Lead, Follow or Cooperate? Sequential versus Collusive Payoffs in Symmetric Duopoly Games

In many strategic settings comparing the payoffs obtained by players under full cooperation to those obtainable at a sequential (Stackelberg) equilibrium can be crucial to determine the outcome of the game. This happens, for instance, in repeated games in which players can break cooperation by acting sequentially, as well as in merger games in which firms are allowed to sequence their actions. Despite the relevance of these and other applications, no full-fledged comparisons between collusive and sequential payoffs have been performed so far. In this paper we show that even in symmetric duopoly games the ranking of cooperative and sequential payoffs can be extremely variable, particularly when the usual linear demand assumption is relaxed. Not surprisingly, the degree of strategic complementarity and substitutability of players' actions (and, hence, the slope of their best replies) appears decisive to determine the ranking of collusive and sequential payoffs. Some applications to endogenous timing are discussed

GENDER DIFFERENCES IN JOINT MOMENTAND POWER MEASUREMENTS DURING VERTICAL JUMP EXERCISES

INTRODUCTION Gender differences are apparent not only in the absolute maximum force level but also in the rates at which the force and/or power is produced(Koml et al., 1978). The predominant requirement for success in a large number of athletic skills IS explosive power. For the lower body, this IS perhaps best exemplified by vertical jump. Vertical jumps a complex ballistic multi-joint movement, where the musculature around the hip, knee and ankle joints collectively operate to produce patterned movements. The purpose of this study was to assess the effect of gender on the mechanical output of the lower limb joints (moments and powers), during vertical jumping exercise. Methods: Eight male (age 22.4 yrs) and eight female ( age 21.7yrs) athletes served as subjects. After 20 min. of standard warm-up, the subjects performed 20 maximal vertical jumps with the arms behind the back. The 3-D coordinates of ten anatomical landmarks ( five per leg) were detected by the opt electronic ELITE system (Ferringno & Pedotti, 1985) with a sampling frequency of 100 HzS simultaneously, the GRF signals were measured and acquired with a sampling frequency of 500 Hz. Internal joint centres and the corresponding moments and powers were estimated from anthropometric and kinematic data using a special software package Group differences were assessed by the Wilcoxon signed rank test Statistical significance was assessed at

GROUND REACTION FORCE PATTERNS FOR THE EVALUATION OR MOTOR RECOVERY IN ATHLETES AFFECTED BY KNEE INJURIES

INTRODUCTION Vertical jump is an exercise widely adopted to evaluate some motor characteristics of the athletes. Vertical component of the ground reaction force (VGRF) is often used to gain more information regarding efficiency and motor coordination of the lower limbs. The aim of this study is to evaluate vertical jump performances of subjects afflicted by ACL injury, by means of VGRF patterns. METHODS Ten healthy rugby players (HP) were the sample of this study, together with four subjects who present a ACL pathology (PP), due to a previous injury. At the time of the acquisition all the pathological subjects had been reintegrated in the team training and competitive programs. The subjects were asked to perform 20 two-legged vertical jumps, as high as possible, keeping one foot at a time over a Kistler force platform. Arms were behind their back, in order to minimize the contribution of the upper part of the body to the thrust of the legs. Ground reaction forces were recorded by means of a force platform at the sampling rate of 1000 Hz, and data were normalized in amplitude to the body mass. Jumping height was computed through the flight time. RESULTS In agreement with previous studies, a common pattern in the GRF for HP subjects was observed; the typical VGRF time course was characterized by an initial decrease of the force until a minimum, followed by two maxima with a further relative minimum in between, the first peak is the absolute maximum. Amplitude and timing of these parameters were examined for the analysis. The mean jump height evidenced statistical diierences only between one PP subject and the mean jump height of the HP group. By considering VGRF amplitude, significative differences have been found only between the amplitude of the first minimum (healthy = 0.25 BW, pathological = 0.36 BW) while no differences were found between the absolute maxima. By considering the timing of the different phases it has been observed that PP group show a longer delay between the initial minimum and the first maximum. As far as the VGRF time course is concerned, we noted for PP subjects individual behaviors in comparison with the average pattern of the HP. Furthermore, the presence of a strong asymmetry between the curves of the healthy and pathological limb, were observed. CONCLUSIONS Jumping height does not seem to be a parameter useful in designating motor impairments in subjects with ACL injuries. However, as far as the VGRF is concerned, intra and inter individual significative differences may be observed. A common characteristics of PP group is the reduced capacity to perform the eccentric phase. While the amplitude of the maxima is similar, VGRF patterns of the PP group show individual characteristics and appreciable asymmetries between the two legs. These results allow to speculate about compensatory motor actions and confm that the majority of the PP subjects were from a complete motor recovery

