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Journal of Dynamics & Games

July 2016 , Volume 3 , Issue 3

Special issue on Hellenic-Latin meetings

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Preface
Alberto Adrego Pinto and Michel Benaim
2016, 3(3): i-i doi: 10.3934/jdg.201603i +[Abstract](445) +[PDF](78.9KB)
Abstract:
The Journal of Dynamics and Games (JDG) is pleased to publish a series of special issues based on research and survey papers presented in the Dynamics and Games Hellenic-Latin meetings: Dynamics, Games and Science III, on the occasion of the 50th birthday of Alberto A. Pinto, Porto; 1st Hellenic-Portuguese meeting, Athens; XV Jornadas Latinoamericanas de Teoría Económica, Guanajuato.
    These annual meetings in game theory and applications, with the help of the scientific committees that gather scientists from all around the world, join some of the most notable scientists with young researchers and PhD students. In these meetings the organization committees promote an exciting and friendly atmosphere that helps immensely the scientific interaction among the participants. In these JDG special issues, scientists from all over the world share their latest insights and important results, including the exploration of emerging and current cutting-edge theories and methods in the field.
    We are very thankful to the invited editors of this series of special issues, Elvio Accinelli, Carlos Hervés Beloso, Ignacio Garcia-Jurado, Onésimo Hernandez-Lerma, Alberto A. Álvarez López, Jordi Massó, Alejandro Neme, Bruno Oliveira, Athanasios Yannacopoulos, Jorge Zubelli.
An asymptotic expression for the fixation probability of a mutant in star graphs
Fabio A. C. C. Chalub
2016, 3(3): 217-223 doi: 10.3934/jdg.2016011 +[Abstract](583) +[PDF](436.4KB)
Abstract:
We consider the Moran process in a graph called the ``star'' and obtain the asymptotic expression for the fixation probability of a single mutant when the size of the graph is large. The expression obtained corrects the previously known expression announced in reference [E Lieberman, C Hauert, and MA Nowak. Evolutionary dynamics on graphs. Nature, 433(7023):312–316, 2005] and further studied in [M. Broom and J. Rychtar. An analysis of the fixation probability of a mutant on special classes of non-directed graphs. Proc. R. Soc. A-Math. Phys. Eng. Sci., 464(2098):2609–2627, 2008]. We also show that the star graph is an accelerator of evolution, if the graph is large enough.
A Malthus-Swan-Solow model of economic growth
Luis C. Corchón
2016, 3(3): 225-230 doi: 10.3934/jdg.2016012 +[Abstract](570) +[PDF](377.9KB)
Abstract:
In this paper we introduce in the Solow-Swan growth model a labor supply based on Malthusian ideas. We show that this model may yield several steady states and that an increase in total factor productivity might decrease the capital-labor ratio in a stable equilibrium.
On the evolution of compliance and regulation with tax evading agents
Yannis Petrohilos-Andrianos and Anastasios Xepapadeas
2016, 3(3): 231-260 doi: 10.3934/jdg.2016013 +[Abstract](701) +[PDF](568.5KB)
Abstract:
We study the evolution of compliance and regulation with tax-evading agents, allowing for imitation rather than rationality in the evolution of available strategies distribution in the population. The general framework of the approach combines a classical model for tax evasion where agents are imitators rather than rational optimizers and form an endogenized subjective probability of audit. A regulator chooses values to available policy instruments, either myopically or optimally -within an optimal control setup-, always with respect to the behavior of agents. A comparison is drawn between the evolutionary and rational case in order to evaluate the differences that occur.
A perturbation approach to a class of discounted approximate value iteration algorithms with borel spaces
Óscar Vega-Amaya and Joaquín López-Borbón
2016, 3(3): 261-278 doi: 10.3934/jdg.2016014 +[Abstract](780) +[PDF](464.1KB)
Abstract:
The present paper gives computable performance bounds for the approximate value iteration (AVI) algorithm when are used approximation operators satisfying the following properties: (i) they are positive linear operators; (ii) constant functions are fixed points of such operators; (iii) they have certain continuity property. Such operators define transition probabilities on the state space of the controlled systems. This has two important consequences: (a) one can see the approximating function as the average value of the target function with respect to the induced transition probability; (b) the approximation step in the AVI algorithm can be thought of as a perturbation of the original Markov model. These two facts enable us to give finite-time bounds for the AVI algorithm performance depending on the operators accuracy to approximate the cost function and the transition law of the system. The results are illustrated with numerical approximations for a class of inventory systems.
Evolution and jump in a Walrasian framework
Elvio Accinelli and Enrique Covarrubias
2016, 3(3): 279-301 doi: 10.3934/jdg.2016015 +[Abstract](591) +[PDF](509.5KB)
Abstract:
Lower profit rates play an importan role in the evolution of an ownership private economy. We argue that if managers look to maximize profits rates, then the decision to change, to those branches, or technologies, that offer higher rates of profits, plays an important role in the characterization of economies. If managers choose to produce according to those technologies that promise higher profit rates, then along the time, the distribution of the firms over the set of available technologies change, and therefore the economic fundamentals change. Under conditions of imperfect information, the imitation of the most successful firms plays can a decisive role in deciding how to produce. Along a path of Walrasian equilibria, regular economies can become singular and if this occurs, big changes must be expected after decisions of the firms for the next period.

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