Marcelo J. Villena

Evolutionary Game Theory and Thorstein Veblen’s Evolutionary Economics: Is EGT Veblenian?

This essay provides an approach to the analysis of the link between Thorstein Veblens evolutionary approach and evolutionary game theory (EGT). We shed some light on the potential contribution of Veblens theory of socioeconomic evolution to the discussion on the application of EGT to social environments. We also investigate to what extent elements of EGT can be used to formalize some of the basic evolutionary principles proposed by Veblen. The methodological imperatives laid down by Veblen, defining an evolutionary approach, are presented. We provide an analytical framework that allows the evaluation of EGT in terms of Veblens evolutionary approach. To better understand the main principles and rationale behind EGT and how it can be applied as a tool for analyzing issues on the diversity, interaction, and evolution of social systems, we discuss this nontraditional approach and its basic concepts. Finally, the main characteristics of EGT are contrasted with Veblens principles.

Spatial Lanchester models

Lanchester equations have been widely used to model combat for many years, nevertheless, one of their most important limitations has been their failure to model the spatial dimension of the problems. Despite the fact that some efforts have been made in order to overcome this drawback, mainly through the use of Reaction-Diffusion equations, there is not yet a consistently clear theoretical framework linking Lanchester equations with these physical systems, apart from similarity. In this paper, a spatial modeling of Lanchester equations is conceptualized on the basis of explicit movement dynamics and balance of forces, ensuring stability and theoretical consistency with the original model. This formulation allows a better understanding and interpretation of the problem, thus improving the current treatment, modeling and comprehension of warfare applications. Finally, as a numerical illustration, a new spatial model of responsive movement is developed, confirming that location influences the results of modeling attrition conflict between two opposite forces.

On the strategic behavior of large investors: A mean-variance portfolio approach

One key assumption of Markowitz’s model is that all traders act as price takers. In this paper, we extend this mean-variance approach in a setting where large investors can move prices. Instead of having an individual optimization problem, we find the investors’ Nash equilibrium and redefine the efficient frontier in this new framework.

Policy making for broadband adoption and usage in Chile through machine learning

For developing countries, such as Chile, we study the influential factors for adoption and usage of broadband services. In particular, subsidies on the broadband price are analyzed to see if this initiative has a significant effect in the broadband penetration. To carry out this study, machine learning techniques are used to identify different household profiles using the data obtained from a survey on access, use, and users of broadband Internet from Chile. Different policies are proposed for each group found, which were then evaluated empirically through Bayesian networks. Results show that an unconditional subsidy for the Internet price does not seem to be very appropriate for everyone since it is only significant for some households groups. The evaluation using Bayesian networks showed that other polices should be considered as well such as the incorporation of computers, Internet applications development, and digital literacy training.

Dynamics and stability in retail competition

Retail competition today can be described by three main features: (i) oligopolistic competition, (ii) multi-store settings, and (iii) the presence of large economies of scale. In these markets, firms usually apply a centralized decisions making process in order to take full advantage of economies of scales, e.g. retail distribution centers. In this paper, we model and analyze the stability and chaos of retail competition considering all these issues. In particular, a dynamic multi-market Cournot-Nash equilibrium with global economies and diseconomies of scale model is developed. We confirm the non-intuitive hypothesis that retail multi-store competition is more unstable than traditional small business that cover the same demand. The main sources of stability are the scale parameter, the number of markets, and the number of firms.

Spatial attrition modeling: Stability conditions for a 2D+t FD formulation

A new general formulation for the spatial modeling of combat is presented, where the main drivers are movement attitudes and struggle evolution. This model in its simplest form is represented by a linear set of two coupled partial differential equations for two independent functions of the space and time variables. Even though the problem has a linear shape, non-negative values for the two functions render this problem as nonlinear. In contrast with other attempts, this model ensures stability and theoretical consistency with the original Lanchester Equations, allowing for a better understanding and interpretation of the spatial modeling. As a numerical illustration a simple combat situation is developed. The model is calibrated to simulate different troop movement tactics that allow an invader force to provoke maximum damage at a minimum cost. The analysis provided here reviews the trade-off between spatial grid and time stepping for attrition cases and then extends it to a new method for guaranteeing good numerical behavior when the solution is expected to grow along the time variable. There is a wide variety of spatial problems that could benefit from this analysis.

Dynamic optimization and its relation to classical and quantum constrained systems

We study the structure of a simple dynamic optimization problem consisting of one state and one control variable, from a physicist’s point of view. By using an analogy to a physical model, we study this system in the classical and quantum frameworks. Classically, the dynamic optimization problem is equivalent to a classical mechanics constrained system, so we must use the Dirac method to analyze it in a correct way. We find that there are two second-class constraints in the model: one fix the momenta associated with the control variables, and the other is a reminder of the optimal control law. The dynamic evolution of this constrained system is given by the Dirac’s bracket of the canonical variables with the Hamiltonian. This dynamic results to be identical to the unconstrained one given by the Pontryagin equations, which are the correct classical equations of motion for our physical optimization problem. In the same Pontryagin scheme, by imposing a closed-loop λ-strategy, the optimality condition for the action gives a consistency relation, which is associated to the Hamilton–Jacobi–Bellman equation of the dynamic programming method. A similar result is achieved by quantizing the classical model. By setting the wave function Ψ(x,t)=eiS(x,t) in the quantum Schrodinger equation, a non-linear partial equation is obtained for the S function. For the right-hand side quantization, this is the Hamilton–Jacobi–Bellman equation, when S(x,t) is identified with the optimal value function. Thus, the Hamilton–Jacobi–Bellman equation in Bellman’s maximum principle, can be interpreted as the quantum approach of the optimization problem.

Stability analysis for spatial attrition with n forces

Close combat between two forces can be modelled through a set of two coupled partial differential equations, of second order in space and first order in time. That problem has been studied and shows a way to find stable solutions by means of a careful selection of the discretization both in time and space and through the use of a simple transformation. The results are generalized here for more interacting forces. It is found that the eigenvalues of the matrix that represent the system dynamics together with the time step size shape up the stability coefficients.