Equilibrium in dynamic economic models

The main theme running through these three chapters is that economic agents are often forced to respond to events that are not a direct result of their actions or other agents actions. The optimal response to these shocks will necessarily depend on agents' understanding of how these shocks arise. The economic environment in the first two chapters is analogous to the classic chain store game. In this setting, the addition of unintended trembles by the agents creates an environment better suited to reputation building. The third chapter considers the competitive equilibrium price dynamics in an overlapping generations environment when there are supply and demand shocks.

The first chapter is a game theoretic investigation of a reputation building game. A sequential equilibrium model, called the "error prone agents" model, is developed. In this model, agents believe that all actions are potentially subjected to an error process. Inclusion of this belief into the equilibrium calculation provides for a richer class of reputation building possibilities than when perfect implementation is assumed.

In the second chapter, maximum likelihood estimation is employed to test the consistency of this new model and other models with data from experiments run by other researchers that served as the basis for prominent papers in this field. The alternate models considered are essentially modifications to the standard sequential equilibrium. While some models perform quite well in that the nature of the modification seems to explain deviations from the sequential equilibrium quite well, the degree to which these modifications must be applied shows no consistency across different experimental designs.

The third chapter is a study of price dynamics in an overlapping generations model. It establishes the existence of a unique perfect-foresight competitive equilibrium price path in a pure exchange economy with a finite time horizon when there are arbitrarily many shocks to supply or demand. One main reason for the interest in this equilibrium is that overlapping generations environments are very fruitful for the study of price dynamics, especially in experimental settings. The perfect foresight assumption is an important place to start when examining these environments because it will produce the ex post socially efficient allocation of goods. This characteristic makes this a natural baseline to which other models of price dynamics could be compared.

Robot navigation in dense crowds : statistical models and experimental studies of human robot cooperation

This thesis explores the problem of mobile robot navigation in dense human crowds. We begin by considering a fundamental impediment to classical motion planning algorithms called the freezing robot problem: once the environment surpasses a certain level of complexity, the planner decides that all forward paths are unsafe, and the robot freezes in place (or performs unnecessary maneuvers) to avoid collisions. Since a feasible path typically exists, this behavior is suboptimal. Existing approaches have focused on reducing predictive uncertainty by employing higher fidelity individual dynamics models or heuristically limiting the individual predictive covariance to prevent overcautious navigation. We demonstrate that both the individual prediction and the individual predictive uncertainty have little to do with this undesirable navigation behavior. Additionally, we provide evidence that dynamic agents are able to navigate in dense crowds by engaging in joint collision avoidance, cooperatively making room to create feasible trajectories. We accordingly develop interacting Gaussian processes, a prediction density that captures cooperative collision avoidance, and a "multiple goal" extension that models the goal driven nature of human decision making. Navigation naturally emerges as a statistic of this distribution.

Most importantly, we empirically validate our models in the Chandler dining hall at Caltech during peak hours, and in the process, carry out the first extensive quantitative study of robot navigation in dense human crowds (collecting data on 488 runs). The multiple goal interacting Gaussian processes algorithm performs comparably with human teleoperators in crowd densities nearing 1 person/m², while a state of the art noncooperative planner exhibits unsafe behavior more than 3 times as often as the multiple goal extension, and twice as often as the basic interacting Gaussian process approach. Furthermore, a reactive planner based on the widely used dynamic window approach proves insufficient for crowd densities above 0.55 people/m². We also show that our noncooperative planner or our reactive planner capture the salient characteristics of nearly any dynamic navigation algorithm. For inclusive validation purposes, we show that either our non-interacting planner or our reactive planner captures the salient characteristics of nearly any existing dynamic navigation algorithm. Based on these experimental results and theoretical observations, we conclude that a cooperation model is critical for safe and efficient robot navigation in dense human crowds.

Finally, we produce a large database of ground truth pedestrian crowd data. We make this ground truth database publicly available for further scientific study of crowd prediction models, learning from demonstration algorithms, and human robot interaction models in general.

