Algorithmic challenges in green data centers

With data centers being the supporting infrastructure for a wide range of IT services, their efficiency has become a big concern to operators, as well as to society, for both economic and environmental reasons. The goal of this thesis is to design energy-efficient algorithms that reduce energy cost while minimizing compromise to service. We focus on the algorithmic challenges at different levels of energy optimization across the data center stack. The algorithmic challenge at the device level is to improve the energy efficiency of a single computational device via techniques such as job scheduling and speed scaling. We analyze the common speed scaling algorithms in both the worst-case model and stochastic model to answer some fundamental issues in the design of speed scaling algorithms. The algorithmic challenge at the local data center level is to dynamically allocate resources (e.g., servers) and to dispatch the workload in a data center. We develop an online algorithm to make a data center more power-proportional by dynamically adapting the number of active servers. The algorithmic challenge at the global data center level is to dispatch the workload across multiple data centers, considering the geographical diversity of electricity price, availability of renewable energy, and network propagation delay. We propose algorithms to jointly optimize routing and provisioning in an online manner. Motivated by the above online decision problems, we move on to study a general class of online problem named "smoothed online convex optimization", which seeks to minimize the sum of a sequence of convex functions when "smooth" solutions are preferred. This model allows us to bridge different research communities and help us get a more fundamental understanding of general online decision problems.

An integrated design approach to power systems : from power flows to electricity markets

Power system is at the brink of change. Engineering needs, economic forces and environmental factors are the main drivers of this change. The vision is to build a smart electrical grid and a smarter market mechanism around it to fulfill mandates on clean energy. Looking at engineering and economic issues in isolation is no longer an option today; it needs an integrated design approach. In this thesis, I shall revisit some of the classical questions on the engineering operation of power systems that deals with the nonconvexity of power flow equations. Then I shall explore some issues of the interaction of these power flow equations on the electricity markets to address the fundamental issue of market power in a deregulated market environment. Finally, motivated by the emergence of new storage technologies, I present an interesting result on the investment decision problem of placing storage over a power network. The goal of this study is to demonstrate that modern optimization and game theory can provide unique insights into this complex system. Some of the ideas carry over to applications beyond power systems.

Markets and microstructure

This document contains three papers examining the microstructure of financial interaction in development and market settings. I first examine the industrial organization of financial exchanges, specifically limit order markets. In this section, I perform a case study of Google stock surrounding a surprising earnings announcement in the 3rd quarter of 2009, uncovering parameters that describe information flows and liquidity provision. I then explore the disbursement process for community-driven development projects. This section is game theoretic in nature, using a novel three-player ultimatum structure. I finally develop econometric tools to simulate equilibrium and identify equilibrium models in limit order markets.

In chapter two, I estimate an equilibrium model using limit order data, finding parameters that describe information and liquidity preferences for trading. As a case study, I estimate the model for Google stock surrounding an unexpected good-news earnings announcement in the 3rd quarter of 2009. I find a substantial decrease in asymmetric information prior to the earnings announcement. I also simulate counterfactual dealer markets and find empirical evidence that limit order markets perform more efficiently than do their dealer market counterparts.

In chapter three, I examine Community-Driven Development. Community-Driven Development is considered a tool empowering communities to develop their own aid projects. While evidence has been mixed as to the effectiveness of CDD in achieving disbursement to intended beneficiaries, the literature maintains that local elites generally take control of most programs. I present a three player ultimatum game which describes a potential decentralized aid procurement process. Players successively split a dollar in aid money, and the final player--the targeted community member--decides between whistle blowing or not. Despite the elite capture present in my model, I find conditions under which money reaches targeted recipients. My results describe a perverse possibility in the decentralized aid process which could make detection of elite capture more difficult than previously considered. These processes may reconcile recent empirical work claiming effectiveness of the decentralized aid process with case studies which claim otherwise.

In chapter four, I develop in more depth the empirical and computational means to estimate model parameters in the case study in chapter two. I describe the liquidity supplier problem and equilibrium among those suppliers. I then outline the analytical forms for computing certainty-equivalent utilities for the informed trader. Following this, I describe a recursive algorithm which facilitates computing equilibrium in supply curves. Finally, I outline implementation of the Method of Simulated Moments in this context, focusing on Indirect Inference and formulating the pseudo model.

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.

