision-making rights are split between a supplier and a retailer. The second essay also examines a vendor-managed inventory (VMI) agreement. The last essay proposes a novel approach to workload balancing for a company that faces deterministic nonstationary demand and has little, or no, ability to hold inventory. The first two essays seek to answer the following research questions: 1) when does decentralized decision making result in the greatest loss in supply chain performance and 2) what effect does the distribution of channel power have on system and individual agent performance. Channel power here refers to an agent’s relative ability to control the decision making process and is modeled using a game-theoretic framework. We characterize optimal policies where possible and we use numerical analysis to generate insights. We find that, from a supply chain perspective, asymmetric power decision structures lead to better performance and customer service. Surprisingly, we identify cases where the lowest costs are incurred at the agent level when the agent is a follower and not a leader in the Stackelberg game. Our analysis also identifies the environmental conditions when the penalty from decentralized decision making is largest and shows that concentrating channel power with one of the agents can represent a viable alternative to coordination mechanisms, when the latter are costly to implement. In the third essay, we use Fourier analysis and Walsh basis functions to decompose an input workload profile into a portfolio of recurrent insourcing and outsourcing contracts to better achieve some desired constant workload level. In addition, we develop mathematical programs based on principles from goal programming formulations to answer important practical questions such as: 1) how should a company create a portfolio of contracts to balance workload over time; 2) how should the portfolio be customized to reflect special needs with respect to time, volume, etc., 3) what is the benefit of holding inventory as a supplement to subcontracting.

Committee:

Dr. Michael Fry (Advisor)

Keywords:

Supply Chain Management; Channel Power; Subcontracting; Workload Balancing; Fourier Analysis; Game Theory; Vendor-Managed Inventory

Perkins, Kyle EricLifesigns: Successful Storytelling in Open-World Games
Bachelor of Science (BS), Ohio University, 2010, Media Arts and Studies
Due to their unique capability to be altered by those experiencing them, games have the potential to tell a more immersive story and evoke a stronger emotional response than traditional entertainment media. Moreover, it is in the nature of open world games to facilitate the most personal and immersive gameplay and narrative experience. Admittedly, sacrifices have to be made on both sides in order for the best match of gameplay and narrative to be found. By studying the shortcomings of other sandbox games, and carefully balancing modular developer controlled content with player freedom, or at least the appearance of player freedom, this potential can be attained.

Committee:

Beth Novak (Advisor)

Keywords:

video game; computer game; digital game; game design; open-world; rpg; role playing game; RPG; sandbox; gameplay; narrative; design document; lifesigns; game theory; story in games; immersive; immersion

Kozy, James E.A Game-Theoretic Analysis of Home Court Advantage and Optimal Offensive Strategy in Basketball
Master of Science, University of Akron, 2011, Applied Mathematics
This paper intends to construct a game-theoretic model with which to analyze the impact of home court advantage on a visiting team's offensive strategy, specifically the balance between two and three-point shots attempted. We develop the Home Court Advantage Model to assist in our analysis. The model determines the optimal offensive strategy when one takes into account parameters that reflect the changes in offensive output by a basketball team when playing on the road. In this case this is manifested in lower shooting percentages, particularly on two-point shot attempts. The model also accounts for statistical data suggesting that three-point shot percentages are not affected as dramatically by home court advantage as are two-point shot percentages. We draw several conclusions, including that as a team's two-point shot percentage decreases, the team should actually shoot more two-point shots to optimize their overall offensive efficiency. We conclude our model with a study of the home court advantage of the 2008-2009 Cleveland Cavaliers, applying the model specifically to post-season play.

Committee:

Gerald Young, Dr. (Advisor); Curtis Clemons, Dr. (Committee Co-Chair); Timothy Norfolk, Dr. (Advisor)

Subjects:

Mathematics

Keywords:

Game Theory; Nash Equilbrium; Basketball

Kimmel, JasonSimple Games on Networks
BA, Oberlin College, 2011, Computer Science
In the same way that traditional game theory captured the minds of economists and allowed complex problems to be studied using simple models, so have games on networks come to be used in computer science. In particular, previous work has focused on extending a two-player base game M over a network G by having each vertex in G chose a strategy from the base game and play it simultaneously against all adjacent nodes. Similarly, the utility for each vertex becomes the sum of the utility of that node in each of the games it plays against its neighbors. The resulting networked game is called M + G. This paper seeks to augment the body of existing work by studying a few similar networked games and finding key characteristics like the existence of Nash equilibria, the price of anarchy, the price of stability, the convergence speed of best response dynamic, and the difficulty of finding the optimal solution. We also reproduce the result that the class of exact potential games is isomorphic to the class of congestion games with a proof that is drastically more readable than the original. Co-authored by Tom Wexler.

