Essays on cooperation and reciprocity

This dissertation comprises three essays that use theory-based experiments to gain understanding of how cooperation and efficiency is affected by certain variables and institutions in different types of strategic interactions prevalent in our society.

Chapter 2 analyzes indefinite horizon two-person dynamic favor exchange games with private information in the laboratory. Using a novel experimental design to implement a dynamic game with a stochastic jump signal process, this study provides insights into a relation where cooperation is without immediate reciprocity. The primary finding is that favor provision under these conditions is considerably less than under the most efficient equilibrium. Also, individuals do not engage in exact score-keeping of net favors, rather, the time since the last favor was provided affects decisions to stop or restart providing favors.

Evidence from experiments in Cournot duopolies is presented in Chapter 3 where players indulge in a form of pre-play communication, termed as revision phase, before playing the one-shot game. During this revision phase individuals announce their tentative quantities, which are publicly observed, and revisions are costless. The payoffs are determined only by the quantities selected at the end under real time revision, whereas in a Poisson revision game, opportunities to revise arrive according to a synchronous Poisson process and the tentative quantity corresponding to the last revision opportunity is implemented. Contrasting results emerge. While real time revision of quantities results in choices that are more competitive than the static Cournot-Nash, significantly lower quantities are implemented in the Poisson revision games. This shows that partial cooperation can be sustained even when individuals interact only once.

Chapter 4 investigates the effect of varying the message space in a public good game with pre-play communication where player endowments are private information. We find that neither binary communication nor a larger finite numerical message space results in any efficiency gain relative to the situation without any form of communication. Payoffs and public good provision are higher only when participants are provided with a discussion period through unrestricted text chat.

Topics in randomized numerical linear algebra

This thesis studies three classes of randomized numerical linear algebra algorithms, namely: (i) randomized matrix sparsification algorithms, (ii) low-rank approximation algorithms that use randomized unitary transformations, and (iii) low-rank approximation algorithms for positive-semidefinite (PSD) matrices.

Randomized matrix sparsification algorithms set randomly chosen entries of the input matrix to zero. When the approximant is substituted for the original matrix in computations, its sparsity allows one to employ faster sparsity-exploiting algorithms. This thesis contributes bounds on the approximation error of nonuniform randomized sparsification schemes, measured in the spectral norm and two NP-hard norms that are of interest in computational graph theory and subset selection applications.

Low-rank approximations based on randomized unitary transformations have several desirable properties: they have low communication costs, are amenable to parallel implementation, and exploit the existence of fast transform algorithms. This thesis investigates the tradeoff between the accuracy and cost of generating such approximations. State-of-the-art spectral and Frobenius-norm error bounds are provided.

The last class of algorithms considered are SPSD "sketching" algorithms. Such sketches can be computed faster than approximations based on projecting onto mixtures of the columns of the matrix. The performance of several such sketching schemes is empirically evaluated using a suite of canonical matrices drawn from machine learning and data analysis applications, and a framework is developed for establishing theoretical error bounds.

In addition to studying these algorithms, this thesis extends the Matrix Laplace Transform framework to derive Chernoff and Bernstein inequalities that apply to all the eigenvalues of certain classes of random matrices. These inequalities are used to investigate the behavior of the singular values of a matrix under random sampling, and to derive convergence rates for each individual eigenvalue of a sample covariance matrix.

Instrumentation for Kinetic-Inductance-Detector-Based Submillimeter Radio Astronomy

A substantial amount of important scientific information is contained within astronomical data at the submillimeter and far-infrared (FIR) wavelengths, including information regarding dusty galaxies, galaxy clusters, and star-forming regions; however, these wavelengths are among the least-explored fields in astronomy because of the technological difficulties involved in such research. Over the past 20 years, considerable efforts have been devoted to developing submillimeter- and millimeter-wavelength astronomical instruments and telescopes.

The number of detectors is an important property of such instruments and is the subject of the current study. Future telescopes will require as many as hundreds of thousands of detectors to meet the necessary requirements in terms of the field of view, scan speed, and resolution. A large pixel count is one benefit of the development of multiplexable detectors that use kinetic inductance detector (KID) technology.

This dissertation presents the development of a KID-based instrument including a portion of the millimeter-wave bandpass filters and all aspects of the readout electronics, which together enabled one of the largest detector counts achieved to date in submillimeter-/millimeter-wavelength imaging arrays: a total of 2304 detectors. The work presented in this dissertation has been implemented in the MUltiwavelength Submillimeter Inductance Camera (MUSIC), a new instrument for the Caltech Submillimeter Observatory (CSO).

A computer-aided investigation of motion detection units in the fly

This work deals with two related areas: processing of visual information in the central nervous system, and the application of computer systems to research in neurophysiology.

Certain classes of interneurons in the brain and optic lobes of the blowfly Calliphora phaenicia were previously shown to be sensitive to the direction of motion of visual stimuli. These units were identified by visual field, preferred direction of motion, and anatomical location from which recorded. The present work is addressed to the questions: (1) is there interaction between pairs of these units, and (2) if such relationships can be found, what is their nature. To answer these questions, it is essential to record from two or more units simultaneously, and to use more than a single recording electrode if recording points are to be chosen independently. Accordingly, such techniques were developed and are described.

One must also have practical, convenient means for analyzing the large volumes of data so obtained. It is shown that use of an appropriately designed computer system is a profitable approach to this problem. Both hardware and software requirements for a suitable system are discussed and an approach to computer-aided data analysis developed. A description is given of members of a collection of application programs developed for analysis of neuro-physiological data and operated in the environment of and with support from an appropriate computer system. In particular, techniques developed for classification of multiple units recorded on the same electrode are illustrated as are methods for convenient graphical manipulation of data via a computer-driven display.

By means of multiple electrode techniques and the computer-aided data acquisition and analysis system, the path followed by one of the motion detection units was traced from open optic lobe through the brain and into the opposite lobe. It is further shown that this unit and its mirror image in the opposite lobe have a mutually inhibitory relationship. This relationship is investigated. The existence of interaction between other pairs of units is also shown. For pairs of units responding to motion in the same direction, the relationship is of an excitatory nature; for those responding to motion in opposed directions, it is inhibitory.

Experience gained from use of the computer system is discussed and a critical review of the current system is given. The most useful features of the system were found to be the fast response, the ability to go from one analysis technique to another rapidly and conveniently, and the interactive nature of the display system. The shortcomings of the system were problems in real-time use and the programming barrier—the fact that building new analysis techniques requires a high degree of programming knowledge and skill. It is concluded that computer system of the kind discussed will play an increasingly important role in studies of the central nervous system.