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Bitran, E., Rivera, P., & Villena, M. J. (2014). Water management problems in the Copiapo Basin, Chile: markets, severe scarcity and the regulator. Water Policy, 16(5), 844–863.
Abstract: This research focuses on the determination of the factors that led to the failure of water management in the Copiapo Basin in Chile. Interestingly, the existence of full private ownership and free tradability of water rights has not prevented the overexploitation of groundwater resources. In the paper, firstly, water regulation and the role of the regulator in Chile are briefly discussed. Secondly, the evolution of water resources in the Copiapo region is characterized and analyzed, and the granting of water use rights in the basin in the last 30 years is concisely described. Thirdly, we examine and analyze prices and quantities traded in the water market of the Copiapo region. We will argue that this crisis is a consequence first of failure in regulatory implementation and second of an extremely rigid regulatory framework that leaves limited room for adjustment to changing conditions, especially regarding the emergence of new information concerning water availability. We believe this investigation is not only relevant for this case in particular, but also for other regions and countries where water markets are in place.
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de Kraker, J., Kujawa-Roeleveld, K., Villena, M. J., & Pabon-Pereira, C. (2019). Decentralized Valorization of Residual Flows as an Alternative to the Traditional Urban Waste Management System: The Case of Penalolen in Santiago de Chile. Sustainability, 11(22), 26 pp.
Abstract: Urban residual flows contain significant amounts of valuable nutrients, which, if recovered, could serve as input for the own city needs or those of its immediate surroundings. In this study, the possibilities for decentralized recovery of nutrient rich residual flows in Santiago, Chile, are studied by means of a case study considering technical and socio-economic criteria. In particular, we calculate circularity indicators for organic matter (OM), nitrogen (N), and phosphorus (P) and cost-benefits of household and community on-site technological alternatives. Kitchen waste (KW) and garden residues (GR) as well as urine were considered as system inputs whereas urban agriculture, municipality green, or peri-urban agriculture were the considered destinations for nutrients recovered. The technologies studied were anaerobic digestion, vermicomposting, and composting, while urine storage and struvite precipitation were considered for nutrient recovery from urine. Material flow analysis was used to visualize the inputs and outputs of the baseline situation (the traditional urban waste management system), and of the different household and municipality resource recovery scenarios (the decentralized valorization systems). Our findings show that decentralized valorization of KW and GR are a clear win-win policy, since they can not only produce important environmental benefits for the city in the long run, but also important cost savings considering the landfill fees and residues transportation of the current centralized waste management system.
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Gonzalez, E., & Villena, M. J. (2011). Spatial attrition modeling: Stability conditions for a 2D + t FD formulation. Comput. Math. Appl., 61(11), 3246–3257.
Abstract: 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. (C) 2011 Elsevier Ltd. All rights reserved.
Keywords: PDE; Stability; Reaction-diffusion; Spatial attrition modeling
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Gonzalez, E., & Villena, M. J. (2020). On the spatial dynamics of vaccination: A spatial SIRS-V model. Comput. Math. Appl., 80(5), 733–743.
Abstract: In this paper, we analyze the effects of vaccination from a spatial perspective. We propose a spatial deterministic SIRS-V model, which considers a non-linear system of partial differential equations with explicit attrition and diffusion terms for the vaccination process. The model allows us to simulate numerically the spatial and temporal dynamics of an epidemic, considering different spatial strategies for the vaccination policy. In particular, in our first example we analyze the classical SIRS-V evolution with the addition of movements due to diffusion, while in the second one we focus on modeling one ring vaccination policy. We expect this model can improve spatial predictions of SIR vaccination models by taking into account the spatial dimension of the problem. (C) 2020 Elsevier Ltd. All rights reserved.
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Quinteros, M. J., & Villena, M. J. (2022). On the Dynamics and Stability of the Crime and Punishment Game. Complexity, 2022, 2449031.
