Essays on economics networks

This thesis belongs to the growing field of economic networks. In particular, we develop three essays in which we study the problem of bargaining, discrete choice representation, and pricing in the context of networked markets. Despite analyzing very different problems, the three essays share the common feature of making use of a network representation to describe the market of interest.

In Chapter 1 we present an analysis of bargaining in networked markets. We make two contributions. First, we characterize market equilibria in a bargaining model, and find that players' equilibrium payoffs coincide with their degree of centrality in the network, as measured by Bonacich's centrality measure. This characterization allows us to map, in a simple way, network structures into market equilibrium outcomes, so that payoffs dispersion in networked markets is driven by players' network positions. Second, we show that the market equilibrium for our model converges to the so called eigenvector centrality measure. We show that the economic condition for reaching convergence is that the players' discount factor goes to one. In particular, we show how the discount factor, the matching technology, and the network structure interact in a very particular way in order to see the eigenvector centrality as the limiting case of our market equilibrium.

We point out that the eigenvector approach is a way of finding the most central or relevant players in terms of the “global” structure of the network, and to pay less attention to patterns that are more “local”. Mathematically, the eigenvector centrality captures the relevance of players in the bargaining process, using the eigenvector associated to the largest eigenvalue of the adjacency matrix of a given network. Thus our result may be viewed as an economic justification of the eigenvector approach in the context of bargaining in networked markets.

As an application, we analyze the special case of seller-buyer networks, showing how our framework may be useful for analyzing price dispersion as a function of sellers and buyers' network positions.

Finally, in Chapter 3 we study the problem of price competition and free entry in networked markets subject to congestion effects. In many environments, such as communication networks in which network flows are allocated, or transportation networks in which traffic is directed through the underlying road architecture, congestion plays an important role. In particular, we consider a network with multiple origins and a common destination node, where each link is owned by a firm that sets prices in order to maximize profits, whereas users want to minimize the total cost they face, which is given by the congestion cost plus the prices set by firms. In this environment, we introduce the notion of Markovian traffic equilibrium to establish the existence and uniqueness of a pure strategy price equilibrium, without assuming that the demand functions are concave nor imposing particular functional forms for the latency functions. We derive explicit conditions to guarantee existence and uniqueness of equilibria. Given this existence and uniqueness result, we apply our framework to study entry decisions and welfare, and establish that in congested markets with free entry, the number of firms exceeds the social optimum.

Interacting single atoms with nanophotonics for chip-integrated quantum networks

Underlying matter and light are their building blocks of tiny atoms and photons. The ability to control and utilize matter-light interactions down to the elementary single atom and photon level at the nano-scale opens up exciting studies at the frontiers of science with applications in medicine, energy, and information technology. Of these, an intriguing front is the development of quantum networks where N >> 1 single-atom nodes are coherently linked by single photons, forming a collective quantum entity potentially capable of performing quantum computations and simulations. Here, a promising approach is to use optical cavities within the setting of cavity quantum electrodynamics (QED). However, since its first realization in 1992 by Kimble et al., current proof-of-principle experiments have involved just one or two conventional cavities. To move beyond to N >> 1 nodes, in this thesis we investigate a platform born from the marriage of cavity QED and nanophotonics, where single atoms at ~100 nm near the surfaces of lithographically fabricated dielectric photonic devices can strongly interact with single photons, on a chip. Particularly, we experimentally investigate three main types of devices: microtoroidal optical cavities, optical nanofibers, and nanophotonic crystal based structures. With a microtoroidal cavity, we realized a robust and efficient photon router where single photons are extracted from an incident coherent state of light and redirected to a separate output with high efficiency. We achieved strong single atom-photon coupling with atoms located ~100 nm near the surface of a microtoroid, which revealed important aspects in the atom dynamics and QED of these systems including atom-surface interaction effects. We present a method to achieve state-insensitive atom trapping near optical nanofibers, critical in nanophotonic systems where electromagnetic fields are tightly confined. We developed a system that fabricates high quality nanofibers with high controllability, with which we experimentally demonstrate a state-insensitive atom trap. We present initial investigations on nanophotonic crystal based structures as a platform for strong atom-photon interactions. The experimental advances and theoretical investigations carried out in this thesis provide a framework for and open the door to strong single atom-photon interactions using nanophotonics for chip-integrated quantum networks.

Sensor networks for geospatial event detection - theory and applications

This thesis presents theories, analyses, and algorithms for detecting and estimating parameters of geospatial events with today's large, noisy sensor networks. A geospatial event is initiated by a significant change in the state of points in a region in a 3-D space over an interval of time. After the event is initiated it may change the state of points over larger regions and longer periods of time. Networked sensing is a typical approach for geospatial event detection. In contrast to traditional sensor networks comprised of a small number of high quality (and expensive) sensors, trends in personal computing devices and consumer electronics have made it possible to build large, dense networks at a low cost. The changes in sensor capability, network composition, and system constraints call for new models and algorithms suited to the opportunities and challenges of the new generation of sensor networks. This thesis offers a single unifying model and a Bayesian framework for analyzing different types of geospatial events in such noisy sensor networks. It presents algorithms and theories for estimating the speed and accuracy of detecting geospatial events as a function of parameters from both the underlying geospatial system and the sensor network. Furthermore, the thesis addresses network scalability issues by presenting rigorous scalable algorithms for data aggregation for detection. These studies provide insights to the design of networked sensing systems for detecting geospatial events. In addition to providing an overarching framework, this thesis presents theories and experimental results for two very different geospatial problems: detecting earthquakes and hazardous radiation. The general framework is applied to these specific problems, and predictions based on the theories are validated against measurements of systems in the laboratory and in the field.