Efficient methods for empirical tests of behavioral economics theories in laboratory and field experiments

In the quest for a descriptive theory of decision-making, the rational actor model in economics imposes rather unrealistic expectations and abilities on human decision makers. The further we move from idealized scenarios, such as perfectly competitive markets, and ambitiously extend the reach of the theory to describe everyday decision making situations, the less sense these assumptions make. Behavioural economics has instead proposed models based on assumptions that are more psychologically realistic, with the aim of gaining more precision and descriptive power. Increased psychological realism, however, comes at the cost of a greater number of parameters and model complexity. Now there are a plethora of models, based on different assumptions, applicable in differing contextual settings, and selecting the right model to use tends to be an ad-hoc process. In this thesis, we develop optimal experimental design methods and evaluate different behavioral theories against evidence from lab and field experiments.

We look at evidence from controlled laboratory experiments. Subjects are presented with choices between monetary gambles or lotteries. Different decision-making theories evaluate the choices differently and would make distinct predictions about the subjects' choices. Theories whose predictions are inconsistent with the actual choices can be systematically eliminated. Behavioural theories can have multiple parameters requiring complex experimental designs with a very large number of possible choice tests. This imposes computational and economic constraints on using classical experimental design methods. We develop a methodology of adaptive tests: Bayesian Rapid Optimal Adaptive Designs (BROAD) that sequentially chooses the "most informative" test at each stage, and based on the response updates its posterior beliefs over the theories, which informs the next most informative test to run. BROAD utilizes the Equivalent Class Edge Cutting (EC²) criteria to select tests. We prove that the EC² criteria is adaptively submodular, which allows us to prove theoretical guarantees against the Bayes-optimal testing sequence even in the presence of noisy responses. In simulated ground-truth experiments, we find that the EC² criteria recovers the true hypotheses with significantly fewer tests than more widely used criteria such as Information Gain and Generalized Binary Search. We show, theoretically as well as experimentally, that surprisingly these popular criteria can perform poorly in the presence of noise, or subject errors. Furthermore, we use the adaptive submodular property of EC² to implement an accelerated greedy version of BROAD which leads to orders of magnitude speedup over other methods.

We use BROAD to perform two experiments. First, we compare the main classes of theories for decision-making under risk, namely: expected value, prospect theory, constant relative risk aversion (CRRA) and moments models. Subjects are given an initial endowment, and sequentially presented choices between two lotteries, with the possibility of losses. The lotteries are selected using BROAD, and 57 subjects from Caltech and UCLA are incentivized by randomly realizing one of the lotteries chosen. Aggregate posterior probabilities over the theories show limited evidence in favour of CRRA and moments' models. Classifying the subjects into types showed that most subjects are described by prospect theory, followed by expected value. Adaptive experimental design raises the possibility that subjects could engage in strategic manipulation, i.e. subjects could mask their true preferences and choose differently in order to obtain more favourable tests in later rounds thereby increasing their payoffs. We pay close attention to this problem; strategic manipulation is ruled out since it is infeasible in practice, and also since we do not find any signatures of it in our data.

In the second experiment, we compare the main theories of time preference: exponential discounting, hyperbolic discounting, "present bias" models: quasi-hyperbolic (α, β) discounting and fixed cost discounting, and generalized-hyperbolic discounting. 40 subjects from UCLA were given choices between 2 options: a smaller but more immediate payoff versus a larger but later payoff. We found very limited evidence for present bias models and hyperbolic discounting, and most subjects were classified as generalized hyperbolic discounting types, followed by exponential discounting.

In these models the passage of time is linear. We instead consider a psychological model where the perception of time is subjective. We prove that when the biological (subjective) time is positively dependent, it gives rise to hyperbolic discounting and temporal choice inconsistency.

We also test the predictions of behavioral theories in the "wild". We pay attention to prospect theory, which emerged as the dominant theory in our lab experiments of risky choice. Loss aversion and reference dependence predicts that consumers will behave in a uniquely distinct way than the standard rational model predicts. Specifically, loss aversion predicts that when an item is being offered at a discount, the demand for it will be greater than that explained by its price elasticity. Even more importantly, when the item is no longer discounted, demand for its close substitute would increase excessively. We tested this prediction using a discrete choice model with loss-averse utility function on data from a large eCommerce retailer. Not only did we identify loss aversion, but we also found that the effect decreased with consumers' experience. We outline the policy implications that consumer loss aversion entails, and strategies for competitive pricing.

In future work, BROAD can be widely applicable for testing different behavioural models, e.g. in social preference and game theory, and in different contextual settings. Additional measurements beyond choice data, including biological measurements such as skin conductance, can be used to more rapidly eliminate hypothesis and speed up model comparison. Discrete choice models also provide a framework for testing behavioural models with field data, and encourage combined lab-field experiments.