Committee:

Tom Wexler, PhD (Advisor)

Subjects:

Computer Science; Mathematics

Keywords:

game theory; graphs; theoretical computer science

Zitnik, Mary E.A Game Theoretic Approach to Advertising Strategy
Master of Science, University of Akron, 2010, Applied Mathematics
Developing an effective advertising strategy is a key component for a firm to be successfully competitive. This paper uses game theory to examine a duopolistic setting in which two firms have the same product. One firm has the higher price and larger market share and both want to compete through advertising. Assuming subgame perfection, we use backward induction to solve the game. We consider how changes in pricing, advertising expenditures and advertising effectiveness affect profit and market shares. We also investigate how changes in the size of the market affect the behavior of all factors. We find that as either firm becomes more effective, the other must respond through pricing and/or advertising. When both firms are highly effective in their advertising, it becomes more beneficial for neither firm to advertise. We also find that while the size of the market will affect the overall advertising expenditures, it will only minimally affect the price per unit and profit per unit to either firm.

Committee:

Gerald Young, Dr. (Advisor); Curtis Clemons, Dr. (Advisor); Timothy Norfolk, Dr. (Advisor)

Subjects:

Business Administration; Marketing

Keywords:

Game Theory; Advertising; Advertising Strategy; Marketing

Krisanda, Sarah JaneKing Abdullah's Game: Autocrats and Globalized Interests
BA, Kent State University, 2013, College of Arts and Sciences / Department of Political Science
King Abdullah of Saudi Arabia is an autocrat facing increasingly globalized political dynamics. Instability in the Middle East calls into question the sustainability of his regime, but by balancing the interests and demands of both his domestic constituents and the international community, King Abdullah has maintained his country's stability. I propose a new model with which political scientists can understand how a leader reacts to transnational political demands. The model will go beyond current game theory analysis to account for the globalization of actors' interests. King Abdullah's Saudi Arabia illustrates a unique application of this model.

Committee:

Julie Mazzei, Dr. (Advisor); Joshua Stacher, Dr. (Committee Member); Patricia Dunmire, Dr. (Committee Member); Sarah Newman, Dr. (Committee Member)

Subjects:

International Relations; Political Science

Keywords:

political science; international relations; strategy; game theory; globalization; Saudi Arabia; King Abdullah; Autocrat; Authoritarian

Hughes, MatthewPrice Signaling in a Two-Market Duopoly
Master of Science, University of Akron, 2016, Applied Mathematics
Within any industry, firms typically produce related products over multiple subsequent periods in an attempt to build consumer loyalty and achieve continued sales. Apple releases new iPhones and car companies produce new models every year, relying on consumers believing each new product is of high quality. Firms rely on the spillover effects from previous markets, where firms are able to more easily demonstrate their product's quality to the consumers before purchase. The goal is to find a range of prices which allows the high quality firm to distinguish its type to consumers via the price pH and if spillover effects in subsequent markets can occur. We look at a duopoly of two firms, of high and low qualities, where each firm produces a product in an initial market and a second, related product in a subsequent market. Using each firm's expected profits, based on Bayesian probabilities, we analyze a firm's mimicking strategy to find the range of pH that allows for a separating equilibrium and spillover effects. In a second market where firms are the same qualities as in the first market, the high quality firm experiences spillover effects and can signal its quality with a lower price than in the first market. When firms change qualities in the second market, no spillover effect occurs and the newly high quality firm must increase pH from the previous market in order to separate.