LOWER LIMB KINETIC VARIABILITY IN VERTICAL JUMPING

For more that 50 years vertical jumping exercises have been widely used in sport practice as a measure of power not only to predict athletic ability but also to obtain indications on same near-muscular and motor characteristics of the athletes. The most interesting work in this area has been done by a research group at the Free University of Amsterdam. The studies of these authors evidenced very elegantly that kinetic analysis provides potentially more diagnostic information force derived indices. However, what the majority of previous studies on human extremely large intra subject variability of the joint kinetic variables. So far, no attempts have been made to gain more insight into the variability inherent in moment and power selected measurements in vertical jumping exercises. To the best of our knowledge, in fact, all the studies employed on or more homogeneous subject groups and presented data describing the average performance groups. Furthermore, frequently, when mean values of kinetic parameters for a group were calculated, only the highest jump of each subject was selected for the calculation. The present experiments were devised to gain more insight into the variability of aforementioned biomechanical parameters in order to determine the appropriate number of trails necessary to obtain a stable mean for these parameters and to investigate the interday variability. Eight recreational athletes were the subjects of this study. In two different test sessions, each subject performed 25 double-legged countermovement vertical jumps without the arm swing. Kinematic data, concerning the spatial position often anatomical landmarks (five per each leg), were recorded by means of an optoelectronic system (ELITE) with a sampling rate of 100 Hz. Simultaneously, ground reaction forces were measured with a Kistler force platform at the sampling rate of 1000 Hz. The internal joint centres, such as the corresponding moments and powers, were estimated by using a special software (SAFLO) which inputs were anthropometric, kinematic and kinetic data. Preliminary results show that, considering all the subjects, power mean value stability ranges from 11 to 16 trials. Interday correlation was higher for hip and ankle and lower for knee values. These results suggest the need to adopt multiple trial protocols to reach reliable results suitable for identifying meaningful performance differences

3-D KINEMATIC ANALYSIS OF CANOEING ON A SIMULATOR: DIFFERENCES BETWEEN ELITE, INTERMEDIATE AND NOVICE CANOISTS

Using 3-D kinematic analysis, this paper identified kinematic variables that govern successful performance in canoeing on a simulator. The presence of side-to-side asymmetries in selected linear and angular variables was investigated. Elite, intermediate and novice canoeists participated. Similar to previously results for symmetrical cyclic sport activities like cross-country skiing, running and cycling, elite athletes evidenced higher movement amplitude and a more symmetric behavior compared with intermediate and novice paddlers. The less experienced athletes evidenced more accentuated saddle and pelvis movements in the frontal plane. Aerobic and anaerobic capacities and technical skills developed over years of training may explain the reported difference

Consumption responses to a large shock to financial wealth: evidence from Italy

We estimate marginal propensities to consume from wealth shocks for Italian households early in the Great Recession. Large asset-price shocks in 2007-2008 underpin instrumental variables. A euro fall in risky financial wealth resulted in cuts in annual total (non-durable) consumption of 8.5-9 (5.5-5.7) cents. We find small effects on food spending. Counterfactuals indicate financial-wealth effects were relatively important for consumption falls in Italy in 2007/08. The estimated effects are consistent with a simulated lifecycle model that captures the wealth shock. Also consistent with the model are findings of stronger wealth effects for agents who were pessimistic about stock returns

THREE-DIMENSIONAL SPORT MOVEMENT ANALYSIS BY MEANS OF FREE FLOATING TV CAMERAS WITH VARIABLE OPTICS

INTRODUCTION: Video analysis and off-line manual digitalization is usually used for 2-D and 3-D studies of human movement in sport science. The main advantage of this approach, with respect to the recourse to opto-electronic automatic motion analyzers, is the high flexibility in system set-up, the avoidance of marking procedures and the possibility of successful operation in a wide range of environmental situations. Such features turn out to be particularly important for recordings to be performed in the frame of high-level competition, when the experimental set-up must be adapted to a pre-defined competitive environment, without interfering with the performances of the athletes. However, when methods proper to conventional close-range photogrammetry are used, most of the advantages offered by the flexibility of video analysis are not obtained. Particularly critical is the restriction of the useful calibrated volume to the field of view made possible by fixed pairs of TV cameras. In this case the useful sequence of images (where the dimension of the acquired subject allows one to limit macroscopic digitalization errors) is often insufficient for the analysis of a complete movement cycle. This limitation hinders a fruitful application of video analysis in the frame of sport activities (alpine and Nordic skiing, swimming, track and field) in which the execution of the particular technical movement is performed within a large physical space. A solution to the problem is proposed based on the use of free moving and zooming cameras. The corresponding dedicated software for repeated calibration based on Direct Linear Transformation (DLT)(Abdel Aziz and Karara, 1971) is described. Results of recording performed in the laboratory are discussed aiming at the validation of the implemented method. The description of the methodology for the recording of sport activities and the presentation of the related results confirm the operational feasibility of the proposed method and the reliability of the resulting quantitative kinematics analysis

Application of functional principal component analysis in race walking: an emerging methodology

This study considered the problem of identifying and evaluating the factors of individual performance during race walking. In particular, the study explored the use of functional principal component analysis (f-PCA), a multivariate data analysis, for assessing and classifying the kinematics and kinetics of the knee joint in competitive race walkers. Seven race walkers of international and national level participated to the study. An optoelectronic system and a force platform were used to capture three-dimensional kinematics and kinetics of lower limbs during the race walking cycle. Functional principal component analysis was applied bilaterally to the sagittal knee angle and net moment data, because knee joint motion is fundamental to race walking technique. Scatterplots of principal component scores provided evidence of athletes' technical differences and asymmetries even when traditional analysis (mean ± s curves) was not effective. Principal components provided indications for race walkers' classification and identified potentially important technical differences between higher and lower skilled athletes. Therefore, f-PCA might represent a future aid for the fine analysis of sports movements, if consistently applied to performance monitoring