Nash equilibria of games with monotonic best replies

We introduce notions of increasingness for the best reply of a game that capture properly the intuitive idea of complementarity among players’ strategies. We show, by generalizing the fixpoint theorems of Veinott and Zhou, that the Nash sets of our games with increasing best replies are nonempty complete lattices. Hence we extend the class of games with strategic complementarities.Complementarity, supermodular games, fixpoint theorem, Nash equilibria

Games with Complementarities

We introduce a class of games with complementarities that has the quasisupermodular games, hence the supermodular games, as a special case. Our games retain the main property of quasisupermodular games : the Nash set is a nonemply complete lattice. We use monotonicity properties on the best reply that are weaker than those in the literature, as well as pretty simple and linked with an intuitive idea of complementarity. The sufficient conditions on the payoffs are weaker than those in quasisupermodular games. We also separate the conditions implying existence of a greatest and a least Nash equilibrium from those, stronger, implying that the Nash set is a complete latticeComplementarity, Quasisupermodularity, Supermodular games, Monotone comparative statics, Nash equilibria

Games with complementarities

We introduce a class of games with complementarities that has the quasisupermodular games, hence the supermodular games, as a special case. Our games retain the main property of quasisupermodular games: the Nash set is a nonempty complete lattice. We use monotonicity properties on the best reply that are weaker than those in the literature, as well as pretty simple and linked with an intuitive idea of complementarity. The sufficient conditions on the payoffs are weaker than those in quasisupermodular games. We also separate the conditions implying existence of a greatest and a least Nash equilibrium from those, stronger, implying that the Nash set is a complete lattice.complementarity, quasisupermodularity, supermodular games, monotone comparative statics, Nash equilibria

The complementarity foundations of industrial organization

In this paper we review the state of the art of Games with Strategic Complementarities (GSC), which are fundamental tools in modern Industrial Organization. The originality of the paper lies in the way the material is presented. Indeed, the mathematical aspects of GSC are complex and scattered in a literature which spans a long time period and a variety of research fields such as economics, applied mathematics and operations research. We organize a large amount of material in a unified and self-contained way, and concentrate on the intuitions and conceptual points that lie in the background of the mathematical modeling, with special emphasis on the modeling of complementarity. On the technical side, we investigate in details the choice and content of the assumptions. The scope of the paper is to allow the applied researcher to understand the theory, so that she may rapidly develop her own ability to deal with concrete problems.strategic complementarity, oligopoly theory, supermodularity, Nash equilibria, lattices

A Characterization of Inefficiency in Stochastic Overlapping Generations Economies

In this paper, we provide a characterization of interim inefficiency in stochastic economies of overlapping generations under possibly sequentially incomplete markets. With respect to the established body of results in the literature, we remove the hypothesis of two-period horizons, by considering longer, though uniformly bounded, horizons for generations. The characterization exploits a suitably Modified Cass Criterion, grounded on the long-rung behavior of compounded safe interest rates and independent of the length of horizons of generations. Thus, the hypothesis of two-period horizons is purely heuristic in establishing a criterion for inefficiency. In addition, for sequentially incomplete markets, we adopt a suitable notion of unambiguous inefficiency, separating the inefficient intertemporal allocation of resources from incomplete risk-sharing. Unambiguous inefficiency reduces to inefficiency when markets are sequentially complete.

A characterization of inefficiency in stochastic overlapping generations economies

In this paper, we provide a characterization of interim inefficiency in stochastic economies ofoverlapping generations under possibly sequentially incomplete markets. With respect to the established body of results in the literature, we remove the hypothesis of two-period horizons,by considering longer, though uniformly bounded, horizons for generations. The characterization exploits a suitably Modified Cass Criterion, grounded on the long-run behavior of compounded safe interest rates and independent of the length of horizons of generations. Thus, the hypothesis of two-period horizons is purely heuristic in establishing a criterion for inefficiency. In addition, for sequentially incomplete markets, we adopt a suitable notion of unambiguous inefficiency, separating the inefficient intertemporal allocation of resources from incomplete risk-sharing. Unambiguous inefficiency reduces to inefficiency when markets are sequentially complete.stochastic overlapping generations economies, inefficiency, competitive prices, cass criterion, social security, incomplete markets

A Note On The Characterization Of Inefficiency In Stochastic Overlapping Generations Economies

In this paper, we provide a characterization of interim ine±ciency in stochastic economies of overlapping generations under possibly sequentially incomplete markets. With respect to the established body of results in the literature, we remove the hypothesis of two-period horizons, by considering longer, though uniformly bounded, horizons for generations. The characteri- zation exploits a suitably Modi¯ed Cass Criterion, grounded on the long-rung behavior of compounded safe interest rates and independent of the length of horizons of generations. Thus, the hypothesis of two-period horizons is purely heuristic in establishing a criterion for ine±ciency. In addition, for sequentially incomplete markets, we adopt a suitable notion of unambiguous ine±ciency, separating the ine±cient intertemporal allocation of resources from incomplete risk-sharing. Unambiguous ine±ciency reduces to ine±ciency when markets are sequentially complete.Stochastic overlapping generations economies; ine±ciency; com-

