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The Journal of Dynamics and Games (JDG) is an applied mathematics journal that publishes high quality peer-review and expository papers at the interface of Dynamical Systems (discrete, continuous, deterministic, or stochastic) and Game Theory. Click here for more information

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Hyperopic topologies on $l^{∞}$
Paulo Klinger Monteiro  , Jaime Orrillo  and  Rudy José Rosas Bazán 
2018, 5(1) : 1-7 doi: 10.3934/jdg.2018001 +[Abstract](256) +[HTML](52) +[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}.

On the linearity property for allocation problems and bankruptcy problems
Joss Sánchez-Pérez 
2018, 5(1) : 9-20 doi: 10.3934/jdg.2018002 +[Abstract](39) +[HTML](34) +[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.

Pricing bond options in emerging markets: A case study
Guillermo Magnou  , Ernesto Mordecki  and  Andrés Sosa 
2018, 5(1) : 21-30 doi: 10.3934/jdg.2018003 +[Abstract](109) +[HTML](23) +[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.

A solution for discrete cost sharing problems with non rival consumption
Adriana Navarro-Ramos  and  William Olvera-Lopez 
2018, 5(1) : 31-39 doi: 10.3934/jdg.2018004 +[Abstract](52) +[HTML](20) +[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.

Transitional dynamics, externalities, optimal subsidy, and growth
Enrique R. Casares  , Lucia A. Ruiz-Galindo  and  María Guadalupe García-Salazar 
2018, 5(1) : 41-59 doi: 10.3934/jdg.2018005 +[Abstract](36) +[HTML](27) +[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.

General limit value in dynamic programming
Jérôme Renault 
2014, 1(3) : 471-484 doi: 10.3934/jdg.2014.1.471 +[Abstract](54) +[PDF](385.9KB) Cited By(7)
Pure and Random strategies in differential game with incomplete informations
Pierre Cardaliaguet  , Chloé Jimenez  and  Marc Quincampoix 
2014, 1(3) : 363-375 doi: 10.3934/jdg.2014.1.363 +[Abstract](94) +[PDF](386.0KB) Cited By(6)
Existence of the uniform value in zero-sum repeated games with a more informed controller
Fabien Gensbittel  , Miquel Oliu-Barton  and  Xavier Venel 
2014, 1(3) : 411-445 doi: 10.3934/jdg.2014.1.411 +[Abstract](46) +[PDF](550.1KB) Cited By(6)
Discrete time dynamic oligopolies with adjustment constraints
Chrystie Burr  , Laura Gardini  and  Ferenc Szidarovszky 
2015, 2(1) : 65-87 doi: 10.3934/jdg.2015.2.65 +[Abstract](51) +[PDF](535.9KB) Cited By(4)
Reversibility and oscillations in zero-sum discounted stochastic games
Sylvain Sorin  and  Guillaume Vigeral 
2015, 2(1) : 103-115 doi: 10.3934/jdg.2015.2.103 +[Abstract](41) +[PDF](364.9KB) Cited By(4)
Approachability, regret and calibration: Implications and equivalences
Vianney Perchet 
2014, 1(2) : 181-254 doi: 10.3934/jdg.2014.1.181 +[Abstract](94) +[PDF](897.5KB) Cited By(4)
Nonzero-sum stochastic differential games with additive structure and average payoffs
Beatris Adriana Escobedo-Trujillo  and  José Daniel López-Barrientos 
2014, 1(4) : 555-578 doi: 10.3934/jdg.2014.1.555 +[Abstract](157) +[PDF](527.0KB) Cited By(4)
Paths to stability in the assignment problem
Bettina Klaus  and  Frédéric Payot 
2015, 2(3/4) : 257-287 doi: 10.3934/jdg.2015004 +[Abstract](45) +[PDF](538.5KB) Cited By(3)
Dynamics of human decisions
Renato Soeiro  , Abdelrahim Mousa  , Tânia R. Oliveira  and  Alberto A. Pinto 
2014, 1(1) : 121-151 doi: 10.3934/jdg.2014.1.121 +[Abstract](83) +[PDF](2417.1KB) Cited By(3)
Optimal strategies for operating energy storage in an arbitrage or smoothing market
Lisa C Flatley  , Robert S MacKay  and  Michael Waterson 
2016, 3(4) : 371-398 doi: 10.3934/jdg.2016020 +[Abstract](147) +[PDF](831.3KB) Cited By(2)
Game theoretical modelling of a dynamically evolving network I: General target sequences
Mark Broom  and  Chris Cannings 
2017, 4(4) : 285-318 doi: 10.3934/jdg.2017016 +[Abstract](59) +[HTML](63) +[PDF](1062.6KB) PDF Downloads(10)
Hyperopic topologies on $l^{∞}$
Paulo Klinger Monteiro  , Jaime Orrillo  and  Rudy José Rosas Bazán 
2018, 5(1) : 1-7 doi: 10.3934/jdg.2018001 +[Abstract](256) +[HTML](52) +[PDF](346.6KB) PDF Downloads(9)
A probability criterion for zero-sum stochastic games
Xiangxiang Huang  , Xianping Guo  and  Jianping Peng 
2017, 4(4) : 369-383 doi: 10.3934/jdg.2017020 +[Abstract](60) +[HTML](28) +[PDF](405.5KB) PDF Downloads(7)
A new perspective on the classical Cournot duopoly
Rabah Amir  and  Igor V. Evstigneev 
2017, 4(4) : 361-367 doi: 10.3934/jdg.2017019 +[Abstract](82) +[HTML](27) +[PDF](272.8KB) PDF Downloads(6)
On the linearity property for allocation problems and bankruptcy problems
Joss Sánchez-Pérez 
2018, 5(1) : 9-20 doi: 10.3934/jdg.2018002 +[Abstract](39) +[HTML](34) +[PDF](333.3KB) PDF Downloads(5)
Pricing bond options in emerging markets: A case study
Guillermo Magnou  , Ernesto Mordecki  and  Andrés Sosa 
2018, 5(1) : 21-30 doi: 10.3934/jdg.2018003 +[Abstract](109) +[HTML](23) +[PDF](329.0KB) PDF Downloads(5)
Transitional dynamics, externalities, optimal subsidy, and growth
Enrique R. Casares  , Lucia A. Ruiz-Galindo  and  María Guadalupe García-Salazar 
2018, 5(1) : 41-59 doi: 10.3934/jdg.2018005 +[Abstract](36) +[HTML](27) +[PDF](485.2KB) PDF Downloads(4)
On the hierarchical optimal control of a chain of distributed systems
Getachew K. Befekadu  and  Eduardo L. Pasiliao 
2015, 2(2) : 187-199 doi: 10.3934/jdg.2015.2.187 +[Abstract](39) +[PDF](506.3KB) PDF Downloads(4)
Stability of the replicator dynamics for games in metric spaces
Saul Mendoza-Palacios  and  Onésimo Hernández-Lerma 
2017, 4(4) : 319-333 doi: 10.3934/jdg.2017017 +[Abstract](213) +[HTML](55) +[PDF](417.9KB) PDF Downloads(4)
A solution for discrete cost sharing problems with non rival consumption
Adriana Navarro-Ramos  and  William Olvera-Lopez 
2018, 5(1) : 31-39 doi: 10.3934/jdg.2018004 +[Abstract](52) +[HTML](20) +[PDF](295.3KB) PDF Downloads(4)

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