(epsilon,k) Equilibria and Well-posedness

The aim of this paper is to discuss a new concept of well-posedness for non cooperative games. Starting from the definition of (e,k)- equilibrium as the point where every player either guarantees at least ''k'' or he (she) does not lose more than ''e'', we introduce an original definition of well-posedness. We study characterizations of this well-posedness and its relations with the more known Tikhonov well-posedness. We prove that this well-posedness is an ordinal property if the payoff functions are bounded from below

An ordinal well posedness property

The aim of this paper is to give, for Nash equilibria, a well posedness criterion in the form of an ordinal property. This property is im- portant for games because it captures the case when players' decisions depend on preferences and not on a special choice of an utility function. The ordinal characteristics of this well posedness criterion comes from considering value bounded approximate equilibria

Deformation imaging

Recent developments in the field of clinical echocardiography allow the ultrasonographer to objectively quantify both regional and global myocardial function. Regional deformation (Strain) and deformation rate (Strain Rate) are novel indices of ventricular function that can be estimated non-invasively by ultrasonographic interrogation of the heart. Deformation Imaging (DI)represents a family of echocardiographic techniques that can be employed to detect, quantify and display the characteristics of physical deformation of the myocardium. The objective of the studies described in this thesis was to investigate Doppler-derived deformation imaging in dogs.This Master's Degree thesis is structured in two separate studies. The initial study compared Doppler-derived DI measures of ventricular function with more traditional invasive indices of cardiovascular function in healthy adult anesthetized dogs over a range of hemodynamic conditions created by serial pharmacologic manipulations. Five adult healthy dogs underwent simultaneous cardiac catheterization and transthoracic echocardiography under general anesthesia. The following invasive indices were monitored during the study: cardiac output (CO), femoral arterial (FA) and left ventricular(LV) pressures, +dP dt[subscript]max, -dP dt[subscript]max, right atrial (RA) and pulmonary arterial(PA) pressures, and pulmonary capillary wedge pressure (PCWP). Sequential manipulations of systolic function, after load and preload were performed,respectively, by means of dobutamine, nitroprusside, and hetastarch infusions.Significant changes were induced in the following invasive hemodynamic parameters: cardiac output (p 30 kg, and group 4: Doberman pinscher dogs). The aim of the study was to collect information on the feasibility, repeatability and reproducibility of Doppler-derived DI performed in a clinical setting. Of the initial 56 dogs from which echocardiographic data were collected, 7 dogs (12.5%) were excluded because of poor image quality, and data from 49 (87.5%) dogs were included in the final analysis. Of a total of 1470 ROIs analyzed, 4.65% yielded good quality curves, 88.3% were characterized by a significant amount of noise but retained a discernible pattern, and 7.14% were considered non-interpretable.Some pair-wise comparisons of the SSR values obtained from the 6 ROIs reached statistically significant difference. DI values in the Doberman pinscher group did not differ significantly compared to values obtained from a BW matched group. DI values in group 1 dogs, but not the traditional indices FS and EF, were significantly higher compared to groups 2 and 3. Results from a Bland-Altman analysis revealed overall poor clinical repeatability and reproducibility, as a result of the wide variability of the data.Based on the results of study 1 we conclude that Doppler-derived SSR represents a useful load-independent index of global systolic function, as demonstrated in anesthetized dogs. However study 2 suggests that, in a population of non-sedated dogs, with a relatively wide range of breeds and BW, Doppler-derived DI measurements are characterized by less than optimalintra-operator and inter-operator variability which may limit its value as a tool to evaluate myocardial function in a clinical setting. Comparison to other newly developed non-invasive techniques to estimate regional myocardial deformation is needed to determine the eventual clinical utility of the method

\u2019\u2019 Value bounded approximations for Nash equilibria\u2019\u2019

The aim of this contribution is to give a well posedness property wich is ordinal

"An Ordinal well posedness property for Nash equilibria' Optimization 61, 2012, selected paper in JOHN NASH: COMMEMORATIVE RESEARCH COLLECTION

The aim of this paper is to give, for Nash equilibria, a well posedness criterion which is an ordinal property. This notion is important for games because it emphasizes the fact that player's decisions are expressed by preferences and not by a special choice of utility function. We show that the ordinal property of this well-posedness criterion comes from considering value bounded approximate equilibria

Potential games and well posedness properties

The aim of this paper is to study Potential Games which are a special class of games; in fact their properties are dictated by a single function called the potential function. We consider Tihkonov well-posedness and other well posedness properties introduced by the authors in previous papers. We relate these properties with the Tihkonov well posedness of the potential function as maximum problem

Stackelberg Well-posedness and Hierarchical Potential Games

The aim of this paper is to study Potential Games which are a special class of games; in fact their properties are dictated by a single function called the potential function. We consider Tihkonov well-posedness and Stackelberg well-posedness of these games, the latter in both the optimistic and pessimistic cases