Abstract: We study the dynamics and stability of the economics of crime and punishment game from an evolutionary perspective. Specifically, we model the interaction between agents and controllers as an asymmetric game exploring the dynamics of the classic static model using a replicator dynamics equation, given exogenous levels of monitoring and criminal sanctions. The dynamics show five possible equilibria, from which three are stable. Our results show that a culture of honest agents is never stable; however when the penalty is high enough, the system will neutrally tend to an equilibrium of honest agents and a monitoring firm. By contrast, when the probability of detecting wrongdoing is small, the system, in some cases, will remain in a transient state, in which it is impossible to predict the proportion of honest agents.
Keywords: CORRUPTION; LAW
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Quinteros, M. J., Villena, M. J., & Villena, M. G. (2022). An evolutionary game theoretic model of whistleblowing behaviour in organizations. IMA J. Manag. Math., 33(2), 289–314.
Abstract: We present a theoretical model of corruption in organizations. Our specific focus is the role of incentives that aim to encourage whistleblowing behaviour. Corruption is modelled as a social norm of behaviour using evolutionary game theory. In particular, the dynamics of whistleblowing behaviour is captured using the replicator dynamics equation with constant and quadratic monitoring costs. We formally explore the local asymptotic stability of the equilibria. Our findings indicate that the traditional recommendations of the Beckerian approach are usually too expensive and/or unstable. We argue that an efficient mechanism for controlling corruption can be achieved by maintaining efficient salaries and imposing high rewards for whistleblowers when they detect wrongdoing. In the long term, employees can only be honest, or corrupt, or corrupt and whistleblowers; honest and whistleblowing behaviour will not coexist in the long run, since one of these two strategies is always dominated by the other.
Keywords: whistleblowing; corruption; social norms; evolutionary games; incentives
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Villena, M. J., & Araneda, A. A. (2017). Dynamics and stability in retail competition. Math. Comput. Simul., 134, 37–53.
Abstract: 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. (C) 2016 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
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Villena, M. J., & Contreras, M. (2019). Global And Local Advertising Strategies: A Dynamic Multi-Market Optimal Control Model. J. Ind. Manag. Optim., 15(3), 1017–1048.
Abstract: Differential games have been widely used to model advertising strategies of companies. Nevertheless, most of these studies have concentrated on the dynamics and market structure of the problem, neglecting their multi-market dimension. Since nowadays competition typically operates on multi-product contexts and usually in geographically separated markets, the optimal advertising strategies must take into consideration the different levels of disaggregation, especially, for example, in retail multi-product and multi-store competition contexts. In this paper, we look into the decision-making process of a multi-market company that has to decide where, when and how much money to invest in advertising. For this purpose, we develop a model that keeps the dynamic and oligopolistic nature of the traditional advertising game introducing the multi-market dimension of today's economies, while differentiating global (i.e. national TV) from local advertising strategies (i.e. a price discount promotion in a particular store). It is important to note, however, that even though this problem is real for most multi-market companies, it has not been addressed in the differential games literature. On the more technical side, we steer away from the traditional aggregated dynamics of advertising games in two aspects. Firstly, we can model different markets at once, obtaining a global instead of a local optimum, and secondly, since we are incorporating a variable that is common to markets, the resulting equations systems for every market are now coupled. In other words, one's decision in one market does not only affect one's competition in that particular market; it also affects one's decisions and one's competitors in all markets.
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Villena, M. J., & Reus, L. (2016). On the strategic behavior of large investors: A mean-variance portfolio approach. Eur. J. Oper. Res., 254(2), 679–688.
Abstract: 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. We also develop a simplified application of the general model, with two assets and two investors to shed light on the potential strategic behavior of large and atomic investors. Our findings validate the claim that large investors enhance their portfolio performance in relation to perfect market conditions. Besides, we show under which conditions atomic investors can benefit in relation to the standard setting, even if they have not total influence on their eventual performance. The 'two investors-two assets' setting allows us to quantify performance and do sensitivity analysis regarding investors' market power, risk tolerance and price elasticity of demand. Finally, for a group of well known ETFs, we empirically show how price variations change depending on the volume traded. We also explain how to set up and use our model with real market data. (C) 2016 Elsevier B.V. All rights reserved.
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