Connectivity and equilibrium in random games

We study how the structure of the interaction graph of a game affects the existence of pure Nash equilibria. In particular, for a fixed interaction graph, we are interested in whether there are pure Nash equilibria arising when random utility tables are assigned to the players. We provide conditions for the structure of the graph under which equilibria are likely to exist and complementary conditions which make the existence of equilibria highly unlikely. Our results have immediate implications for many deterministic graphs and generalize known results for random games on the complete graph. In particular, our results imply that the probability that bounded degree graphs have pure Nash equilibria is exponentially small in the size of the graph and yield a simple algorithm that finds small nonexistence certificates for a large family of graphs. Then we show that in any strongly connected graph of n vertices with expansion $(1+\Omega(1))\log_2(n)$ the distribution of the number of equilibria approaches the Poisson distribution with parameter 1, asymptotically as $n \to +\infty$.Comment: Published in at http://dx.doi.org/10.1214/10-AAP715 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Searches for the Higgs Boson in CMS

The CMS potential for the Higgs boson discovery is discussed in the framework of the Standard Model (SM) and its Minimal Supersymmetric extension (MSSM)

Stretching Method-Based Operational Modal Analysis of An Old Masonry Lighthouse.

We present in this paper a structural health monitoring study of the Egyptian lighthouse of Rethymnon in Crete, Greece. Using structural vibration data collected on a limited number of sensors during a 3-month period, we illustrate the potential of the stretching method for monitoring variations in the natural frequencies of the structure. The stretching method compares two signals, the current that refers to the actual state of the structure, with the reference one that characterizes the structure at a reference healthy condition. For the structure under study, an 8-day time interval is used for the reference quantity while the current quantity is computed using a time window of 24 h. Our results indicate that frequency shifts of 1% can be detected with high accuracy allowing for early damage assessment. We also provide a simple numerical model that is calibrated to match the natural frequencies estimated using the stretching method. The model is used to produce possible damage scenarios that correspond to 1% shift in the first natural frequencies. Although simple in nature, this model seems to deliver a realistic response of the structure. This is shown by comparing the response at the top of the structure to the actual measurement during a small earthquake. This is a preliminary study indicating the potential of the stretching method for structural health monitoring of historical monuments. The results are very promising. Further analysis is necessary requiring the deployment of the instrumentation (possibly with additional instruments) for a longer period of time

Robust seismic velocity change estimation using ambient noise recordings

We consider the problem of seismic velocity change estimation using ambient noise recordings. Motivated by [23] we study how the velocity change estimation is affected by seasonal fluctuations in the noise sources. More precisely, we consider a numerical model and introduce spatio-temporal seasonal fluctuations in the noise sources. We show that indeed, as pointed out in [23], the stretching method is affected by these fluctuations and produces misleading apparent velocity variations which reduce dramatically the signal to noise ratio of the method. We also show that these apparent velocity variations can be eliminated by an adequate normalization of the cross-correlation functions. Theoretically we expect our approach to work as long as the seasonal fluctuations in the noise sources are uniform, an assumption which holds for closely located seismic stations. We illustrate with numerical simulations and real measurements that the proposed normalization significantly improves the accuracy of the velocity change estimation

Does A Short, Thick Neck Predict Obstructive Sleep Apnea?: The Role of Physical Examination in OSA Screening

Purpose: The purpose of this study was to determine whether a short neck, alone or together with a thick neck, can predict obstructive sleep apnea (OSA). Methods: The laryngeal heights of 169 new adult patients presenting to a sleep medicine physician were measured over a period of 5 months. Neck circumference, Mallampati score, and body-mass index (BMI) were also determined, together with medical history, smoking status, and serum bicarbonate. Lastly, patients’ polysomnograms were obtained in order to ascertain the presence or absence of OSA as indicated by the apnea-hypopnea index, as well as other sleep study parameters. Results: No association was found between laryngeal height and presence of OSA, bicarbonate concentration or oxygen saturation. Of interest, neck circumference was also not significantly associated with any of the aforementioned parameters, although there was a trend towards significance in its association with OSA (p=0.055). Still, a combined short laryngeal height and large neck circumference was associated with lower nadir SaO2 (p=0.018). Of all clinical parameters we measured, only higher BMI, older age and male sex were positively associated with OSA (p\u3c0.05). Conclusion: This study challenges the popular notion that short necks predict OSA

Computer-aided verification in mechanism design

In mechanism design, the gold standard solution concepts are dominant strategy incentive compatibility and Bayesian incentive compatibility. These solution concepts relieve the (possibly unsophisticated) bidders from the need to engage in complicated strategizing. While incentive properties are simple to state, their proofs are specific to the mechanism and can be quite complex. This raises two concerns. From a practical perspective, checking a complex proof can be a tedious process, often requiring experts knowledgeable in mechanism design. Furthermore, from a modeling perspective, if unsophisticated agents are unconvinced of incentive properties, they may strategize in unpredictable ways. To address both concerns, we explore techniques from computer-aided verification to construct formal proofs of incentive properties. Because formal proofs can be automatically checked, agents do not need to manually check the properties, or even understand the proof. To demonstrate, we present the verification of a sophisticated mechanism: the generic reduction from Bayesian incentive compatible mechanism design to algorithm design given by Hartline, Kleinberg, and Malekian. This mechanism presents new challenges for formal verification, including essential use of randomness from both the execution of the mechanism and from the prior type distributions. As an immediate consequence, our work also formalizes Bayesian incentive compatibility for the entire family of mechanisms derived via this reduction. Finally, as an intermediate step in our formalization, we provide the first formal verification of incentive compatibility for the celebrated Vickrey-Clarke-Groves mechanism

A Direct Reduction from k-Player to 2-Player Approximate Nash Equilibrium

We present a direct reduction from k-player games to 2-player games that preserves approximate Nash equilibrium. Previously, the computational equivalence of computing approximate Nash equilibrium in k-player and 2-player games was established via an indirect reduction. This included a sequence of works defining the complexity class PPAD, identifying complete problems for this class, showing that computing approximate Nash equilibrium for k-player games is in PPAD, and reducing a PPAD-complete problem to computing approximate Nash equilibrium for 2-player games. Our direct reduction makes no use of the concept of PPAD, thus eliminating some of the difficulties involved in following the known indirect reduction.Comment: 21 page

Efficiency in Multi-objective Games

In a multi-objective game, each agent individually evaluates each overall action-profile on multiple objectives. I generalize the price of anarchy to multi-objective games and provide a polynomial-time algorithm to assess it. This work asserts that policies on tobacco promote a higher economic efficiency