Committee:

Francesco Renna, Dr. (Advisor); Stefan Forcey, Dr. (Advisor); Curtis Clemons, Dr. (Committee Member)

Subjects:

Applied Mathematics; Economic Theory; Economics; Management; Mathematics

Keywords:

signaling; price; duopoly; game theory; economics; mathematics; equilibrium; bayesian game

Magner, MarkThe Evolutionary Paradox: Using Nash Equilibria to Understand Microbial Social Interactions
Bachelor of Arts, Miami University, 2005, College of Arts and Sciences - Microbiology
Because microbes are colonial by nature, selective pressures such as limited resource availability affect colonial populations as a whole. For example, Escherichia coli strains will enter a slowed metabolic state at stationary phase induced by limited resources. Superficially, this selective pressure seems to merely affect each cell individually because if each cell entered a rest state, it would be more likely to survive through the time of famine. The fact remains, however, that if one lone cell were to ‘cheat’ by entering the rest state later than the other cells, it could benefit from some of the remaining resources and reproduce normally for some n generations. Use of Nash equilibria allows one to understand this inherent incentive for the hypothetical cheater cell to develop. Upon understanding the dynamics of ‘cheating’, one can quickly see that even complex mechanisms like enhanced clonality or induced apoptosis could arise in intra-species examples to curb cheating and that reward/punishment models could develop in inter-species examples to limit cheating at any moment x.

Committee:

Matthew Fields (Advisor)

Subjects:

Biology, Microbiology

Keywords:

Nash equilibrium; game theory; E. coli; rhizobia

Angelis, John N.Decision Models for Growing Firms: Obstacles and Opportunities
Doctor of Philosophy, Case Western Reserve University, 2009, Operations

This dissertation is comprised of three essays. The first, “Optimal Marketing Strategies for Competing New Ventures in a Nascent Industry” has been originally accepted for publication in the International Journal of Entrepreneurship and Innovation Management. It considers new ventures that are pioneering a nascent industry. Just as their established counterparts do, these ventures strive to increase profit by acquiring sales of rival new ventures. However, new ventures can also grow by attracting unrealized sales. The essay investigates the resulting tradeoff in marketing expenditures via a differential game between two competing new ventures. Extensive numerical analysis suggests that an increase in a new venture’s unit profit margin, effectiveness in gaining new sales, or initial sales level, but a decrease in sales decay, may cause a positive spillover for its rival.

The second essay, “Integrating Customer Preferences with Technology Adoption and Product Redesign in a Duopoly” focuses on a firm’s decision to add a technology that changes how customers interact with the firm’s product. We formulate a two-stage game-theoretic framework to investigate the conditions under which two competing firms should add a technology, and how a firm that adopts technology should redesign its product to incorporate technology. We investigate how prospective and existing customers’ preferences for the technology and the product-technology fit should affect the firm’s adoption and product redesign decisions. We articulate conditions for the existence of a Nash equilibrium where both firms add technology, and demonstrate that customer preferences for technology standardization may actually impede standardization.

The third essay, “New Product Positioning for a Segmented Market” focuses on how competing firms should set price and quality for a new technologically-advanced product. The targeted market is comprised of two customer segments that differ in innovativeness. We analyze a closed-loop Stackelberg game with perfect information and find that a late entrant’s ability to challenge an incumbent is most affected by production cost. If a firm has a large enough production cost advantage relative to its rival, it can attract customers from both segments; however, such a firm should not necessarily be the first mover.

Committee:

Moren Levesque (Advisor); Lisa Maillart (Committee Member); Bo Carlsson (Committee Member); Danny Solow (Committee Member)

Subjects:

Management; Operations Research; Technology

Keywords:

Technology Management; Entrepreneurship; Innovation; Technology Adoption; Game Theory; Growing Firms; Technology Selection; Differential Games; New Ventures

