# American Institute of Mathematical Sciences

ISSN:
2164-6066

eISSN:
2164-6074

All Issues

## Journal of Dynamics & Games

January 2018 , Volume 5 , Issue 1

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2018, 5(1): 1-7 doi: 10.3934/jdg.2018001 +[Abstract](1103) +[HTML](319) +[PDF](346.6KB)
Abstract:

Myopic economic agents are well studied in economics. They are impatient. A myopic topology is a topology such that every continuous preference relation is myopic. If the space is \begin{document}$l^{∞}$\end{document}, the Mackey topology \begin{document}$τ _{M}(l^{∞},l^{1})$\end{document}, is the largest locally convex such topology. However there is a growing interest in patient consumers. In this paper we analyze the extreme case of consumers who only value the long run. We call such a consumer hyperopic. We define hyperopic preferences and hyperopic topologies. We show the existence of the largest locally convex hyperopic topology, characterize its dual and determine its relationship with the norm dual of \begin{document}$l^{∞}$\end{document}.

2018, 5(1): 9-20 doi: 10.3934/jdg.2018002 +[Abstract](737) +[HTML](288) +[PDF](333.3KB)
Abstract:

This work provides an analysis of linear rules for bankruptcy problems and allocation problems from an axiomatic point of view and we extend the study of the additivity property presented in Bergantiños and Méndez-Naya [1] and Bergantiños and Vidal-Puga [2]. We offer a decomposition for the space of allocation problems into direct sum of subspaces that are relevant to the study of linear rules and obtain characterizations of certain classes of rules. Furthermore, for bankruptcy problems we propose an alternative version of the additivity property.

2018, 5(1): 21-30 doi: 10.3934/jdg.2018003 +[Abstract](796) +[HTML](266) +[PDF](329.0KB)
Abstract:

We propose two methodologies to price sovereign bond options in emerging markets. The motivation is to provide hedging protection against price fluctuations, departing from the not liquid data provided by the stock exchange. Taking this into account, we first compute prices provided by the Jamshidian formula, when modeling the interest rate through Vasicek model, with parameters estimated with the help of the Kalman filter. The second methodology is the pricing strategy provided by the Black-Derman-Toy tree model. A numerical comparison is carried out. The first equilibrium approach provides parsimonious modeling, is less sensitive to daily changes and more robust, while the second non-arbitrage approach provides more fluctuating but also what can be considered more accurate option prices.

2018, 5(1): 31-39 doi: 10.3934/jdg.2018004 +[Abstract](676) +[HTML](244) +[PDF](295.3KB)
Abstract:

In this paper we show several results regarding to the classical cost sharing problem when each agent requires a set of services but they can share the benefits of one unit of each service, i.e. there is non rival consumption. Specifically, we show a characterized solution for this problem, mainly adapting the well-known axioms that characterize the Shapley value for TU-games into our context. Finally, we present some additional properties that the shown solution satisfy.

2018, 5(1): 41-59 doi: 10.3934/jdg.2018005 +[Abstract](736) +[HTML](415) +[PDF](485.2KB)
Abstract:

We develop an endogenous growth model with two sectors, manufacturing (learning) and non-manufacturing (non-learning). Domestic technological knowledge is only produced in the manufacturing sector through learning by doing. The knowledge produced in the manufacturing sector is available to the non-manufacturing sector. We obtain policy functions for the market economy and the social planner's economy. Thus, with the Pareto-optimal solution, we obtain the path of the optimal investment subsidy rate to the manufacturing sector for the market economy. The optimal investment subsidy rate increases as the market economy moves to the Pareto-optimal steady state.