Dynamic Models for International Environmental Agreements

In this paper we develop a model to analyze, in a dynamic framework, how countries join international environmental agreements (IEAs). In the model, where countries suffer from the same environmental damage as a result of the total global emissions, a non-signatory country decides its emissions by maximizing its own welfare, whereas a signatory country decides its emissions by maximizing the aggregate welfare of all signatory countries. Signatory countries are assumed to be able to punish the non-signatories at a cost. When countries decide on their pollution emissions they account for the evolution of the pollution over time. Moreover, we propose a mechanism to describe how countries reach a stable IEA. The model is able to capture situations with partial cooperation in an IEA stable over time. It also captures situations where all countries participate in a stable agreement, or situations where no stable agreement is feasible. When more than one possibility coexists, the long-term outcome of the game depends on the initial conditions (i.e. the size of the initial group of signatory countries and the pollution level).International Environmental Agreements, Non-Cooperative Dynamic Game, Coalition Stability

Intra-brand competition in a differentiated oligopoly

In this paper we consider a differentiated oligopoly with two product varieties that are supplied by two groups of firms. After computing the Cournot solution of the game, we study its sensitivity to different sources of competition, namely the degree of product substitutability and market composition. Market composition can change either via new firms entering one industry or via firms switching production techniques, thus modifying the intensity of intra-brand competition. After studying the welfare consequences of an intensification of competition, we identify the equilibrium market composition when firms are driven by profit considerations. All the results are expressed in terms of the degree of product substitutability and of what we define “weighted relative efficiency” (WRE), which is a parameter combining both firm characteristics and market conditions

Oligopoly Games with Local Monopolistic Approximation

We propose a repeated oligopoly game where quantity setting firms have incomplete knowledge of the demand function of the market in which they operate. At each time step they solve a profit maximization problem by using a subjective approximation of the demand function based on a local estimate its partial derivative, computed at the current values of prices and outputs, obtained through market experiments. At each time step they extrapolate such local approximation by assuming a linear demand function and ignoring the effects of the competitors outputs. Despite a so rough approximation, that we call "Local Monopolistic Approximation" (LMA), the repeated game may converge to a Nash equilibrium of the true oligopoly game, i.e. the game played under the assumption of full information. An explicit form of the dynamical system that describes the time evolution of oligopoly games with LMA is given for arbitrary differentiable demand functions, provided that the cost functions are linear or quadratic. Sufficient conditions for the local stability of Nash Equilibria are given. In the particular case of an isoelastic demand function, we show that the repeatead game based on LMA always converges to a Nash equilibrium, both with linear and quadratic cost functions. This stability result is compared with "best reply" dynamics, obtained under the assumption of isoelastic demand (fully known by the players) and linear costs.Oligopoly games, bounded rationality, subjective demand, Nash equilibrium, dynamical systems, stability

Disease-Modifying Therapies and Coronavirus Disease 2019 Severity in Multiple Sclerosis

Objective: This study was undertaken to assess the impact of immunosuppressive and immunomodulatory therapies on the severity of coronavirus disease 2019 (COVID-19) in people with multiple sclerosis (PwMS). Methods: We retrospectively collected data of PwMS with suspected or confirmed COVID-19. All the patients had complete follow-up to death or recovery. Severe COVID-19 was defined by a 3-level variable: mild disease not requiring hospitalization versus pneumonia or hospitalization versus intensive care unit (ICU) admission or death. We evaluated baseline characteristics and MS therapies associated with severe COVID-19 by multivariate and propensity score (PS)-weighted ordinal logistic models. Sensitivity analyses were run to confirm the results. Results: Of 844 PwMS with suspected (n = 565) or confirmed (n = 279) COVID-19, 13 (1.54%) died; 11 of them were in a progressive MS phase, and 8 were without any therapy. Thirty-eight (4.5%) were admitted to an ICU; 99 (11.7%) had radiologically documented pneumonia; 96 (11.4%) were hospitalized. After adjusting for region, age, sex, progressive MS course, Expanded Disability Status Scale, disease duration, body mass index, comorbidities, and recent methylprednisolone use, therapy with an anti-CD20 agent (ocrelizumab or rituximab) was significantly associated (odds ratio [OR] = 2.37, 95% confidence interval [CI] = 1.18-4.74, p = 0.015) with increased risk of severe COVID-19. Recent use (<1 month) of methylprednisolone was also associated with a worse outcome (OR = 5.24, 95% CI = 2.20-12.53, p = 0.001). Results were confirmed by the PS-weighted analysis and by all the sensitivity analyses. Interpretation: This study showed an acceptable level of safety of therapies with a broad array of mechanisms of action. However, some specific elements of risk emerged. These will need to be considered while the COVID-19 pandemic persists