Noble, Gregory DanielInventory Systems with Transshipments and Quantity Discounts
Doctor of Philosophy (PhD), Wright State University, 2012, Engineering PhD
This research advances knowledge in the area of inventory systems and the relationship between competing retailers and suppliers of goods. This dissertation studies retailers that face uncertainty in the demand for goods and who purchase the goods from a single supplier. A game theoretic methodology is developed to analyze supplier pricing decisions and retailer quantity decisions and interactions in a competitive transshipment system where quantity discounts are offered. The system studied differs from previous work in the subject by introducing quantity discounts from supplier to retailer into a system of competitive retailers that transship stock. Analysis of these systems focuses on the identification of potential equilibrium actions by the retailers and how the supplier can influence the retailers through its choices. This dissertation identifies new criteria for stability within these systems. Understanding stable relationships is critical to the supplier’s ability to influence the system to achieve coordinated, optimal performance. In a one supplier, two retailer transshipment system, all entities can achieve larger expected profits when the supplier offers the retailer a pricing contract with a two-block tariff quantity discount rather than a standard fixed pricing contract. Additionally, the supplier pricing decisions are examined. This analysis leads to a set of rules for setting the pricing contract parameters that maximize the supplier’s expected profit. Three quantity discount schemes are examined in the two retailer transshipment system: a two-block tariff, a two-part tariff, and an all-units discount. The two-block tariff discount results in the largest expected profit and greatest flexibility for the supplier. The topic is further researched through the examination of a three retailer system with transshipment and quantity discounts where there is a central retailer. The examination of this system shows the potential value to each entity of one of the retailers entering into a transshipment contract with another retailer.

Committee:

Frank Ciarallo, Ph.D. (Advisor); Xinhui Zhang, Ph.D. (Committee Member); Pratik Parikh, Ph.D. (Committee Member); James Hamister, Ph.D. (Committee Member); Steven Harrod, Ph.D. (Committee Member)

Subjects:

Engineering; Industrial Engineering; Operations Research

Keywords:

Transshipment; Inventory Systems; Quantity Discounts; Game Theory; Newsvendor Model; Nash Equilibrium

Pedersen, Frank AlfredVariation of monetary reward and social involvement in a two-person game /
Doctor of Philosophy, The Ohio State University, 1960, Graduate School

Committee:

Not Provided (Other)

Subjects:

Psychology

Keywords:

Game theory

Lutzker, Daniel RobertInternationalism, sex role and amount of information as variables in a two-person, non-zero sum game /
Doctor of Philosophy, The Ohio State University, 1959, Graduate School

Committee:

Not Provided (Other)

Subjects:

Psychology

Keywords:

Factor analysis;Game theory;Personality

Chattopadhyay, DipayanDistributed Decision Tree Induction Using Multi-agent Based Negotiation Protocol
MS, University of Cincinnati, 2014, Engineering and Applied Science: Computer Science
Exponential growth of data and its distributed nature has made data analysis tasks difficult. Most distributed databases are also sensitive to moving data between different data sites due to privacy and security concerns. Learning of decision trees from distributed databases has been implemented as cases of cooperative multi-agent systems that provide summaries needed from the participating datasets. Most such algorithms also fail to create intermediate models, classify minority instances in skewed databases, and provide classification accuracies that are not at par with accuracies from centralized data. This work proposes a novel approach, based on competing multiple agents that engage in game-theoretic bidding, for inducing decision trees from distributed databases without exchanging any data summaries with other databases. We demonstrate the efficacy and validity of our approach with a number of datasets.

Committee:

Raj Bhatnagar, Ph.D. (Committee Chair); Karen Davis, Ph.D. (Committee Member); Chia Han, Ph.D. (Committee Member); Paul Talaga, Ph.D. (Committee Member)

Subjects:

Computer Science

Keywords:

Game theory;Negotiation;Multi-Agent Systems;Distributed;Decision Trees;Rule based induction

McGough, Erin PatrickAnalyzing the Relationship Between Player Personnel and Optimal Mixed Strategies in American Football
Master of Science, University of Akron, 2009, Mathematics
The purpose of this paper is to explore how the optimal mix of run and pass is affected by a change in player personnel in American football. To investigate this notion, we construct a model under the hypothesis that the offense has recently acquired a proven quarterback that will increase the production of the passing game. We then solve the game, and in the process construct Nash equilibrium functions that depend on the influence of the new quarterback. Lastly, as an example, we use empirical data and model results to examine how the addition of Jay Cutler impacts the mix of run and pass for the 2009 Chicago Bears.

