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Economic unions are international agreements oriented to increase economic efficiency and establishing political and cultural ties between the member countries. Becoming a member of an existing union usually requires the approval of both the candidate and members, while leaving it may require only the unilateral will of the exiting country. There are many examples of accession of states to previously consolidated economic unions, and a recent example of leaving is the withdrawal of the United Kingdom from the European Union. Motivated by the Brexit process, in this paper we propose an agent-based model to study the determinant factors driving withdrawals from an economic union. We show that both Union and local taxes promote the exits, whereas customs fees out of the Union boost cohesion. Furthermore, heterogeneity in both business conditions and wealth distribution promotes withdrawals, while countries' size diversity does not have a significant effect on them. We also deep into the individual causes that lead to dissatisfaction and, ultimately, to exits. We found that, for low Union taxes, the wealth inequality within the country is the leading cause of anti-Union opinion spreading. Conversely, for high Union taxes, the country's performance turns out to be the main driving force, resulting in a risk of wealthier countries leaving the Union. These findings will be helpful for the design of economic policies and effective informative campaigns., Comment: 7 figures, 1 table

Since M. A. Nowak & R. May’s (1992) influential paper, limiting each agent’s interactions to a few neighbors in a network of contacts has been proposed as the simplest mechanism to support the evolution of cooperation in biological and socio-economic systems. The network allows cooperative agents to self-assort into clusters, within which they reciprocate cooperation. This (induced) network reciprocity has been observed in several theoreticalmodels and shown to predict the fixation of cooperation under a simple rule: the benefit produced by an act of cooperation must outweigh the cost of cooperating with all neighbors. However, the experimental evidence among humans is controversial: though the rule seems to be confirmed, the underlying modeling assumptions are not. Specifically, models assume that agents update their strategies by imitating better performing neighbors, even though imitation lacks rationality when interactions are far from all-to-all. Indeed, imitation did not emerge in experiments. What did emerge is that humans are conditioned by their own mood and that, when in a cooperative mood, they reciprocate cooperation. To help resolve the controversy, we design a model in which we rationally confront the two main behaviors emerging from experiments—reciprocal cooperation and unconditional defection—in a networked prisoner’s dilemma. Rationality is introduced by means of a predictive rule for strategy update and is bounded by the assumed model society. We show that both reciprocity and a multi-step predictive horizon are necessary to stabilize cooperation, and sufficient for its fixation, provided the game benefit-to-cost ratio is larger than a measure of network connectivity. We hence rediscover the rule of network reciprocity, underpinned however by a different evolutionary mechanism.

Since Nowak & May's (1992) influential paper, network reciprocity--the fact that individuals' interactions repeated within a local neighborhood support the evolution of cooperation--has been confirmed in several theoretical models. Essentially, local interactions allow cooperators to stay protected from exploiters by assorting into clusters, and the heterogeneity of the network of contacts--the co-presence of low- and high-connected nodes--has been shown to further favor cooperation. The few available large-scale experiments on humans have however missed these effects. The reason is that, while models assume that individuals update strategy by imitating better performing neighbors, experiments showed that humans are more prone to reciprocate cooperation than to compare payoffs. Inspired by the empirical results, we rethink network reciprocity as a rational form of direct reciprocity on networks--networked rational reciprocity--indeed made possible by the locality of interactions. We show that reciprocal altruism in a networked prisoner's dilemma can invade and fixate in any network of rational agents, profit-maximizing over an horizon of future interactions. We find that networked rational reciprocity works better at low average connectivity and we unveil the role of network heterogeneity. Only if cooperating hubs invest in the initial cost of exploitation, the invasion of cooperation is boosted; it is otherwise hindered. Although humans might not be as rational as here assumed, our results could help the design and interpretation of new experiments in social and economic networks

A general procedure to formulate asexual (unstructured, deterministic) population dynamical models resulting from individual pairwise interactions is proposed. Individuals are characterized by a continuous strategy that represents all their behavioral, morphological, and functional traits. Populations group conspecific individuals with identical strategy and are measured by densities in space. Species can be monomorphic, if only one strategy is present, or polymorphic otherwise. The procedure highlights the structural properties fulfilled by the population per-capita growth rates. In particular, the effect of perturbing a set of similar strategies is proportional to the product of the corresponding densities, with a proportionality coefficient that is density-dependent only through the total density. This generalizes the law of mass action, which traditionally refers to the case in which the per-capita growth rates are linearly density-dependent and insensitive to joint strategy perturbations. Being underpinned with individual strategies, the proposed procedure is most useful for evolutionary considerations, in the case strategies are inheritable. The developed body of theory is exemplified on a Holling-type-II many-prey-one-predator system and on a model of a cannibalistic community., Submitted to Journal of Mathematical Biology on Feb. 3, 2014

