Browsing by Subject "Common knowledge"

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Open Access
Analysis of blood cell production under growth factors switching
(Elsevier B.V., 2017) Djema, W.; Özbay, Hitay; Bonnet, C.; Fridman, E.; Mazenc, F.; Clairambault, J.
Hematopoiesis is a highly complicated biological phenomenon. Improving its mathematical modeling and analysis are essential steps towards consolidating the common knowledge about mechanisms behind blood cells production. On the other hand, trying to deepen the mathematical modeling of this process has a cost and may be highly demanding in terms of mathematical analysis. In this paper, we propose to describe hematopoiesis under growth factor-dependent parameters as a switching system. Thus, we consider that different biological functions involved in hematopoiesis, including aging velocities, are controlled through multiple growth factors. Then we attempt a new approach in the framework of time-delay switching systems, in order to interpret the behavior of the system around its possible positive steady states. We start here with the study of a specific case in which switching is assumed to result from drug infusions. In a broader context, we expect that interpreting cell dynamics using switching systems leads to a good compromise between complexity of realistic models and their mathematical analysis. © 2017
Open Access
Common knowledge and state-dependent equilibria
(Springer, Berlin, Heidelberg, 2012) Dalkıran, Nuh Aygun; Hoffman, M.; Paturi, R.; Ricketts, D.; Vattani, A.
Many puzzling social behaviors, such as avoiding eye contact, using innuendos, and insignificant events that trigger revolutions, seem to relate to common knowledge and coordination, but the exact relationship has yet to be formalized. Herein, we present such a formalization. We state necessary and sufficient conditions for what we call state-dependent equilibria - equilibria where players play different strategies in different states of the world. In particular, if everybody behaves a certain way (e.g. does not revolt) in the usual state of the world, then in order for players to be able to behave a different way (e.g. revolt) in another state of the world, it is both necessary and sufficient for it to be common p-believed that it is not the usual state of the world, where common p-belief is a relaxation of common knowledge introduced by Monderer and Samet [16]. Our framework applies to many player r-coordination games - a generalization of coordination games that we introduce - and common (r,p)-beliefs - a generalization of common p-beliefs that we introduce. We then apply these theorems to two particular signaling structures to obtain novel results. © 2012 Springer-Verlag.