This thesis consists of three essays in economic theory, two on search models with information acquisition and one on repeated games when precise information about discount factors is unavailable. In the first essay, I develop a model in which optimal costly information acquisition by individual firms causes adverse selection in the market as a whole. Each firm’s information acquisition policy determines which customers it serves, which in turn affects the distribution of remaining customers and hence other firms’ incentives. I show that when information acquisition is ‘smooth’, the adverse selection externality due to each firm is dampened, and in equilibrium all firms make positive profits. By contrast, with lumpy information acquisition, only a limited number of firms are profitable. I establish that my results apply to a broad class of continuous-time information acquisition processes. The second essay explores information acquisition in labor markets. Noting that African-Americans face shorter employment durations than similar whites, we hypothesize that employers discriminate in acquiring ability-relevant information. We construct a model with a binary information generating process, ‘monitoring’, at the disposal of firms. Monitoring black but not white workers is self-sustaining. This ‘bad’ equilibrium is not merely a matter of coordination; rather, it is determined by history and not easily reversed. The model’s additional predictions, lower lifetime incomes and longer unemployment durations for blacks, are both strongly empirically supported. In the third essay, we investigate the possibility of repeated games equilibria that are robust to the discount factors. We prove a negative result which shows that a sizable part of the set of feasible individually rational payoffs can never be produced by such equilibria. We find the cutoff defining this region and interpret it as a limit on the ability to punish deviations when future rewards for randomization cannot be finely calibrated. Furthermore, we present a robust folk theorem to support payoffs in the complementary region with strategies that remain Subgame Perfect Nash Equilibria at all greater discount factors.

This thesis is composed of three chapters. Chapter 1 considers the existence of equilibria in games with complete information, where players may have non-ordered and discontinuous preferences. Chapter 2 studies the issues on the existence of pure and behavioral strategy equilibria in games with incomplete information and discontinuous payoffs. We consider the standard setting with Bayesian preferences as well as the case in which players may face ambiguity. Chapter 3 extends the classical results on the Walras-core existence and equivalence to an ambiguous asymmetric information economy, where agents maximize maximin expected utilities (MEU). These results are based on the papers He and Yannelis (2014, 2015a,b,c, 2016a,b). In the first chapter, we propose the condition of "continuous inclusion property" to handle the difficulty of discontinuous payoffs in various general equilibrium and game theory models. Such discontinuities arise naturally in economic situations, including auction, price competition of firms and also patent races. Based on the continuous inclusion property, we establish the equilibrium existence result in a very general framework with discontinuous payoffs. On one hand, this condition is sufficiently general from the methodological point of view, as it unifies almost all special conditions proposed in the literature. On the other hand, our condition is also potentially useful from the realistic point of view, as it could be applied to deal with many economic models which cannot be studied before because of the presence of the discontinuity. In the second chapter, I study the existence problem of pure and behavioral strategy equilibria in discontinuous games with incomplete information. The framework of games with incomplete information is standard as in the literature, except for that we allow players' payoffs to be discontinuous. We illustrate by examples that the Bayesian equilibria may not exist in such games and the previous results are not applicable to handle this problem. We propose some general conditions to retain the existence of both pure strategy and behavioral strategy Bayesian equilibrium, and show that our condition is tight. In addition, we study the equilibrium existence problem in discontinuous games under incomplete information and ambiguity, and show that the maximin framework solves the equilibrium existence issue without introducing any additional condition. In the last chapter, I study a general equilibrium model with incomplete information by adopting the maximin expected utilities. The model is powerful enough to describe the behaviors of risk averse agents that cannot be explained by the standard assumption of subjective expected utilities. I use this new formulation to extend many classical results in general equilibrium theory by incorporating ambiguity into the model. In addition, the desirable incentive compatibility property is shown in our model with maximin expected utilities, while this property will typically fail in the traditional setup. Specifically, the existence results are shown for various equilibrium notions in a general equilibrium model, and the incentives can be guaranteed when all agents use the maximin expected utilities.

