American Institute of Mathematical Sciences

ISSN:
2164-6066

eISSN:
2164-6074

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Journal of Dynamics & Games

July 2018 , Volume 5 , Issue 3

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2018, 5(3): 189-201 doi: 10.3934/jdg.2018012 +[Abstract](255) +[HTML](176) +[PDF](458.0KB)
Abstract:

In this paper we study the theoretical plausibility of the conjecture that inflation arises because imperfectly competitive markets (ICM in the sequel) translate cost pushes in large price increases. We define two different measures of inflation transmission. We compared these measures in several models of ICM and in perfectly competitive markets (PCM in the sequel). In each case we find a necessary and sufficient condition for an ICM to transmit more inflation -according to the two measures-than that transmitted by a PCM.

2018, 5(3): 203-221 doi: 10.3934/jdg.2018013 +[Abstract](286) +[HTML](248) +[PDF](442.62KB)
Abstract:

We study the equivalences between two matching models, where the agents in one side of the market, the workers, have responsive preferences on the set of agents of the other side, the firms. We modify the firms' preferences on subsets of workers and define a function between the set of many-to-many matchings and the set of related many-to-one matchings. We prove that this function restricted to the set of stable matchings is bijective and that preserves the stability of the corresponding matchings in both models. Using this function, we prove that for the many-to-many problem with substitutable preferences for the firms and responsive preferences for the workers, the set of stable matchings is non-empty and has a lattice structure.

2018, 5(3): 223-230 doi: 10.3934/jdg.2018014 +[Abstract](390) +[HTML](253) +[PDF](384.4KB)
Abstract:

Scanning a system's dynamics for critical transitions, i.e. sudden shifts from one system state to another, with the methodology of Early Warning Signals has been shown to yield promising results in many scientific fields. So far however, such investigations focus on aggregated system dynamics modeled with equation-based methods. In this paper the methodology of Early Warning Signals is applied to critical transitions found in the context of Cooperation Games. Since equation-based methods are not well suited to account for interactions in game theoretic settings, an agent-based model of a repeated Cooperation Game is used to generate data. We find that Early Warning Signals can be detected in agent-based simulations of such systems.

2018, 5(3): 231-242 doi: 10.3934/jdg.2018015 +[Abstract](128) +[HTML](73) +[PDF](304.41KB)
Abstract:

This paper compares the outcomes of two three-stage games of two firms competing for quantity with managerial delegation. In fact, we prove that simultaneous choice of managers by the proprietors of the firms followed by Stackelberg-type competition is equivalent to sequential choice of managers followed by Cournot-type competition. We prove equivalence in a general setting, namely, when the duopolistic model is characterised by a non-linear inverse demand function of the form \begin{document}$p_i = a-(q_i)^n-γ (q_j)^n$\end{document}, \begin{document}$i,j = 1,2$\end{document} and \begin{document}$n∈\mathbb{N}$\end{document}.

2018, 5(3): 243-264 doi: 10.3934/jdg.2018016 +[Abstract](359) +[HTML](175) +[PDF](432.4KB)
Abstract:

Radicalization is the process by which people come to adopt increasingly extreme political or religious ideologies. While radical thinking is by no means problematic in itself, it becomes a threat to national security when it leads to violence. We introduce a simple compartmental model (similar to epidemiology models) to describe the radicalization process. We then extend the model to allow for multiple ideologies. Our approach is similar to the one used in the study of multi-strain diseases. Based on our models, we assess several strategies to counter violent extremism.