Strong and safe Nash equilibrium in some repeated 3-player games

We consider a 3-player game in the normal form, in which each player has two actions. We assume that the game is symmetric and repeated infinitely many times. At each stage players make their choices knowing only the average payoffs from previous stages of all the players. A strategy of a player in the repeated game is a function defined on the convex hull of the set of payoffs. Our aim is to construct a strong Nash equilibrium in the repeated game, i.e. a strategy profile being resistant to deviations by coalitions. Constructed equilibrium strategies are safe, i.e. the non-deviating player payoff is not smaller than the equilibrium payoff in the stage game, and deviating players' payoffs do not exceed the non-deviating player payoff more than a positive constant which can be arbitrary small and chosen by the non-deviating player. Our construction is inspired by Smale's good strategies described in \cite{smale}, where the repeated Prisoner's Dilemma was considered. In proofs we use arguments based on approachability and strong approachability type results.Comment: 19 page

Hyperbolicity of systems describing value functions in differential games which model duopoly problems

Based on the Bressan and Shen approach ([2] or [7]), we present the extension of the class of non-zero sum dierential games for which value functions are described by a weakly hyperbolic Hamilton-Jacobi system. The considered value functions are determined by a Pareto optimality condition for instantaneous gain functions, for which we compare two methods of the unique choice Pareto optimal strategies. We present the procedure of applying this approach for duopoly

Polish paralympic sports in the opinion of athletes and coaches in retrospective studies

The study aimed to identify the limitations observed in Polish Paralympic sport depending on the environment in which athletes train on a daily basis. The study included 581 persons divided into two basic groups. The first group consists of athletes (n = 324) and coaches (n = 88) appointed to the national team by associations and unions providing sports training exclusively for athletes with disabilities. The second group consisted of athletes with disabilities (n = 146) and their coaches (n = 23), who work in national sports associations working for both able-bodied and disabled people. The study used the diagnostic survey method with a questionnaire developed by Sobiecka. The difficulties indicated by the respondents referred to various aspects related to the activity in professional sport. Particularly emphasised difficulties were related to organizational and financial limitations as well as the management and coaching staff. At the same time, it was demonstrated that the environment was a differentiating factor between the studied groups of athletes and coaches

Semi-Cooperative Strategies in Differential Games Which Model Duopoly Problems

Dynamiczne modele duopolu są obiektem zainteresowania osób zajmujących się teorią gier od wielu lat. Typowym podejściem do rozwiązania tak zadanego problemu jest poszukiwanie równowag Nasha wśród strategii w pętli zamkniętej. Sposób ten opiera się na pomocniczym wykorzystaniu funkcji wartości, które spełniają układ równań różniczkowych cząstkowych pierwszego rzędu. Niestety, uzyskany w ten sposób układ w ogólności nie jest dobrze postawionym problemem, co oznacza, że niezasadne jest poszukiwanie numerycznego rozwiązania zagadnienia. Nowym podejściem są strategie semi-kooperatywne, pozwalające na badanie ukrytej kooperacji między graczami. W tym wypadku układ równań różniczkowych opisujących funkcje wypłaty jest hiperboliczny, co jest niezbędne, by jego rozwiązanie istniało i było wyznaczone jednoznacznie. Teoria ta może być efektywnie wykorzystana w przypadku modelu Lanchestera, co zostanie pokazane w niniejszym artykule.In the present paper, there is considered a class of non-cooperative differential finite horizon games for two players. Firstly, Nash equilibrium in feedback form are presented. In general, the systems of Hamilton-Jacobi equations generated by this strategies are ill-posed. Secondly, the paper is concerned with semi-cooperative strategies. In this case, the system of Hamilton-Jacobi equations is hyperbolic for duopoly problems. As semi-cooperative strategies are not unique, there is presented the application of Nash solution for bargaining problems to receive unique strategies. This approach is proper also for non-symetric situations. The theory is illustrated by Lanchester model

Hyperbolicity of systems describing value functions in differential games which model duopoly problems

Tyt. z nagłówka.Bibliogr. s. 100.Based on the Bressan and Shen approach (Bressan and Shen, 2004; Shen, 2009), we present an extension of the class of non-zero sum differential games for which value functions are described by a weakly hyperbolic Hamilton–Jacobi system. The considered value functions are determined by a Pareto optimality condition for instantaneous gain functions, for which we compare two methods of the unique choice Pareto optimal strategies. We present the procedure of applying this approach for duopoly.Dostępny również w formie drukowanej.KEYWORDS: duopoly models, semi-cooperative feedback strategies, Pareto optimality, hyperbolic partial differential equations

Tourism in rural areas of Castilla-la Mancha

The rural areas of Castilla-La Mancha have managed to preserve a unique natural and cultural character. A great diversity of touristic qualities makes the region especially attractive for development of rural tourism. For many years, the autonomous community of Castilla-La Mancha had to cope with numerous socio-economic difficulties. Development of the tourist industry resulted in diversification of income sources and higher level of employment. Another positive effect of the process was activation of female members of the community. The principle aim of this article is to underline the complementary role of tourism in rural areas in relation to agriculture and urban tourism

Endometriotic Peritoneal Fluid Stimulates Recruitment of CD4+CD25highFOXP3+ Treg Cells

Endometriosis is a common gynecological disorder characterized by the presence of endometrial-like tissue outside the uterus. The disease is associated with disturbed local and systemic immunity. It has been reported that the proportion of CD4+CD25highFOXP3+ Treg cells may be significantly increased in the peritoneal fluid of patients with endometriosis. Therefore, the aim of our study was to investigate whether the proportions of Treg cells in the peritoneal cavity of patients with endometriosis are related to the chemotactic and stimulatory activity of the local peritoneal milieu. The peritoneal fluid was collected from 13 women with ovarian endometriosis and 12 control women without the disease. T cell populations were analyzed by flow cytometry, cytokines and chemokines were evaluated using the cytometric bead kit, and cell chemotaxis was studied by cell migration assay. We confirmed that the proportions of Treg cells are increased in the peritoneal fluid of women with endometriosis as compared to the control women. Endometriosis was also associated with elevated concentrations of IL-6, IL-10, and TGF-β1/2 as well as CCL20, CXCL8, CXCL9, and CXCL10. We did not reveal any changes in the proportion of peritoneal Th17 cells and concentrations of IL-17A. Peritoneal Treg cells positively correlated with concentrations of TGF-β, IL-10, and CCL20. Endometriotic peritoneal fluid stimulated chemotaxis of both CD4+ and Treg cells. This chemotactic activity positively correlated with concentrations of CCL20. CCL20 stimulated the migration of Treg cells, and the chemotactic activity of the endometriotic peritoneal fluid was inhibited by neutralizing anti-CCL20 antibodies. These results imply that increased proportions of the peritoneal Treg cells in women with endometriosis may result from attraction and activation by local chemokines and cytokines, especially CCL20 and TGF-β. Since Treg cells contribute to the immunopathogenesis of endometriosis, their chemotaxis and activation may be considered as a target for therapeutic intervention