Committee:

Gerald Young, Dr. (Advisor); Curtis Clemons, Dr. (Advisor); Michael Ferrara, Dr. (Advisor)

Subjects:

Mathematics

Keywords:

game theory; football; optimal mix; free agency

Konovalov, ArkadyEssays in Behavioral Economics
Doctor of Philosophy, The Ohio State University, 2017, Economics
In this thesis, I show how non-choice data (response times and gaze data) can be used in economics, specifically in the individual preferences domain, strategic settings, and value learning. Particularly, the first two chapters demonstrate how response times (RTs) can be used to infer individual preferences or and thus can be considered and/or manipulated in strategic settings. In the last chapter, I use gaze data to identify attention effects in reinforcement learning. In the first chapter of the dissertation, “Revealed Indifference: Using Response Times to Infer Preferences”, response time data are used to estimate individual utility functions. Revealed preference is the dominant approach for inferring preferences, but it relies on discrete, stochastic choices. The choice process also produces response times which are continuous and can often be observed in the absence of informative choice outcomes. Moreover, there is a consistent relationship between RTs and strength-of-preference, namely that people make slower decisions as they approach indifference. This relationship arises from optimal solutions to sequential information sampling problems. We investigate several ways in which this relationship can be used to infer preferences when choice outcomes are uninformative or unavailable. We show that RTs from a single binary-choice problem are enough to usefully rank people according to their risk preferences. The second chapter, titled “On The Strategic Use of Response Times”, further investigates the role of response times in strategic settings. We designed a laboratory experiment with a the bargaining game has two periods, where a seller with zero marginal costs makes two price offers to a buyer with a value randomly drawn from a uniform distribution, and profits are discounted if a deal is made in the second period. We found that the RTs were negatively correlated with the buyers’ values: low value buyers were faster to say “no” in the first round. In the second part of the experiment, participants were able to correctly infer the values and earn higher profits. In the final part of the experiment, subjects in the role of buyers were more likely to pick an offer that was made in response to a faster RT, as if they were manipulating their RTs to get better offers. The last chapter, “Attention Effects in Model-Based and Model-Free Reinforcement Learning” uses eye-tracking to study learning strategies known as model-free and model-based value learning; the former is mere reinforcement of previously rewarded actions and the latter is a forward-looking strategy that involves evaluation of action-state transition probabilities. Prior work has used neural data to argue that both model-based and model-free learners implement a value comparison process at trial onset, but model-based learners assign more weight to forward-looking computations. Using eye-tracking, we report evidence for a different interpretation of prior results: model-based subjects make their choices prior to trial onset. In contrast, model-free subjects tend to ignore model-based aspects of the task and instead seem to treat the decision problem as a simple comparison process.

Committee:

Ian Krajbich (Advisor); Paul Healy (Committee Member); John Kagel (Committee Member)

Subjects:

Economics

Keywords:

economics, bargaining, response times, game theory, learning, model-based learning, reinforcement learning

