In finite games, the graph of the Nash equilibrium correspondence is a semialgebraic set (i.e. it is defined by finitely many polynomial inequalities). This fact implies many game theoretical results about the structure of equilibria. We show that many of these results can be readily exported to Poisson games even if the expected utility functions are not polynomials. We do this proving that, in Poisson games, the graph of the Nash equilibrium correspondence is a globaly subanalytic set. Many of the properties of semialgebraic sets follow from a set of axioms that the collection of globaly subanalytic sets also satisfy. Hence, we easily show that every Poisson game has finitely many connected components and that at least one of them contains a stable set of equilibria. By the same reasoning, we also show how generic determinacy results in finite games can be extended to Poisson games.

In Poisson games, an extension of perfect equilibrium based on perturbations of the strategy space does not guarantee that players use admissible actions. This observation suggests that such a class of perturbations is not the correct one. We characterize the right space of perturbations to define perfect equilibrium in Poisson games. Furthermore, we use such a space to define the corresponding strategically stable sets of equilibria. We show that they satisfy existence, admissibility, and robustness against iterated deletion of dominated strategies and inferior replies.

A recent literature has found a positive relationship between the disproportionality of the electoral system and the convergence of parties' positions. Such a relationship depends crucially on the assumption that voting is sincere. We show that, when voters are players in the game and not simply automatons that vote for their favorite party, two policy-motivated parties always take extreme positions in equilibrium.

In Poisson games, an extension of perfect equilibrium based on perturbations of the strategy space does not guarantee that players use admissible actions. This observation suggests that such a class of perturbations is not the correct one. We characterize the right space of perturbations to define perfect equilibrium in Poisson games. Furthermore, we use such a space to define the corresponding strategically stable sets of equilibria. We show that they satisfy existence, admissibility, and robustness against iterated deletion of dominated strategies and inferior replies.

Health and school achievement play a crucial role in the integration of migrant students. This study aims to conduct an umbrella review of the effectiveness of school-based strategies on the academic and health outcomes of migrant school-aged children and youth and to link these intervention typologies to the Health Promoting School (HPS) approach. The study was conducted according to the PRISMA statement. Twenty-one reviews were analyzed, and 18 strategies were identified and categorized according to the six components of the HPS whole-school approach: individual skills, the school physical environment, school social environment, school policies, health and social services, and community links. Strategies related to five of the six components were identified, demonstrating that the HPS approach is a fitting framework to address migrant students’ needs. Moreover, evidence about the effects on both health and learning was shown; however, the integration of these two areas should be further explored. Finally, significant conditions that enhance or hinder implementation are described. Multi-component interventions and stakeholder engagement improve intervention impacts, while the relevance of cultural adaptation needs to be clarified. These results contribute to understanding the complexity of the challenges faced by migrant students and of the effective school-based strategies to promote their health and learning.