465 research outputs found

    Ad auctions and cascade model: GSP inefficiency and algorithms

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    The design of the best economic mechanism for Sponsored Search Auctions (SSAs) is a central task in computational mechanism design/game theory. Two open questions concern the adoption of user models more accurate than that one currently used and the choice between Generalized Second Price auction (GSP) and Vickrey-Clark-Groves mechanism (VCG). In this paper, we provide some contributions to answer these questions. We study Price of Anarchy (PoA) and Price of Stability (PoS) over social welfare and auctioneer's revenue of GSP w.r.t. the VCG when the users follow the famous cascade model. Furthermore, we provide exact, randomized, and approximate algorithms, showing that in real-world settings (Yahoo! Webscope A3 dataset, 10 available slots) optimal allocations can be found in less than 1s with up to 1000 ads, and can be approximated in less than 20ms even with more than 1000 ads with an average accuracy greater than 99%.Comment: AAAI16, to appea

    Monotonicity and 1-dimensional symmetry for solutions of an elliptic system arising in Bose-Einstein condensation

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    We study monotonicity and 1-dimensional symmetry for positive solutions with algebraic growth of the following elliptic system: {Δu=uv2in RNΔv=u2vin RN, \begin{cases} -\Delta u = -u v^2 & \text{in $\R^N$}\\ -\Delta v= -u^2 v & \text{in $\R^N$}, \end{cases} for every dimension N2N \ge 2. In particular, we prove a Gibbons-type conjecture proposed by H. Berestycki, T. C. Lin, J. Wei and C. Zhao

    Extensive-Form Perfect Equilibrium Computation in Two-Player Games

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    We study the problem of computing an Extensive-Form Perfect Equilibrium (EFPE) in 2-player games. This equilibrium concept refines the Nash equilibrium requiring resilience w.r.t. a specific vanishing perturbation (representing mistakes of the players at each decision node). The scientific challenge is intrinsic to the EFPE definition: it requires a perturbation over the agent form, but the agent form is computationally inefficient, due to the presence of highly nonlinear constraints. We show that the sequence form can be exploited in a non-trivial way and that, for general-sum games, finding an EFPE is equivalent to solving a suitably perturbed linear complementarity problem. We prove that Lemke's algorithm can be applied, showing that computing an EFPE is PPAD\textsf{PPAD}-complete. In the notable case of zero-sum games, the problem is in FP\textsf{FP} and can be solved by linear programming. Our algorithms also allow one to find a Nash equilibrium when players cannot perfectly control their moves, being subject to a given execution uncertainty, as is the case in most realistic physical settings.Comment: To appear in AAAI 1

    Quasi-Perfect Stackelberg Equilibrium

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    Equilibrium refinements are important in extensive-form (i.e., tree-form) games, where they amend weaknesses of the Nash equilibrium concept by requiring sequential rationality and other beneficial properties. One of the most attractive refinement concepts is quasi-perfect equilibrium. While quasi-perfection has been studied in extensive-form games, it is poorly understood in Stackelberg settings---that is, settings where a leader can commit to a strategy---which are important for modeling, for example, security games. In this paper, we introduce the axiomatic definition of quasi-perfect Stackelberg equilibrium. We develop a broad class of game perturbation schemes that lead to them in the limit. Our class of perturbation schemes strictly generalizes prior perturbation schemes introduced for the computation of (non-Stackelberg) quasi-perfect equilibria. Based on our perturbation schemes, we develop a branch-and-bound algorithm for computing a quasi-perfect Stackelberg equilibrium. It leverages a perturbed variant of the linear program for computing a Stackelberg extensive-form correlated equilibrium. Experiments show that our algorithm can be used to find an approximate quasi-perfect Stackelberg equilibrium in games with thousands of nodes

    Analysis of the Q^2-dependence of charged-current quasielastic processes in neutrino-nucleus interactions

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    We discuss the observed disagreement between the Q^2 distributions of neutrino-nucleus quasielastic events, measured by a number of recent experiments, and the predictions of Monte Carlo simulations based on the relativistic Fermi gas model. The results of our analysis suggest that these discrepancies are likely to be ascribable to both the breakdown of the impulse approximation and the limitations of the Fermi gas description. Several issues related to the extraction of the Q^2 distributions from the experimental data are also discussed, and new kinematical variables, which would allow for an improved analysis, are proposed.Comment: 8 pages, 8 figures, 1 tabl

    Neutrino-nucleus cross section in the impulse approximation regime

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    In the impulse approximation regime the nuclear response to a weakly interacting probe can be written in terms of the measured nucleon structure fuctions and the target spectral function, yielding the energy and momentum distribution of the constituent nucleons. We discuss a calculation of charged current neutrino-oxygen interactions in the quasielastic channel, carried out within nuclear many body theory. The proposed approach, extensively and successfully employed in the analysys of electron-nucleus scattering data, allows for a parameter free prediction of the neutrino-nucleus cross section, whose quantitative understanding will be critical to the analysis of the next genaration of high precision neutrino oscillation experiments.Comment: 4 pages, 3 Figs. Presented in the poster session at NUINT04. To be published in the Proceeding