Yoon, YeochangEssays on Information Economics
Doctor of Philosophy, The Ohio State University, 2016, Economics
In the first chapter, I develop a theoretical model to investigate why and how information senders are biased. In this paper, a rational Bayesian consumer decides whether or not to purchase a new product. His utility from purchasing depends on the quality of the product and his idiosyncratic preference for the product. Before making his decision, the consumer can receive a signal of the product's quality by actively choosing an information sender. An information sender would like to attract more consumers by providing more accurate signals, but it is costly. In the paper, an information structure consists of a probability of recommending the product when the quality is high and that of not recommending it when the quality is low. An information sender's bias is defined as the difference between the accuracy of the signal in the high quality state and that in the low quality state. On the other hand, the sender's overall accuracy depends on the sum of the accuracy of the signals. A consumer does not have direct utility from biased information but it is shown that his expected utility from an information sender is increasing in the sender's bias when the consumer subscribe to a like-minded information sender holding the sender's overall accuracy constant. The indirect demand for information bias gives an incentive to the sender to be biased. As a result, no matter how many information senders are in the market, they have an incentive to be biased. Moreover, as more information senders are potentially able to enter the market, overall accuracy is weakly increasing and bias is weakly decreasing due to competition effects. In the second chapter, I explore a rational social learning model in which a consumer can observe other consumers' ratings for a product and past purchase decisions. In this paper, I demonstrate how ratings work as an additional information source in a social learning model, and investigate whether or not additional ratings information improves learning. It is common in the social learning literature to model the history of the purchase as the observable, but in this paper, product ratings are also incorporated as an additional source of information; consumers can observe the history of both purchase decisions and ratings. Ratings provide additional information about how previous buyers felt about the product they purchased. I find that with ratings, low quality products are not chosen, but high quality products may also be ignored which causes incorrect herds in the long-run. Interestingly, the probability of high quality products being ignored is not monotonic in the accuracy of ratings. The more accurate information might lower the probability of making correct decisions in the long-run. When consumers believe that ratings are more accurate than private signals, they rely more on ratings and ignore other information sources. In that case, a small number of negative ratings can prevent later buyers from purchasing high quality products. Moreover, the probability of incorrect herds with high quality products might be higher in an environment with ratings, even when the ratings are more accurate than private signals. These results imply that the additional information source does not always guarantee better learning. Finally, the third chapter studies the case in which observing others actions is noisy in diffusion of innovations. I consider a three stage game where only finite number of early adopters receive private signals about the state of nature and make their decision about whether to adopt the new technology in the first stage. In the second stage, all remaining decision makers observe the early adopters' decisions, but the observation is noisy. I show how the noisy observation affects the dynamics in diffusion of innovations. The dynamics are related to inefficiency of the model because it is desirable that the majority adopts the new technology earlier when its quality is good. The inefficiency tends to decrease as agents can observe others' actions with higher probability, however, it might locally increase in some areas.

Committee:

James Peck (Advisor); Paul J. Healy (Committee Member); Huanxing Yang (Committee Member)

Subjects:

Economics

Keywords:

Economics; Game Theory; Information Economics; Media Economics; Social Learning; Technology Adoption

Rossin, SamuelSteiner Tree Games
BA, Oberlin College, 2016, Computer Science
Prize-collecting Steiner tree is a network design problem in which a utility provider located at some position in a graph attempts to construct a network (subtree) of maximum profit based on the value of the vertices in the graph and the costs of the edges. I consider three network formation games where the players represent competing providers attempting to build networks in the same market. These games seek to preserve the key feature of Prize-Collecting Steiner tree, namely that players must each build a subtree that attempts to include customers who are of high value or are easy to reach. I analyze the price of anarchy and price of stability of each of these games.

Committee:

Kevin Woods (Advisor)

Subjects:

Computer Science

Keywords:

prize-collecting Steiner tree;algorithmic game theory;Steiner tree games;facility location;Steiner tree;Nash equilibrium;price of anarchy;price of stability;PoA;PoS;network design games;

Wang, XiaohuiSingularity Theory of Strategy Functions Under Dimorphism Equivalence
Doctor of Philosophy, The Ohio State University, 2015, Mathematics
We study dimorphisms by applying adaptive dynamics theory and singularity theory based on a new type of equivalence relation called dimorphism equivalence. Dimorphism equivalence preserves ESS singularities, CvSS singularities, and dimorphisms for strategy functions. Specifically, we classify and compute normal forms and universal unfoldings for strategy functions with low codimension singularities up to dimorphism equivalence. These calculations lead to the classification of local mutual invasibility plots that can be seen in systems of two parameters. This problem is complicated because the allowable coordinate changes are restricted to those that preserve dimorphisms and the singular nature of strategy functions; hence the singularity theory applied in this thesis is not a standard one.

Committee:

Martin Golubitsky, Dr. (Advisor); Yuan Lou, Dr. (Committee Member); King-Yeung Lam, Dr. (Committee Member); Rephael Wenger, Dr. (Committee Member)

Subjects:

Evolution and Development; Mathematics

Keywords:

Singularity Theory, Adaptive Dynamics, Evolutionary Game Theory

Zunis, Anthony AlanA Game Theoretic Analysis and Simulation of Non-Incumbent Elections
Master of Science, University of Akron, 2014, Applied Mathematics
We develop a model that provides evidence to explain the changes in policy platform during a non-incumbent, two candidate election. We propose a modification to a well known model presented by Hummel [1], and predict the behavior of candidates in a selection of varying scenarios. We show voter support convergence for all models, and show evidence for convergence for bimodal voter ideology distributions through numerical simulations. We conclude that candidates adjust strategies in order to seek the highest local concentration of voters.

