The strategic behavior of rational novices

There is a growing amount of experimental evidence that suggests people often deviate from the predictions of game theory. Some scholars attempt to explain the observations by introducing errors into behavioral models. However, most of these modifications are situation dependent and do not generalize. A new theory, called the rational novice model, is introduced as an attempt to provide a general theory that takes account of erroneous behavior. The rational novice model is based on two central principals. The first is that people systematically make inaccurate guesses when they are evaluating their options in a game-like situation. The second is that people treat their decisions similar to a portfolio problem. As a result, non optimal actions in a game theoretic sense may be included in the rational novice strategy profile with positive weights.

The rational novice model can be divided into two parts: the behavioral model and the equilibrium concept. In a theoretical chapter, the mathematics of the behavioral model and the equilibrium concept are introduced. The existence of the equilibrium is established. In addition, the Nash equilibrium is shown to be a special case of the rational novice equilibrium. In another chapter, the rational novice model is applied to a voluntary contribution game. Numerical methods were used to obtain the solution. The model is estimated with data obtained from the Palfrey and Prisbrey experimental study of the voluntary contribution game. It is found that the rational novice model explains the data better than the Nash model. Although a formal statistical test was not used, pseudo R^2 analysis indicates that the rational novice model is better than a Probit model similar to the one used in the Palfrey and Prisbrey study.

The rational novice model is also applied to a first price sealed bid auction. Again, computing techniques were used to obtain a numerical solution. The data obtained from the Chen and Plott study were used to estimate the model. The rational novice model outperforms the CRRAM, the primary Nash model studied in the Chen and Plott study. However, the rational novice model is not the best amongst all models. A sophisticated rule-of-thumb, called the SOPAM, offers the best explanation of the data.

The development of an asymmetric palladium-catalyzed conjugate addition and its application toward the total syntheses of taiwaniaquinoid natural products

The asymmetric synthesis of quaternary stereocenters remains a challenging problem in organic synthesis. Past work from the Stoltz laboratory has resulted in methodology to install quaternary stereocenters α- or γ- to carbonyl compounds. Thus, the asymmetric synthesis of β-quaternary stereocenters was a desirable objective, and was accomplished by engineering the palladium-catalyzed addition of arylmetal organometallic reagents to α,β-unsaturated conjugate acceptors.

Herein, we described the rational design of a palladium-catalyzed conjugate addition reactions utilizing a catalyst derived from palladium(II) trifluoroacetate and pyridinooxazole ligands. This reaction is highly tolerant of protic solvents and oxygen atmosphere, making it a practical and operationally simple reaction. The mild conditions facilitate a remarkably high functional group tolerance, including carbonyls, halogens, and fluorinated functional groups. Furthermore, the reaction catalyzed conjugate additions with high enantioselectivity with conjugate acceptors of 5-, 6-, and 7-membered ring sizes. Extension of the methodology toward the asymmetric synthesis of flavanone products is presented, as well.

A computational and experimental investigation into the reaction mechanism provided a stereochemical model for enantioinduction, whereby the α-methylene protons adjacent the enone carbonyl clashes with the tert-butyl groups of the chiral ligand. Additionally, it was found that the addition of water and ammonium hexafluorophosphate significantly increases the reaction rate without sacrificing enantioselectivity. The synergistic effects of these additives allowed for the reaction to proceed at a lower temperature, and thus facilitated expansion of the substrate scope to sensitive functional groups such as protic amides and aryl bromides. Investigations into a scale-up synthesis of the chiral ligand (S)-tert-butylPyOx are also presented. This three-step synthetic route allowed for synthesis of the target compound of greater than 10 g scale.

Finally, the application of the newly developed conjugate addition reaction toward the synthesis of the taiwaniaquinoid class of terpenoid natural products is discussed. The conjugate addition reaction formed the key benzylic quaternary stereocenter in high enantioselectivity, joining together the majority of the carbons in the taiwaniaquinoid scaffold. Efforts toward the synthesis of the B-ring are presented.

Rational design of zinc phosphide heterojunction photovoltaics

The prospect of terawatt-scale electricity generation using a photovoltaic (PV) device places strict requirements on the active semiconductor optoelectronic properties and elemental abundance. After reviewing the constraints placed on an "earth-abundant" solar absorber, we find zinc phosphide (α-Zn₃P₂) to be an ideal candidate. In addition to its near-optimal direct band gap of 1.5 eV, high visible-light absorption coefficient (>10⁴ cm^-1), and long minority-carrier diffusion length (>5 μm), Zn₃P₂ is composed of abundant Zn and P elements and has excellent physical properties for scalable thin-film deposition. However, to date, a Zn₃P₂ device of sufficient efficiency for commercial applications has not been demonstrated. Record efficiencies of 6.0% for multicrystalline and 4.3% for thin-film cells have been reported, respectively. Performance has been limited by the intrinsic p-type conductivity of Zn₃P₂ which restricts us to Schottky and heterojunction device designs. Due to our poor understanding of Zn₃P₂ interfaces, an ideal heterojunction partner has not yet been found.

The goal of this thesis is to explore the upper limit of solar conversion efficiency achievable with a Zn₃P₂ absorber through the design of an optimal heterojunction PV device. To do so, we investigate three key aspects of material growth, interface energetics, and device design. First, the growth of Zn₃P₂ on GaAs(001) is studied using compound-source molecular-beam epitaxy (MBE). We successfully demonstrate the pseudomorphic growth of Zn₃P₂ epilayers of controlled orientation and optoelectronic properties. Next, the energy-band alignments of epitaxial Zn₃P₂ and II-VI and III-V semiconductor interfaces are measured via high-resolution x-ray photoelectron spectroscopy in order to determine the most appropriate heterojunction partner. From this work, we identify ZnSe as a nearly ideal n-type emitter for a Zn₃P₂ PV device. Finally, various II-VI/Zn₃P₂ heterojunction solar cells designs are fabricated, including substrate and superstrate architectures, and evaluated based on their solar conversion efficiency.

Probability in Quantum Mechanics: The Everett Interpretation and the Decision-Theoretic Program

The Everett interpretation of quantum mechanics is an increasingly popular alternative to the traditional Copenhagen interpretation, but there are a few major issues that prevent the widespread adoption. One of these issues is the origin of probabilities in the Everett interpretation, which this thesis will attempt to survey. The most successful resolution of the probability problem thus far is the decision-theoretic program, which attempts to frame probabilities as outcomes of rational decision making. This marks a departure from orthodox interpretations of probabilities in the physical sciences, where probabilities are thought to be objective, stemming from symmetry considerations. This thesis will attempt to offer evaluations on the decision-theoretic program.