Combinatorial games are intriguing and have a tendency to engross students and lead them into a serious study of mathematics. The engaging nature of games is the basis for this thesis. Two combinatorial games along with some educational tools were developed in the pursuit of the solution of these games. The game of Nim is at least centuries old, possibly originating in China, but noted in the 16th century in European countries. It consists of several stacks of tokens, and two players alternate taking one or more tokens from one of the stacks, and the player who cannot make a move loses. The formal and intense study of Nim culminated in the celebrated Sprague-Grundy Theorem, which is now one of the centerpieces in the theory of impartial combinatorial games. We study a variation on Nim, played on a graph. Graph Nim, for which the theory of Sprague-Grundy does not provide a clear strategy, was originally developed at the University of Colorado Denver. Graph Nim was first played on graphs of three vertices. The winning strategy, and losing position, of three vertex Graph Nim has been discovered, but we will expand the game to four vertices and develop the winning strategies for four vertex Graph Nim. Graph Theory is a markedly visual field of mathematics. It is extremely useful for graph theorists and students to visualize the graphs they are studying. There exists software to visualize and analyze graphs, such as SAGE, but it is often extremely difficult to learn how use such programs. The tools in GeoGebra make pretty graphs, but there is no automated way to make a graph or analyze a graph that has been built. Fortunately GeoGebra allows the use of JavaScript in the creation of buttons which allow us to build useful Graph Theory tools in GeoGebra. We will discuss two applets we have created that can be used to help students learn some of the basics of Graph Theory. The game of thrones is a two-player impartial combinatorial game played on an oriented complete graph (or tournament) named after the popular fantasy book and TV series. The game of thrones relies on a special type of vertex called a king. A king is a vertex, k, in a tournament, T, which for all x in T either k beats x or there exists a vertex y such that k beats y and y beats x. Players take turns removing vertices from a given tournament until there is only one king left in the resulting tournament. The winning player is the one which makes the final move. We develop a winning position and classify those tournaments that are optimal for the first or second-moving player.

The most common method of diagnosing Obsessive-Compulsive Disorder is the Yale-Brown Obsessive Compulsive Scale, which measures the severity of symptoms without regard to compulsions. However, this scale is limited to only considering the quantifiable time and energy lost to compulsions. Conversely, current systems of brain imaging arrest mobility and thus make it virtually impossible to observe compulsions at all, focusing instead on neurological responses to external stimuli. There is little research which merges both approaches, to consider the neuro-physiological effects of obsessions as well as the physical response through compulsions. As such, this research is focused on developing a model of compulsivity based upon neurological chemical pathways. The objective is to develop a model which would predict, given a set of environmental parameters, the probability of an individual with OCD performing compulsive behavior and the prevalence of such behavior. By applying this concept to a neural system known as the worry circuit, a computer program was composed and simulations run by this program suggest that the likelihood of compulsive behavior can be predicted using a function of the number of compulsions performed previously. In this model, each neurological agent in the worry circuit, represented by an automaton, has a certain probability of reacting to a stimulus and moving into one of two distinct excited states. Based on the final state of the automaton, the agent will send excitatory or inhibitory signals to surrounding agents, which also have a certain probability of changing states. If the final agent within the cycle shifts into an excited state, the subject will perform a compulsion. These results may be considered preliminary, given the sample size of the case study and the primitive nature of the model.

This dissertation comprises three essays in experimental economics. The first investigates the extent of strategic behaviour in jury voting models. Existing experimental evidence in jury voting models shows subjects largely act in accordance with theoretical predictions, implying that they have the insight to condition their votes upon their own pivotality. The experiment presented here tests the extent of these abilities, finding that a large portion of subjects behave consistently with such insight in the face of several variations on the basic jury voting game, but largely fail to do so in another, perhaps due to the difficulty of extracting informational implications from counterintuitive strategies. The second investigates the extent to which hypothetical thinking - the ability to condition upon and extract information from hypothetical events - persists across different strategic environments. Two games of considerable interest in the experimental literature - jury voting games and common value auctions - each contain the feature that a sophisticated player can simplify the problem by conditioning upon a hypothetical event - pivotality and winning the auction, respectively - and extract from it information about the state of the world that might affect their own behaviour. This common element suggests that the capability that leads to sophisticated play in one should lead to the same in the other. This paper tests this connection through a within-subject experiment in which subjects each play both games. Little evidence is found that play in one relates to play in the other in any meaningful way. Finally, the third, co-authored with Evan Friedman, investigates the nature of errors relative to Nash equilibrium play in a family of two-by-two games. Using data on one- shot games, we study the mapping from the distribution of player j’s actions to the distribution of player i’s beliefs (over player j’s actions) and the mapping from player i’s payoffs (given beliefs) to the distribution over player i’s actions. In our laboratory experiment, subjects play a set of fully mixed 2 × 2 games without feedback and state their beliefs about which actions they expect their opponents to play. We find that (i) belief distributions tend to shift in the same direction as changes in opponents’ actions, (ii) beliefs are systematically biased–“conservative” for one player role and “extreme” for the other, (iii) rates of best response vary systematically across games, and (iv) systematic failures to maximize expected payoffs (given beliefs) are well explained by risk aversion. To better understand the belief formation process, we collect subject-level measures of strategic sophistication based on dominance solvable games. We find that (v) the player role itself has a strong effect on sophistication, (vi) sophistication measured in dominance solvable games strongly predicts behavior in fully mixed games, and (vii) belief elicitation significantly effects actions in a direction consistent with increasing sophistication.