Committee:

Stefan Forcey, Dr. (Advisor); Francesco Renna, Dr. (Advisor); Gerald Young, Dr. (Committee Member); Curtis Clemons, Dr. (Committee Member)

Subjects:

Applied Mathematics; Economic Theory; Economics; Mathematics; Political Science; Public Policy

Keywords:

game theory; political science; elections; electoral spatial models; median voter theorem

Pavlic, Theodore PaulDesign and Analysis of Optimal Task-Processing Agents
Doctor of Philosophy, The Ohio State University, 2010, Electrical and Computer Engineering

This dissertation is given in two parts followed by concluding remarks. The first three chapters describe the generalization of optimal foraging theory for the design of solitary task-processing agents. The following two chapters address the coordinated action of distributed independent agents to achieve a desirable global result. The short concluding part summarizes contributions and future research directions.

Optimal foraging theory (OFT) uses ecological models of energy intake to predict behaviors favored by natural selection. Using models of the long-term rate of energetic gain of a solitary forager encountering a variety of food opportunities at a regular rate, it predicts characteristics of optimal solutions that should be expressed in nature. Several engineered agents can be modeled similarly. For example, an autonomous air vehicle (AAV) that flies over a region encounters targets randomly just as an animal will encounter food as it travels. OFT describes the preferences that the animal is likely to have due to natural selection. Thus, OFT applied to mobile vehicles describes the preferences of successful vehicle designs.

Although OFT has had success in existing engineering applications, rate maximization is not a good fit for many applications that are otherwise analogous to foraging. Thus, in the first part of this dissertation, the classical OFT methods are rediscovered for generic optimization objectives. It is shown that algorithms that are computationally equivalent to those inspired by classical OFT can perform better in realistic scenarios because they are based on more feasible optimization objectives. It is then shown how the design of foraging-like algorithms provides new insight into behaviors observed and expected in animals. The generalization of the classical methods extracts fundamental properties that may have been overlooked in the biological case. Consequently, observed behaviors that have been previously been called irrational are shown to follow from the extension of the classical methods.

The second part of the dissertation describes individual agent behaviors that collectively result in the achievement of a global optimum when the distributed agents operate in parallel. In the first chapter, collections of agents that are each similar to the agents from the early chapters are considered. These agents have overlapping capabilities, and so one agent can share the task processing burden of another. For example, an AAV patrolling one area can request the help of other vehicles patrolling other areas that have a sparser distribution of targets. We present a method of volunteering to answer the request of neighboring agents such that sensitivity to the relative loading across the network emerges. In particular, agents that are relatively more loaded answer fewer task-processing requests and receive more answers to their own requests. The second chapter describes a distributed numerical optimization method for optimization under inseparable constraints. Inseparable constraints typically require some direct coordination between distributed solver agents. However, we show how certain implementations allow for stigmergy, and so far less coordination is needed among the agents. For example, intelligent lighting, which maintains illumination constraints while minimizing power usage, is one application where the distributed algorithm can be applied directly.

Committee:

Kevin M. Passino (Advisor); Andrea Serrani (Committee Member); Atilla Eryilmaz (Committee Member)

Subjects:

Animals; Biology; Computer Science; Ecology; Economics; Electrical Engineering; Engineering; Mathematics; Robots; Systems Design; Technology

Keywords:

optimization; foraging theory; agent-based modeling; autonomous vehicles; game theory

Addo, Sandra E.A Game-Theoretic Framework To Competitive Individual Targeting
Master of Science, University of Akron, 2009, Applied Mathematics
Individual targeting is the process whereby a firm offers promotional incentives to individuals that the firm deems potential customers. With today's information-intensive marketing environments, most firms have considerable information about consumers in their databases, allowing them to determine those that are loyal to them and those that are potential customers. Firms are taking advantage of this new found ability to target individuals with promotions in order to increase both patronage and their customer loyalty base. We develop a game-theoretic model to investigate simultaneous price and quality competition where the firms are allowed to both manipulate the quality of their product and target individuals with promotional incentives. The firms play a two-stage game of price and quality competition and promotions in which regular prices are chosen in the first stage and then strategies for promotion are chosen in the second stage.We find that in an industry where a larger firm is promoting, customers who are highly sensitive to quality should be targeted to ensure increasing profit. The smaller firm should focus its sales and marketing activities on customers who are less price sensitive and should focus on building customer loyalty.

