# American Institute of Mathematical Sciences

ISSN:
2164-6066

eISSN:
2164-6074

All Issues

## Journal of Dynamics & Games

July 2020 , Volume 7 , Issue 3

Special issue on complex systems in economics

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2020, 7(3): i-ii doi: 10.3934/jdg.2020011 +[Abstract](839) +[HTML](244) +[PDF](91.92KB)
Abstract:
2020, 7(3): 175-184 doi: 10.3934/jdg.2020012 +[Abstract](914) +[HTML](196) +[PDF](398.03KB)
Abstract:

Macroeconomic theory and central Banks' policy recommendations have analyzed for decades the link between the expected value of future inflation and its subsequent realization. Agents' inflation expectations have thus become a fundamental input of the economic policy: they allow to know if economic agents are synchronized with the policies and allow the Central Banks to anticipate the market trends. In this paper, we found evidence for the case of Uruguay of a discrepancy between the distribution of agents' inflation expectations and the distribution expected by traditional models. A first consequence is an increase in uncertainty in the estimates; problems related to its asymptotic distribution and the assumptions that arise from this aggregate distribution are analyzed. Another consequence is related to the existence of a structure in the data and the notion of equilibrium in the model. It is concluded that a discussion regarding the nature of the economic phenomenon is essential for the correct specification of the model studied.

2020, 7(3): 185-196 doi: 10.3934/jdg.2020013 +[Abstract](858) +[HTML](169) +[PDF](442.46KB)
Abstract:

This paper generalizes the classical model of determination of production prices for two commodities by introducing a dynamics generated by the possibility that the profit rate can be computed using prices of different stages. In this theoretical framework, the prices show a codependency between the two sectors, given by the rate of profit, and inter-industry transactions. In this setup and using discrete time, the general model can be represented by a nonlinear two dimensional dynamical system of difference equations of second order. The study shows that the dynamical system admits a unique solution for any initial condition and that there is a unique nontrivial equilibrium. In addition, it can be shown that locally the dynamical system can be represented in the canonical form \begin{document}$x_{t+1} = f(x_{t})$\end{document} and that the stability of the equilibrium depends on the parameters of the production process. Future research includes the extension of the model to the case of several commodities and the closed solution of the model.

2020, 7(3): 197-208 doi: 10.3934/jdg.2020014 +[Abstract](1386) +[HTML](220) +[PDF](965.23KB)
Abstract:

This paper presents a reformulation of the classical Solow-Swan growth model where a dynamic of the endogenous population is incorporated. In our model, the population growth rate continually depends on per capita consumption. We find that – as in the classic Solow-Swan model – there is a steady state for the capital-labour ratio, which is always lower than that deduced from the original model with zero population growth rate, but it is not necessarily unique. Under certain conditions, there is an odd amount, and only the smallest and the largest are locally stable. Finally, a study of comparative static of stationary states is performed by varying the total factor productivity, and the results are compared with those of the original model. It is found that the effects of exogenous variables on endogenous variables differ from the original model.

2020, 7(3): 209-224 doi: 10.3934/jdg.2020015 +[Abstract](873) +[HTML](178) +[PDF](732.05KB)
Abstract:

In a complex system model we simulate runs for different strategies of economic agents to study diverse types of fluctuations. The liquidity of financial assets arises as a result of agent's interaction and not as intrinsic properties of the assets. Small differences in the strategic rules adopted by the agents lead to divergent paths of market liquidity. Our simulation also supports the idea that the higher the maximum local allowed fluctuation the higher the path divergence.

2020, 7(3): 225-237 doi: 10.3934/jdg.2020016 +[Abstract](768) +[HTML](176) +[PDF](539.27KB)
Abstract:

One consequence of the fact that a large number of agents with different behaviors operate in financial systems is the emergence of certain statistical properties in some time series. Some of these properties contradict the hypotheses that are established in the traditional models of efficient market and portfolio optimization. Among them is the long-range dependence that is the objective of this work. The approach is proposed by fractional calculus, as a generalization of the classic approach to financial markets through semi-martingales. This paper study the existence of this property in variables dependent on the term structure curves of Uruguayan sovereign debt after the 2002 economic crisis.

2020, 7(3): 239-252 doi: 10.3934/jdg.2020017 +[Abstract](781) +[HTML](197) +[PDF](400.68KB)
Abstract:

This paper develops a subgraph network random effects error components structure for network data to perform analysis of variance. In particular, it proposes a model for evaluating the network interdependence of nodes attributes allowing for edge and triangle specific components. The latter serve as a basal model for modeling more general network effects. Consistent estimators of the variance components and Lagrange Multiplier specification tests for evaluating the appropriate model of random components in networks structures is proposed. Monte Carlo simulations show that the tests have good performance in finite samples. The proposed tests is applied to the unsecured (Call) interbank market network in Argentina.