Evolutionary Solutions and Internet Applications for Algorithmic Game Theory

The growing pervasiveness of the internet has created a new class of algorithmic problems: those in which the strategic interaction of autonomous, self-interested entities must be accounted for. So motivated, we seek to (1) use game theoretic models and techniques to study practical problems in load balancing, data streams and internet traffic congestion, and (2) demonstrate the usefulness of evolutionary game theory's adaptive learning model as an analytical and evaluative tool.First we consider the evolutionary game theory concept of stochastic stability, and propose the price of stochastic anarchy as an alternative to the price of anarchy for quantifying the cost of having no central authority. Unlike Nash equilibria, stochastically stable states are the result of natural dynamics of large populations of computationally bounded agents, and are resilient to small perturbations from ideal play. To illustrate the utility of stochastic stability, we study the load balancing game on related machines, which has an unbounded price of anarchy, even in the case of two jobs and two machines. We show that in contrast, even in the general case, the price of stochastic anarchy is bounded.Next, we propose auction-based mechanisms for admission control of continuous queries to a Data Stream Management System. When submitting a query, each user also submits a bid: how much she is willing to pay for her query to run. Our mechanisms must admit queries and set payments in a way that maximizes system revenue while incentivizing customers to use the system honestly. We propose several manipulation-resistant payment mechanisms and prove that one guarantees a profit close to a standard profit benchmark, and the others perform well experimentally.Finally, we study the long standing problem of congestion control at bottleneck routers on the internet. We examine the effectiveness of commonly-used queuing policies when each network endpoint is self-interested and has no information about the other endpoints' actions or preferences. By employing evolutionary game theory, we find that while bottleneck routers face heavy congestion at stochastically stable states under policies being currently deployed, a practical policy that was recently proposed yields fair and efficient conditions with no congestion

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

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

Solving Multi-objective Integer Programs using Convex Preference Cones

Esta encuesta tiene dos objetivos: en primer lugar, identificar a los individuos que fueron víctimas de algún tipo de delito y la manera en que ocurrió el mismo. En segundo lugar, medir la eficacia de las distintas autoridades competentes una vez que los individuos denunciaron el delito que sufrieron. Adicionalmente la ENVEI busca indagar las percepciones que los ciudadanos tienen sobre las instituciones de justicia y el estado de derecho en Méxic

Fuelling the zero-emissions road freight of the future: routing of mobile fuellers

The future of zero-emissions road freight is closely tied to the sufficient availability of new and clean fuel options such as electricity and Hydrogen. In goods distribution using Electric Commercial Vehicles (ECVs) and Hydrogen Fuel Cell Vehicles (HFCVs) a major challenge in the transition period would pertain to their limited autonomy and scarce and unevenly distributed refuelling stations. One viable solution to facilitate and speed up the adoption of ECVs/HFCVs by logistics, however, is to get the fuel to the point where it is needed (instead of diverting the route of delivery vehicles to refuelling stations) using "Mobile Fuellers (MFs)". These are mobile battery swapping/recharging vans or mobile Hydrogen fuellers that can travel to a running ECV/HFCV to provide the fuel they require to complete their delivery routes at a rendezvous time and space. In this presentation, new vehicle routing models will be presented for a third party company that provides MF services. In the proposed problem variant, the MF provider company receives routing plans of multiple customer companies and has to design routes for a fleet of capacitated MFs that have to synchronise their routes with the running vehicles to deliver the required amount of fuel on-the-fly. This presentation will discuss and compare several mathematical models based on different business models and collaborative logistics scenarios