Committee:

Gerald Young, PhD (Advisor); Michael Ferrara, PhD (Advisor); Curtis Clemons, PhD (Advisor)

Subjects:

Marketing; Mathematics

Keywords:

Game Theory; Nash Equilibrium; Subgames; Customer loyalty; Perceived Price; Individual Targeting;Price-Quality Competition

Hosny, Sameh Shawky IbrahimMOBILITY AND CONTENT TRADING IN DEVICE-TO-DEVICE CACHING NETWORKS
Doctor of Philosophy, The Ohio State University, 2016, Electrical and Computer Engineering
The mismatch between user demand and service supply creates a congestion in mobile wireless networks. The literature has a strong evidence that user behavior is highly predictable. Service Providers (SPs) can track, learn and predict user demand and mobility patterns. Taking advantage of user demand predictability allows SPs to smooth out the network load. Caching some of the data items in the off-peak times shifts some of the network load and reduces the incurred service cost. Moreover, the Device-to-Device (D2D) communication allows users to share their proactive downloads with other users in their neighborhood. Therefore, users find their request either in their local cache or with other users around them. Nevertheless, harnessing the information about user mobility enhances SP's caching decisions and reduces the incurred service cost. The information about users trajectories allows the SP to predict their presence in some popular locations, which experience high demand levels. Finding an optimal caching strategy alleviates the network congestion in these locations and improves the network performance. This dissertation introduces a study to extend the capabilities of D2D caching networks and investigates how to enhance its performance. The research consists of three main directions: (1) exploiting user behavior predictability to smooth out the network load, (2) leveraging the relations between users to introduce a content trading marketplace, and (3) leveraging the information about user mobility to enhance the caching strategy. We start by investigating how to exploit the user behavior predictability to cache some data contents during off-peak times for a future possible request during peak times. This part of the research creates a benchmark that allows us to evaluate the performance of the proposed models. We compare the gains achieved by this proactive caching scheme with the flat pricing scenario. The gains achieved later, by content trading and mobility-aware D2D caching networks, are compared with the gains of this proactive caching scheme. Further, we highlight how to leverage the relations between users demand to introduce another benefit of the cached data items. Predicting users requests for peak times, correlated with the SP smart pricing, guides them to proactively cache some data contents during off-peak times. Moreover, users are equipped with D2D communication and SP helps them by announcing some anonymous information about users demand. This motivates the SP to hold a marketplace where users can trade their proactive downloads. Remarkably, we show that an appropriate manipulation of this marketplace allows the SP to maximize its profit, while users minimize their payments, and an equilibrium can be attained. Our research plan extends to shed light on the impact of user mobility on the caching decision. We consider both centralized and decentralized caching schemes. Users carry cached data while they are moving and share it at the popular locations using the D2D communication. Most of the users demand are served through the D2D communication which alleviates the network congestion in these locations. This model allows users to minimize their payment while the SP minimizes the incurred service cost and hence achieves a higher profit.

Committee:

Hesham ElGamal (Advisor); Atilla Eryilmaz (Advisor); Yuejie Chi (Committee Member); Jian Tan (Committee Member)

Subjects:

Electrical Engineering

Keywords:

Proactive Caching, Mobility, Content Trading, Game Theory, Optimization Theory, Wireless Networks

Schrank, Martin BennettAn analysis of the decision-making process /
Doctor of Philosophy, The Ohio State University, 1967, Graduate School

Committee:

Not Provided (Other)

Subjects:

Psychology

Keywords:

Decision making;Game theory

Chapman, Laura H.Game theory as an analytical tool for inquiry in art education /
Doctor of Philosophy, The Ohio State University, 1966, Graduate School

Committee:

Not Provided (Other)

Subjects:

Education

Keywords:

Game theory;Art

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