Selfish versus coordinated routing in network games

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2004.Includes bibliographical references (p. 159-170) and index.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.A common assumption in network optimization models is that a central authority controls the whole system. However, in some applications there are independent users, and assuming that they will follow directions given by an authority is not realistic. Individuals will only accept directives if they are in their own interest or if there are incentives that encourage them to do so. Actually, it would be much easier to let users make their own decisions hoping that the outcome will be close to the authority's goals. Our main contribution is to show that, in static networks subject to congestion, users' selfish decisions drive the system close to optimality with respect to various common objectives. This connection to individual decision making proves fruitful; not only does it provide us with insights and additional understanding of network problems, but it also allows us to design approximation algorithms for computationally difficult problems. More specifically, the conflicting objectives of the users prompt the definition of a network game in which they minimize their own latencies. We show that the so-called price of anarchy is small in a quite general setting. Namely, for networks with side constraints and non-convex, non-differentiable, and even discontinuous latency functions, we show that although an arbitrary equilibrium need not be efficient, the total latency of the best equilibrium is close to that of an optimal solution. In addition, when the measure of the solution quality is the maximum latency, equilibria in networks without constraints are also near-optimal. We provide the first analysis of the problem of minimizing that objective in static networks with congestion.(cont.) As this problem is NP-hard, computing an equilibrium represents a constant-factor approximation algorithm. In some situations, the network authority might still want to do better than in equilibrium. We propose to use a solution that minimizes the total latency, subject to constraints designed to improve the solution's fairness. For several real-world instances, we compute traffic assignments of notably smaller total latency than an equilibrium, yet of similar fairness. Furthermore, we provide theoretical results that explain the conclusions derived from the computational study.by Nicolás E. Stier-Moses.Ph.D

Nudging Cooperation in a Crowd Experiment

We examine the hypothesis that driven by a competition heuristic, people don't even reflect or consider whether a cooperation strategy may be better. As a paradigmatic example of this behavior we propose the zero-sum game fallacy, according to which people believe that resources are fixed even when they are not. We demonstrate that people only cooperate if the competitive heuristic is explicitly overridden in an experiment in which participants play two rounds of a game in which competition is suboptimal. The observed spontaneous behavior for most players was to compete. Then participants were explicitly reminded that the competing strategy may not be optimal. This minor intervention boosted cooperation, implying that competition does not result from lack of trust or willingness to cooperate but instead from the inability to inhibit the competition bias. This activity was performed in a controlled laboratory setting and also as a crowd experiment. Understanding the psychological underpinnings of these behaviors may help us improve cooperation and thus may have vast practical consequences to our society.Fil: Niella, Tamara. Universidad Torcuato di Tella; ArgentinaFil: Stier, Nicolas. Universidad Torcuato di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Sigman, Mariano. Universidad Torcuato di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Métodos de división preferencial para simulación

En el area de computación y redes de comunicaciones, se da frecuentemente la necesidad de estimar probabilidades en relación con la eficiencia y confíabilidad. Normalmente se requiere que ellas sean pequeñas. Esta situación incentivó la investigación de métodos de reducción de varianza. Dichos métodos buscan lograr estimadores eficientes, sin utilizar simulaciones excesivamente caras. El objetivo de este trabajo es el de analizar una clase particular de estos métodos denominada importance splitting. Para el análisis se asignan costos a los estimadores para poder compararlos utilizando dicha medida. Si la eficiencia de algunos de estos métodos cuando la probabilidad a estimar tiende a cero es óptima, el método es denominado asintóticamente óptimo. Aquí buscamos condiciones necesarias y suficientes para los modelos y los parámetros del método que nos aseguren dicha optimalidad. Además analizamos varias alternativas para lograr que el método sea aún más rápido. Para terminar, exploramos diferentes implementaciones y discutimos una implementación real. Incluímos salidas de simulaciones en forma de tablas y gráficos para ilustrar y ejemplificar lo desarrollado durante el trabajo.In the area of computer and communication systems, we are often interested in estimating probabilities that happen to be very low. This has motivated a huge ammount of research into variance reduction methods, that aim to achieve efficient estimations without using very expensive simulations, The subject of this work is to analize one particular subclass of these methods called importance splitting. We assign a cost to estimators and compare them using this measure. If the method works as good as possible when the probability of interest tends to zero we say that it is asymptoticaly optimal. We look for neccesary and sufficient conditions for the models and parameters of the method that assure optimality. We analyze some posibilities for rendering this method faster. Finaly, different implementation schemas are explored and the actual implementation is discussed. We include simulation outputs in the form of tables and plots in order to illustrate and examplify what we developed here.Fil:Stier Moses, Nicolás E.. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

Decision, Risk & Operations Working Papers Series ROBUST WARDROP EQUILIBRIUM

Abstract. Network games can be used to model competitive situations in which players select routes to maximize their utility. Common applications include traffic, telecommunication and distribution networks. Although traditional network models have assumed that utilities only depend on congestion, in most applications they also have an uncertain component. In this work, we extend Wardrop’s network game (1952) by explicitly incorporating uncertainty in utility functions. Players are utility maximizers and select their route by solving a robust optimization problem, which takes the uncertainty into account. We define a robust Wardrop equilibrium as a solution under which all players are assigned to an optimal solution to their robust problems. Such a solution always exists and can be computed through efficient column generation methods. We show through a computational study that a robust Wardrop equilibrium tends to be more fair than the classic Wardrop equilibrium which ignores the uncertainty. Hence, a robust Wardrop equilibrium is more stable than the nominal counterpart as it reduces the regret that players experience after the uncertainty is revealed. Finally, we show that a pricing mechanism allows the network planner to coordinate players into a socially optimal solution, and show how the necessary tolls can be computed. 1