The theory of dynamical systems studies the behavior of solutions of systems, like nonlinear ordinary differential equations (ODEs), depending upon parameters. Using qualitative methods of bifurcation theory, the behavior of the system is characterized for various parameter combinations. In particular, the catalog of system behaviors showing qualitative differences can be identified, together with the regions in parameter space where the different behaviors occur. Bifurcations delimit such regions. Symbolic and analytical approaches are in general infeasible, but numerical bifurcation analysis is a powerful tool that aids in the understanding of a nonlinear system. When computing power became widely available, algorithms for this type of analysis matured and the first codes were developed. With the development of suitable algorithms, the advancement in the qualitative theory has found its way into several software projects evolving over time. The availability of software packages allows scientists to study and adjust their models and to draw conclusions about their dynamics.

gráficos In this thesis, we have reviewed the theory of Adaptive Dynamics, a theoretical background originated in evolutionary biology linking demographic dynamics to evolutionary changes, allowing it to describe evolutionary dynamics in the long-term when considering innovations as small and rare events in the market time scale. From this perspective, three mathematical models have been formulated to describe evolutionary branching: the coexistence between resident and similar innovative technologies and their further divergence in the evolutionary space. The first model addresses the problem of determining conditions on the energy market diversification from adaptive dynamics and the impact the imposition/allocation of taxes/subsidies may have on controlling market diversification. The second model explores the Coffee Berry Borer (Hypothenemus hampei) and its role in the evolutionary diversification of the coffee market; the influence that consumer's preference and control practices have on diversification is studied in detail, and correspond to the main source of insights. Finally, the third model in the fifth chapter, describes the competition among public transport systems, considering the number of transported passengers as the differentiation attribute is presented, the analysis allows to answer the question of under what condition the market diversifies, and which are the levels of transported passengers that will be reached in the long term depending on the budget allocation rate destined to increase the number of users. Adaptive dynamics describes evolution through an ordinary differential equation known as the canonical equation, which smooths on a continuous path the successive processes of innovation and substitution. This approach considers interactions to be the evolutionary driving force and considers the feedback between evolutionary change and the selection forces that agents undergo. One of the main (general) contributions of this thesis is to illustrate in detail how the theory of adaptive dynamics is very useful in areas of knowledge quite distant from evolutionary biology, in particular for engineering, given that its results predict the systems' long-term dynamics, as well as to control in the demographic/market timescale and to influence the long-term behavior of the evolving attributes in the evolutionary timescale. (Texto tomado de la fuente) En la ejecución de esta tesis, hemos revisado la teoría de la dinámicas adaptativas, un trasfondo teórico que se origina en la biología evolutiva, que vincula la dinámica demográfica con los cambios evolutivos, y permite describir la dinámica evolutiva a largo plazo al considerar las innovaciones como eventos pequeños y raros en la escala de tiempo del mercado. Desde esta perspectiva, se han formulado tres modelos matemáticos que permiten describir la ramificación evolutiva, es decir, la coexistencia entre tecnologías innovadoras residentes y similares y su posterior divergencia en el espacio evolutivo. El primer modelo aborda el problema de determinar las condiciones para la diversificación del mercado energético a partir de las dinámicas adaptativas y el impacto que la imposición/asignación de impuestos/subsidios puede tener en el control de la diversificación del mercado. El segundo modelo explora la broca del café (Hypothenemus hampei) y su papel en la diversificación evolutiva del mercado cafetero; la influencia que las preferencias de los consumidores y las prácticas de control tienen sobre la diversificación se estudia en detalle y corresponde a la principal fuente de información. Además, en el quinto capítulo, se presenta un modelo para la competencia entre los sistemas de transporte público, considerando el número de pasajeros transportados como el atributo de diferenciación; el análisis permite responder a la pregunta bajo qué condiciones se diversifica el mercado y cuáles son los niveles de pasajeros transportados que se alcanzarán a largo plazo dependiendo de la tasa de asignación presupuestaria destinada a aumentar el número de usuarios. La teoría de las dinámicas adaptativas describe la evolución a través de una ecuación diferencial ordinaria conocida como ecuación canónica, que suaviza en una trayectoria continua los procesos sucesivos de innovación y sustitución. Este enfoque considera las interacciones como la fuerza impulsora de la evolución y tiene en cuenta la retroalimentación entre el cambio evolutivo y las fuerzas de selección que sufren los agentes. Una de las principales contribuciones mas generales de esta tesis es ilustrar en detalle cómo la teoría de las dinámicas adaptativas es útil en áreas de conocimiento bastante distantes de la biología evolutiva, en particular para la ingeniería, dado que sus resultados permiten predecir el comportamiento de los sistemas a largo plazo, así como controlar dicho comportamiento en la escala de tiempo demográfica/de mercado e influir en la dinámica a largo plazo de los atributos en evolución en la escala de tiempo evolutiva. Doctorado Doctor en Ingeniería - Ingeniería Automática Mathematical modeling of innovations and technological change Eléctrica, Electrónica, Automatización Y Telecomunicaciones