Wind-driven desertification: process modeling, remote monitoring, and forecasting

Arid and semiarid landscapes comprise nearly a third of the Earth's total land surface. These areas are coming under increasing land use pressures. Despite their low productivity these lands are not barren. Rather, they consist of fragile ecosystems vulnerable to anthropogenic disturbance.

The purpose of this thesis is threefold: (I) to develop and test a process model of wind-driven desertification, (II) to evaluate next-generation process-relevant remote monitoring strategies for use in arid and semiarid regions, and (III) to identify elements for effective management of the world's drylands.

In developing the process model of wind-driven desertification in arid and semiarid lands, field, remote sensing, and modeling observations from a degraded Mojave Desert shrubland are used. This model focuses on aeolian removal and transport of dust, sand, and litter as the primary mechanisms of degradation: killing plants by burial and abrasion, interrupting natural processes of nutrient accumulation, and allowing the loss of soil resources by abiotic transport. This model is tested in field sampling experiments at two sites and is extended by Fourier Transform and geostatistical analysis of high-resolution imagery from one site.

Next, the use of hyperspectral remote sensing data is evaluated as a substantive input to dryland remote monitoring strategies. In particular, the efficacy of spectral mixture analysis (SMA) in discriminating vegetation and soil types and detennining vegetation cover is investigated. The results indicate that hyperspectral data may be less useful than often thought in determining vegetation parameters. Its usefulness in determining soil parameters, however, may be leveraged by developing simple multispectral classification tools that can be used to monitor desertification.

Finally, the elements required for effective monitoring and management of arid and semiarid lands are discussed. Several large-scale multi-site field experiments are proposed to clarify the role of wind as a landscape and degradation process in dry lands. The role of remote sensing in monitoring the world's drylands is discussed in terms of optimal remote sensing platform characteristics and surface phenomena which may be monitored in order to identify areas at risk of desertification. A desertification indicator is proposed that unifies consideration of environmental and human variables.

Relativistic quark models and the current algebra

In this thesis we are concerned with finding representations of the algebra of SU(3) vector and axial-vector charge densities at infinite momentum (the "current algebra") to describe the mesons, idealizing the real continua of multiparticle states as a series of discrete resonances of zero width. Such representations would describe the masses and quantum numbers of the mesons, the shapes of their Regge trajectories, their electromagnetic and weak form factors, and (approximately, through the PCAC hypothesis) pion emission or absorption amplitudes.

We assume that the mesons have internal degrees of freedom equivalent to being made of two quarks (one an antiquark) and look for models in which the mass is SU(3)-independent and the current is a sum of contributions from the individual quarks. Requiring that the current algebra, as well as conditions of relativistic invariance, be satisfied turns out to be very restrictive, and, in fact, no model has been found which satisfies all requirements and gives a reasonable mass spectrum. We show that using more general mass and current operators but keeping the same internal degrees of freedom will not make the problem any more solvable. In particular, in order for any two-quark solution to exist it must be possible to solve the "factorized SU(2) problem," in which the currents are isospin currents and are carried by only one of the component quarks (as in the K meson and its excited states).

In the free-quark model the currents at infinite momentum are found using a manifestly covariant formalism and are shown to satisfy the current algebra, but the mass spectrum is unrealistic. We then consider a pair of quarks bound by a potential, finding the current as a power series in 1/m where m is the quark mass. Here it is found impossible to satisfy the algebra and relativistic invariance with the type of potential tried, because the current contributions from the two quarks do not commute with each other to order 1/m³. However, it may be possible to solve the factorized SU(2) problem with this model.

The factorized problem can be solved exactly in the case where all mesons have the same mass, using a covariant formulation in terms of an internal Lorentz group. For a more realistic, nondegenerate mass there is difficulty in covariantly solving even the factorized problem; one model is described which almost works but appears to require particles of spacelike 4-momentum, which seem unphysical.

Although the search for a completely satisfactory model has been unsuccessful, the techniques used here might eventually reveal a working model. There is also a possibility of satisfying a weaker form of the current algebra with existing models.