COVID-19 Severity in Multiple Sclerosis: Putting Data Into Context

Background and objectives: It is unclear how multiple sclerosis (MS) affects the severity of COVID-19. The aim of this study is to compare COVID-19-related outcomes collected in an Italian cohort of patients with MS with the outcomes expected in the age- and sex-matched Italian population. Methods: Hospitalization, intensive care unit (ICU) admission, and death after COVID-19 diagnosis of 1,362 patients with MS were compared with the age- and sex-matched Italian population in a retrospective observational case-cohort study with population-based control. The observed vs the expected events were compared in the whole MS cohort and in different subgroups (higher risk: Expanded Disability Status Scale [EDSS] score > 3 or at least 1 comorbidity, lower risk: EDSS score ≤ 3 and no comorbidities) by the χ2 test, and the risk excess was quantified by risk ratios (RRs). Results: The risk of severe events was about twice the risk in the age- and sex-matched Italian population: RR = 2.12 for hospitalization (p < 0.001), RR = 2.19 for ICU admission (p < 0.001), and RR = 2.43 for death (p < 0.001). The excess of risk was confined to the higher-risk group (n = 553). In lower-risk patients (n = 809), the rate of events was close to that of the Italian age- and sex-matched population (RR = 1.12 for hospitalization, RR = 1.52 for ICU admission, and RR = 1.19 for death). In the lower-risk group, an increased hospitalization risk was detected in patients on anti-CD20 (RR = 3.03, p = 0.005), whereas a decrease was detected in patients on interferon (0 observed vs 4 expected events, p = 0.04). Discussion: Overall, the MS cohort had a risk of severe events that is twice the risk than the age- and sex-matched Italian population. This excess of risk is mainly explained by the EDSS score and comorbidities, whereas a residual increase of hospitalization risk was observed in patients on anti-CD20 therapies and a decrease in people on interferon

DMTs and Covid-19 severity in MS: a pooled analysis from Italy and France

We evaluated the effect of DMTs on Covid-19 severity in patients with MS, with a pooled-analysis of two large cohorts from Italy and France. The association of baseline characteristics and DMTs with Covid-19 severity was assessed by multivariate ordinal-logistic models and pooled by a fixed-effect meta-analysis. 1066 patients with MS from Italy and 721 from France were included. In the multivariate model, anti-CD20 therapies were significantly associated (OR = 2.05, 95%CI = 1.39–3.02, p < 0.001) with Covid-19 severity, whereas interferon indicated a decreased risk (OR = 0.42, 95%CI = 0.18–0.99, p = 0.047). This pooled-analysis confirms an increased risk of severe Covid-19 in patients on anti-CD20 therapies and supports the protective role of interferon

Self-image and the Stability of International Environmental Agreements

In this paper we examine the stability of international environmental agreements about a (common) emissions target. By signing the agreement, the parties develop a sense of responsibility to the commitment made, gaining a self-image that contributes to their utility. We study a dynamic two-stage game where all countries act individualistically. We investigate how two fundamental components of the model, that is, the ambition of the pledge and the relative importance given to compliance to the commitment, affect the stability and efficiency of the agreement in terms of global welfare and total emissions. We find that participation is the key driver of all the results and that it is negatively related to the ambition of the pledge and positively related to countries’ level of concern about environmental issues

Evolutionary Dynamics in Heterogeneous Oligopolies for the Exploitation of Renewable Natural Resources

In this paper we provide an overview of some dynamic oligopoly models proposed in the literature to describe the exploitation of a common pool renewable natural resource (e.g. fisheries) when agents can switch between different harvesting strategies. We suggest a switching mechanism which is an alternative version of the discrete-time replicator dynamics based on expected profits and myopic imitation of the better performing behaviors, often denoted as exponential replicator. We finally provide a general framework for modeling situations where authorities allow for different alternative strategies to exploit a natural resource and agents can choose among such possibilities by updating their decisions at discrete times on the basis of profitability considerations