The improvement of water quality in the streams of the Glenelg Hopkins catchment is a priority of the Glenelg Hopkins regional strategy. A major source of water pollution in the region is linked to agricultural activities as high nutrient levels from runoff have the potential to increase the incidence of blue-green algae in the waterways. Land use change, reduced rainfall, more frequent extreme rainfall events and higher temperatures associated with climate change are likely to exacerbate this trend. Water testing data of the Total Phosphorus (TP) levels in the Hopkins River and at other sites within the Hopkins Catchment indicate increasing incidence of TP above the Environment Protection Authority's target levels for extended periods of each year. Earlier research indicated that phosphorus in runoff increases when pasture fertility increases and that fertiliser management practices should be considered as an element of preventative action for reducing nutrient pollution. During our research, a survey was undertaken in the Hopkins River catchment, to determine the current management of phosphorus (P) fertilisers on grazing and mixed enterprise farms, the attitude of farmers to natural resource management and their understanding of nutrient pollution. The survey also gathered information on the way farmers made fertiliser management decisions. If cooperation relating to phosphorus fertiliser application could be facilitated between groups of farmers, it may be possible to reduce nutrient runoff into the Hopkins waterways. Cooperative game theory has successfully been used worldwide in the resolution of environmental problems where there is an economic impact to the decision making process. In this project, the amount of phosphorus applied per hectare was used in a cooperative game theory model assessing the potential for cooperative action on phosphorus management by groups of farmers, based on the trade off between the economic cost of pollution to the region waterways and the economic production benefits to the individual. The outcome of this work was individual optimal strategies for fertiliser application, allowing individual farmers to reduce their impact of agricultural production on the health of the catchment. Involving the farmer groups, while undertaking the project, raised awareness amongst the farming population of the regional nutrient pollution caused by runoff from agricultural land, and enlisted their assistance towards adopting a cooperative approach to the problem. In addition, the results have been mapped using a Geographical Information System (GIS) for visual presentation and to demonstrate the use of this process in natural resource management with the farmer groups.

將賽局理論應用於捐贈行為的文獻並不多，其中多數假設聶許臆測(Nash conjectures)且僅集中探討私人捐贈均衡條件以及其效率性問題，並未更進一步探討，政府如何運用有效的政策工具以達成福利的提升。而傳統利他(Altruism)理論多單純地以現金或實物型態的移轉支付為研究對象，認為捐贈者所關心的是受贈者的效用或消費水準。然真實生活中，常觀察到捐贈者常以現金贈與他人，受贈者雖有自由支配的權利，但捐贈者卻仍然關心受贈者如何使用此一贈款，不同的消費種類對捐贈者的效用有不同的影響（註一）。 　　本文嘗試建立一捐贈行為的賽局模型，假設受贈者消費二種不同性質的財貨勞務。首先簡單地針對一個捐贈者與一個受贈者的行為來分析，私人捐贈均衡的決定，檢視均衡是否具效率，並指出政府如何有效地運用政策工具以達成私人捐贈均衡的效率水準等三課題。此外，更進一步擴充模型放寬聶許臆測的假設，針對二個捐贈者與一個受贈者行為，同樣分析上述三項課題。 　　本文結論發現，私人捐贈均衡的決定受到捐贈者及受贈者對不同性質財貨或勞務偏好的影響。且捐贈者只有在完全搭配行為(Complete matching behavior)的臆測下，均衡才具效率。除此之外，其他臆測均衡均不具效率性。政府的介入方式若為對捐贈者進行課稅或補貼，其政策效果並不確定甚或無效；反之，政府若對受贈者的消費予以課稅或補貼，則其可明確地達成提升杜會福利的政策目標。

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 152-166).

This thesis is aimed at the optimum design of uncertain mechanical components and systems involving multiple objectives and constraints. There are various mechanical and design problems that are encountered every now and then which require the output that equalize several conflicting objectives. In recent years several methods have been developed to find a solution to multiobjective problems. The most efficient method for obtaining a compromise solution is the game theory method, which is based on the Pareto minimum or optimum solution. A thorough methodology is developed, and subsequently applied to three examples problems. The first problem is to design four helical springs which are further used to support a milling machine. The objective is to minimize the weight of the spring, also to minimize the deflection, and to maximize the natural frequency thus making the problem as a multiobjective problem. Further the subjected constraint is the shear stress constraint. After finding the optimized solution of the deterministic problem, the problem is again solved using Stochastic Nonlinear Programming, and after that it is solved using Interval Analysis. Game theory is used individually in all the three cases. The second problem is to design a gear box where the objectives are defined as the weight of the gear box, stress developed in the shaft 1, and the stress developed in shaft 2. It is subjected to nine constraints which are bending stress in teeth, contact stress of teeth, transverse displacement of shafts 1 and 2, and constraints related to the torque. The third problem is to design a power screw and the objective is to minimize the volume of the screw, and to maximize the critical buckling load and thus making it a multiobjective problem. It is subjected to constraints of being screw to be self locking, then the shear stress in screw thread, and the bearing stress in threads. The results of all the three problems that are achieved using Deterministic, Stochastic Nonlinear Programming, and Interval Analysis Method are tabulated, and the value of each objective achieved using these three methods for each problem at a time are compared to find out the most optimized solution.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2006. / Includes bibliographical references (leaves 73-75). Also available in electronic version.