Cloud computing services for seismic networks

This thesis describes a compositional framework for developing situation awareness applications: applications that provide ongoing information about a user's changing environment. The thesis describes how the framework is used to develop a situation awareness application for earthquakes. The applications are implemented as Cloud computing services connected to sensors and actuators. The architecture and design of the Cloud services are described and measurements of performance metrics are provided. The thesis includes results of experiments on earthquake monitoring conducted over a year. The applications developed by the framework are (1) the CSN --- the Community Seismic Network --- which uses relatively low-cost sensors deployed by members of the community, and (2) SAF --- the Situation Awareness Framework --- which integrates data from multiple sources, including the CSN, CISN --- the California Integrated Seismic Network, a network consisting of high-quality seismometers deployed carefully by professionals in the CISN organization and spread across Southern California --- and prototypes of multi-sensor platforms that include carbon monoxide, methane, dust and radiation sensors.

New applications that come from extending seismic networks into buildings

This thesis describes engineering applications that come from extending seismic networks into building structures. The proposed applications will benefit the data from the newly developed crowd-sourced seismic networks which are composed of low-cost accelerometers. An overview of the Community Seismic Network and the earthquake detection method are addressed. In the structural array components of crowd-sourced seismic networks, there may be instances in which a single seismometer is the only data source that is available from a building. A simple prismatic Timoshenko beam model with soil-structure interaction (SSI) is developed to approximate mode shapes of buildings using natural frequency ratios. A closed form solution with complete vibration modes is derived. In addition, a new method to rapidly estimate total displacement response of a building based on limited observational data, in some cases from a single seismometer, is presented. The total response of a building is modeled by the combination of the initial vibrating motion due to an upward traveling wave, and the subsequent motion as the low-frequency resonant mode response. Furthermore, the expected shaking intensities in tall buildings will be significantly different from that on the ground during earthquakes. Examples are included to estimate the characteristics of shaking that can be expected in mid-rise to high-rise buildings. Development of engineering applications (e.g., human comfort prediction and automated elevator control) for earthquake early warning system using probabilistic framework and statistical learning technique is addressed.

Physical characterization of the rack effect and hydrogen bond networks in blue copper proteins

A summary of previous research is presented that indicates that the purpose of a blue copper protein's fold and hydrogen bond network, aka, the rack effect, enforce a copper(II) geometry around the copper(I) ion in the metal site. In several blue copper proteins, the C-terminal histidine ligand becomes protonated and detaches from the copper in the reduced forms. Mutants of amicyanin from Paracoccus denitrificans were made to alter the hydrogen bond network and quantify the rack effect by pK_a shifts.

The pK_a's of mutant amicyanins have been measured by pH-dependent electrochemistry. P94F and P94A mutations loosen the Northern loop, allowing the reduced copper to adopt a relaxed conformation: the ability to relax drives the reduction potentials up. The measured potentials are 265 (wild type), 380 (P94A), and 415 (P94F) mV vs. NHE. The measured pK_a's are 7.0 (wild type), 6.3 (P94A), and 5.0 (P94F). The additional hydrogen bond to the thiolate in the mutants is indicated by a red-shift in the blue copper absorption and an increase in the parallel hyperfine splitting in the EPR spectrum. This hydrogen bond is invoked as the cause for the increased stability of the C-terminal imidazole.

Melting curves give a measure of the thermal stability of the protein. A thermodynamic intermediate with pH-dependent reversibility is revealed. Comparisons with the electrochemistry and apoamicyanin suggest that the intermediate involves the region of the protein near the metal site. This region is destabilized in the P94F mutant; coupled with the evidence that the imidazole is stabilized under the same conditions confirms an original concept of the rack effect: a high energy configuration is stabilized at a cost to the rest of the protein.

Selective data gathering in community sensor networks

Smartphones and other powerful sensor-equipped consumer devices make it possible to sense the physical world at an unprecedented scale. Nearly 2 million Android and iOS devices are activated every day, each carrying numerous sensors and a high-speed internet connection. Whereas traditional sensor networks have typically deployed a fixed number of devices to sense a particular phenomena, community networks can grow as additional participants choose to install apps and join the network. In principle, this allows networks of thousands or millions of sensors to be created quickly and at low cost. However, making reliable inferences about the world using so many community sensors involves several challenges, including scalability, data quality, mobility, and user privacy.

This thesis focuses on how learning at both the sensor- and network-level can provide scalable techniques for data collection and event detection. First, this thesis considers the abstract problem of distributed algorithms for data collection, and proposes a distributed, online approach to selecting which set of sensors should be queried. In addition to providing theoretical guarantees for submodular objective functions, the approach is also compatible with local rules or heuristics for detecting and transmitting potentially valuable observations. Next, the thesis presents a decentralized algorithm for spatial event detection, and describes its use detecting strong earthquakes within the Caltech Community Seismic Network. Despite the fact that strong earthquakes are rare and complex events, and that community sensors can be very noisy, our decentralized anomaly detection approach obtains theoretical guarantees for event detection performance while simultaneously limiting the rate of false alarms.