Price of Anarchy in Bernoulli Congestion Games with Affine Costs

We consider an atomic congestion game in which each player participates in the game with an exogenous and known probability $p_{i}\in[0,1]$, independently of everybody else, or stays out and incurs no cost. We first prove that the resulting game is potential. Then, we compute the parameterized price of anarchy to characterize the impact of demand uncertainty on the efficiency of selfish behavior. It turns out that the price of anarchy as a function of the maximum participation probability $p=\max_{i} p_{i}$ is a nondecreasing function. The worst case is attained when players have the same participation probabilities $p_{i}\equiv p$. For the case of affine costs, we provide an analytic expression for the parameterized price of anarchy as a function of $p$. This function is continuous on $(0,1]$, is equal to $4/3$ for $0<p\leq 1/4$, and increases towards $5/2$ when $p\to 1$. Our work can be interpreted as providing a continuous transition between the price of anarchy of nonatomic and atomic games, which are the extremes of the price of anarchy function we characterize. We show that these bounds are tight and are attained on routing games -- as opposed to general congestion games -- with purely linear costs (i.e., with no constant terms).Comment: 29 pages, 6 figure

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

Convergence of Large Atomic Congestion Games

We consider the question of whether, and in what sense, Wardrop equilibria provide a good approximation for Nash equilibria in atomic unsplittable congestion games with a large number of small players. We examine two different definitions of small players. In the first setting, we consider a sequence of games with an increasing number of players where each player's weight tends to zero. We prove that all (mixed) Nash equilibria of the finite games converge to the set of Wardrop equilibria of the corresponding nonatomic limit game. In the second setting, we consider again an increasing number of players but now each player has a unit weight and participates in the game with a probability tending to zero. In this case, the Nash equilibria converge to the set of Wardrop equilibria of a different nonatomic game with suitably defined costs. The latter can also be seen as a Poisson game in the sense of Myerson (1998), establishing a precise connection between the Wardrop model and the empirical flows observed in real traffic networks that exhibit stochastic fluctuations well described by Poisson distributions. In both settings we give explicit upper bounds on the rates of convergence, from which we also derive the convergence of the price of anarchy. Beyond the case of congestion games, we establish a general result on the convergence of large games with random players towards Poisson games.Comment: 34 pages, 3 figure

System-Optimal Routing of Traffic Flows with User Constraints in Networks with Congestion

The design of route-guidance systems faces a well-known dilemma. The approach that theoretically yields the system-optimal traffic pattern may discriminate against some users, for the sake of favoring others. Proposed alternate models, however, do not directly address the system perspective and may result in inferior performance. We propose a novel model and corresponding algorithms to resolve this dilemma. We present computational results on real-world instances and compare the new approach with the well-established traffic assignment model. The quintessence is that system-optimal routing of traffic flow with explicit integration of user constraints leads to a better performance than the user equilibrium while simultaneously guaranteeing a superior fairness compared to the pure system optimum

Non-Neutrality of Search Engines and its Impact on Innovation

International audienceThe search neutrality debate is about whether search engines should or should not be allowed to uprank certain results among the organic content matching a query. This debate is related to that of network neutrality, which focuses on whether all bytes being transmitted through the Internet should be treated equally. In a recent paper, we have formulated a model that formalizes this question and characterized an optimal ranking policy for a search engine. The model relies on the trade-off between short-term revenues, captured by the benefits of highly-paying results, and long-term revenues which can increase by providing users with more relevant results to minimize churn. In this article, we apply that model to investigate the relations between search neutrality and innovation. We illustrate through a simple setting and computer simulations that a revenue-maximizing search engine may indeed deter innovation at the content level. Our simple setting obviously simplifies reality, but this has the advantage of providing better insights on how optimization by some actors impacts other actors

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