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.

Möbius-like groups of homeomorphisms of the circle

A group G → Homeo_+(S^1) is a Möbius-like group if every element of G is conjugate in Homeo(S^1) to a Mobius transformation. Our main result is: given a Mobus like like group G which has at least one global fixed point, G is conjugate in Homeo(S^1) to a Möbius group if and only if the limit set of G is all of S^1 . Moreover, we prove that if the limit set of G is not SI, then after identifying some closed subintervals of S^1 to points, the induced action of G is conjugate to an action of a Möbius group.

We also show that the above result does not hold in the case when G has no global fixed points. Namely, we construct examples of Möbius-like groups with limit set equal to S^1, but these groups cannot be conjugated to Möbius groups.

Descriptive set theory and the ergodic theory of countable groups

The primary focus of this thesis is on the interplay of descriptive set theory and the ergodic theory of group actions. This incorporates the study of turbulence and Borel reducibility on the one hand, and the theory of orbit equivalence and weak equivalence on the other. Chapter 2 is joint work with Clinton Conley and Alexander Kechris; we study measurable graph combinatorial invariants of group actions and employ the ultraproduct construction as a way of constructing various measure preserving actions with desirable properties. Chapter 3 is joint work with Lewis Bowen; we study the property MD of residually finite groups, and we prove a conjecture of Kechris by showing that under general hypotheses property MD is inherited by a group from one of its co-amenable subgroups. Chapter 4 is a study of weak equivalence. One of the main results answers a question of Abért and Elek by showing that within any free weak equivalence class the isomorphism relation does not admit classification by countable structures. The proof relies on affirming a conjecture of Ioana by showing that the product of a free action with a Bernoulli shift is weakly equivalent to the original action. Chapter 5 studies the relationship between mixing and freeness properties of measure preserving actions. Chapter 6 studies how approximation properties of ergodic actions and unitary representations are reflected group theoretically and also operator algebraically via a group's reduced C^*-algebra. Chapter 7 is an appendix which includes various results on mixing via filters and on Gaussian actions.

An examination of strategic opportunities provided by the conference committee procedure in the U.S. Congress

Deference to committees in Congress has been a much studied phenomena for close to 100 years. This deference can be characterized as the unwillingness of a potentially winning coalition on the House floor to impose its will on a small minority, a standing committee. The congressional scholar is then faced with two problems: observing such deference to committees, and explaining it. Shepsle and Weingast have proposed the existence of an ex-post veto for standing committees as an explanation of committee deference. They claim that as conference reports in the House and Senate are considered under a rule that does not allow amendments, the conferees enjoy agenda-setting power. In this paper I describe a test of such a hypothesis (along with competing hypotheses regarding the effects of the conference procedure). A random-utility model is utilized to estimate legislators' ideal points on appropriations bills from 1973 through 1980. I prove two things: 1) that committee deference can not be said to be a result of the conference procedure; and moreover 2) that committee deference does not appear to exist at all.

Class two p groups as fixed point free automorphism groups

Suppose that AG is a solvable group with normal subgroup G where (|A|, |G|) = 1. Assume that A is a class two odd p group all of whose irreducible representations are isomorphic to subgroups of extra special p groups. If p^c ≠ r^d + 1 for any c = 1, 2 and any prime r where r^2d+1 divides |G| and if C_G(A) = 1 then the Fitting length of G is bounded by the power of p dividing |A|.

The theorem is proved by applying a fixed point theorem to a reduction of the Fitting series of G. The fixed point theorem is proved by reducing a minimal counter example. IF R is an extra spec r subgroup of G fixed by A₁, a subgroup of A, where A₁ centralizes D(R), then all irreducible characters of A₁R which are nontrivial on Z(R) are computed. All nonlinear characters of a class two p group are computed.

Normal structures and automorphism groups of t-designs

Combinatorial configurations known as t-designs are studied. These are pairs ˂B, ∏˃, where each element of B is a k-subset of ∏, and each t-design occurs in exactly λ elements of B, for some fixed integers k and λ. A theory of internal structure of t-designs is developed, and it is shown that any t-design can be decomposed in a natural fashion into a sequence of “simple” subdesigns. The theory is quite similar to the analysis of a group with respect to its normal subgroups, quotient groups, and homomorphisms. The analogous concepts of normal subdesigns, quotient designs, and design homomorphisms are all defined and used.

This structure theory is then applied to the class of t-designs whose automorphism groups are transitive on sets of t points. It is shown that if G is a permutation group transitive on sets of t letters and ф is any set of letters, then images of ф under G form a t-design whose parameters may be calculated from the group G. Such groups are discussed, especially for the case t = 2, and the normal structure of such designs is considered. Theorem 2.2.12 gives necessary and sufficient conditions for a t-design to be simple, purely in terms of the automorphism group of the design. Some constructions are given.

Finally, 2-designs with k = 3 and λ = 2 are considered in detail. These designs are first considered in general, with examples illustrating some of the configurations which can arise. Then an attempt is made to classify all such designs with an automorphism group transitive on pairs of points. Many cases are eliminated of reduced to combinations of Steiner triple systems. In the remaining cases, the simple designs are determined to consist of one infinite class and one exceptional case.

Nuclear magnetic resonance studies of protein conformation: I. Ribonuclease S. II. Hemoglobin

Fluorine nuclear magnetic resonance techniques have been used to study conformational processes in two proteins labeled specifically in strategic regions with covalently attached fluorinated molecules. In ribonuclease S, the ϵ-amino groups of lysines 1 and 7 were trifluoroacetylated without diminishing enzymatic activity. As inhibitors bound to the enzyme, changes in orientation of the peptide segment containing the trifluoroacetyl groups were detected in the nuclear magnetic resonance spectrum. pH Titration of one of the histidines in the active site produced a reversal of the conformational process.

Hemoglobin was trifluoroacetonylated at the reactive cysteine 93 of each β chain. The nuclear magnetic resonance spectrum of the fluorine moiety reflected changes in the equilibrium position of the β chain carboxy terminus upon binding of heme ligands and allosteric effectors. The chemical shift positions observed in deoxy- and methemoglobin were pH dependent, undergoing an abnormally steep apparent titration which was not observed in hemoglobin from which histidine β 146 had been removed enzymatically. The abnormal sharpness of these pH dependent processes is probably due to interactions between several ionizing groups.

The carbon monoxide binding process was studied by concurrent observation of the visible and nuclear magnetic resonance spectra of trifluoroacetonylated hemoglobin at fractional ligand saturations throughout the range 0-1.0. Comparison of the ligand binding process observed in these two ways yields evidence for a specific order of ligand binding. The sequence of events is sensitive to the pH and organic phosphate concentration of the medium, demonstrating the delicately balanced control system produced by interactions between the hemoglobin subunits and the effectors.