Spotlight on Cardiovascular Scoring Systems in Covid-19: Severity Correlations in Real-world Setting

Objectives and Methods: the current understanding of the interplay between cardiovascular (CV) risk and Covid-19 is grossly inadequate. CV risk-prediction models are used to identify and treat high risk populations and to communicate risk effectively. These tools are unexplored in Covid-19. The main objective is to evaluate the association between CV scoring systems and chest X ray (CXR) examination (in terms of severity of lung involvement) in 50 Italian Covid-19 patients. Results only the Framingham Risk Score (FRS) was applicable to all patients. The Atherosclerotic Cardiovascular Disease Score (ASCVD) was applicable to half. 62% of patients were classified as high risk according to FRS and 41% according to ASCVD. Patients who died had all a higher FRS compared to survivors. They were all hypertensive. FRS≥30 patients had a 9.7 higher probability of dying compared to patients with a lower FRS. We found a strong correlation between CXR severity and FRS and ASCVD (P < 0.001). High CV risk patients had consolidations more frequently. CXR severity was significantly associated with hypertension and diabetes. 71% of hypertensive patients’ CXR and 88% of diabetic patients’ CXR had consolidations. Patients with diabetes or hypertension had 8 times greater risk of having consolidations. Conclusions: High CV risk correlates with more severe CXR pattern and death. Diabetes and hypertension are associated with more severe CXR. FRS offers more predictive utility and fits best to our cohort. These findings may have implications for clinical practice and for the identification of high-risk groups to be targeted for the vaccine precedence

Assessment of asthma severity in adults with ever asthma: a continuous score

Background In epidemiological studies, continuous measures of asthma severity should be used to catch the heterogeneity of phenotypes. This study aimed at developing and validating continuous measures of asthma severity in adult patients with ever asthma from the general population, to be used in epidemiological studies. Methods Respiratory symptoms, anti-asthmatic treatment and lung function were measured on 520 patients with ever asthma aged 20–64 years from the general Italian population (GEIRD study; 2007/2010). The variables that represent the same dimension of asthma severity were identified through an exploratory factor analysis and were summarized through a multiple factor analysis. Results Only respiratory symptoms and anti-asthmatic treatment were summarized in a continuous score (STS). STS ranges from 0 (no symptoms/treatment) to 10 (maximum symptom frequency and treatment intensity). STS was positively correlated with the Global Initiative for Asthma classification of asthma severity computed on the 137 cases with a doctor's diagnosis (Spearman’s coefficient = 0.61, p-value<0.0001) (concurrent validity). Furthermore, using a cohort of 1,097 European asthmatics (ECRHS II study; 1999/2002), increasing STS levels at baseline (1991/1993) were positively associated with long-term outcomes (hospitalization and lost workdays for breathing problems, asthma attack frequency and use of asthma controllers) (predictive validity). Finally, the STS scores computed from the GEIRD and ECRHS II data were comparable (Lin’s coefficient = 0.95, p-value<0.0001) (replication analysis). Conclusions STS is a valid and replicable measure of asthma severity in adults, which could be used in association studies

Extracellular vesicles from rat-bone-marrow mesenchymal stromal/stem cells improve tendon repair in rat Achilles tendon injury model in dose-dependent manner: A pilot study

Mesenchymal stromal/stem cells (MSCs) are increasingly employed for tissue regeneration, largely mediated through paracrine actions. Currently, extracellular vesicles (EVs) released by MSCs are major mediators of these paracrine effects. We evaluated whether rat-bone-marrow-MSC-derived EVs (rBMSCs-EVs) can ameliorate tendon injury in an in vivo rat model. Pro-collagen1A2 and MMP14 protein are expressed in rBMSC-EVs, and are important factors for extracellular-matrix tendon-remodeling. In addition, we found pro-collagen1A2 in rBMSC-EV surface-membranes by dot blot. In vitro on cells isolated from Achilles tendons, utilized as rBMSC -EVs recipient cells, EVs at both low and high doses induce migration of tenocytes; at higher concentration, they induce proliferation and increase expression of Collagen type I in tenocytes. Pretreatment with trypsin abrogate the effect of EVs on cell proliferation and migration, and the expression of collagen I. When either low- or high-dose rBMSCs-EVs were injected into a rat-Achilles tendon injury-model (immediately after damage), at 30 days, rBMSC-EVs were found to have accelerated the remodeling stage of tendon repair in a dose-dependent manner. At histology and histomorphology evaluation, high doses of rBMSCs-EVs produced better restoration of tendon architecture, with optimal tendon-fiber alignment and lower vascularity. Higher EV-concentrations demonstrated greater expression of collagen type I and lower expression of collagen type III. BMSC-EVs hold promise as a novel cell-free modality for the management of tendon injuries