Analytical models for well-mixed populations of cooperators and defectors under limiting resources

In the study of the evolution of cooperation, resource limitations are usually assumed just to provide a finite population size. Recently, however, agent-based models have pointed out that resource limitation may modify the original structure of the interactions and allow for the survival of unconditional cooperators in well-mixed populations. Here, we present analytical simplified versions of two types of agent-based models recently published: one in which the limiting resource constrains the ability of reproduction of individuals but not their survival, and a second one where the limiting resource is necessary for both reproduction and survival. One finds that the analytical models display, with a few differences, the same qualitative behavior of the more complex agent-based models. In addition, the analytical models allow us to expand the study and identify the dimensionless parameters governing the final fate of the system, such as coexistence of cooperators and defectors, or dominance of defectors or of cooperators. We provide a detailed analysis of the occurring phase transitions as these parameters are varied.Comment: 7 pages, 8 figure

Stability and robustness analysis of cooperation cycles driven by destructive agents in finite populations

The emergence and promotion of cooperation are two of the main issues in evolutionary game theory, as cooperation is amenable to exploitation by defectors, which take advantage of cooperative individuals at no cost, dooming them to extinction. It has been recently shown that the existence of purely destructive agents (termed jokers) acting on the common enterprises (public goods games) can induce stable limit cycles among cooperation, defection, and destruction when infinite populations are considered. These cycles allow for time lapses in which cooperators represent a relevant fraction of the population, providing a mechanism for the emergence of cooperative states in nature and human societies. Here we study analytically and through agent-based simulations the dynamics generated by jokers in finite populations for several selection rules. Cycles appear in all cases studied, thus showing that the joker dynamics generically yields a robust cyclic behavior not restricted to infinite populations. We also compute the average time in which the population consists mostly of just one strategy and compare the results with numerical simulations.Financial support from the Ministerio de Ciencia y Tecnología (Spain) under Projects No. FIS2009-13730-C02-02 (A.A.) and No. FIS2009-13370-C02-01 (J.C. and R.J.R.), MOSAICO, PRODIEVO, and Complexity-NET RESINEE (J.A.C.); from the Barcelona Graduate School of Economics and the government of Catalonia (A.A.); from the Generalitat de Catalunya under Projects No. 2009SGR0838 (A.A.) and No. 2009SGR0164 (J.C. and R.J.R.); and from Comunidad de Madrid under Project MODELICO-CM (J.A.C.) is appreciated. R.J.R. acknowledges the financial support of the Universitat Autònoma de Barcelona and the Spanish government

The Joker effect: cooperation driven by destructive agents

Understanding the emergence of cooperation is a central issue in evolutionary game theory. The hardest setup for the attainment of cooperation in a population of individuals is the Public Goods game in which cooperative agents generate a common good at their own expenses, while defectors "free-ride" this good. Eventually this causes the exhaustion of the good, a situation which is bad for everybody. Previous results have shown that introducing reputation, allowing for volunteer participation, punishing defectors, rewarding cooperators or structuring agents, can enhance cooperation. Here we present a model which shows how the introduction of rare, malicious agents -that we term jokers- performing just destructive actions on the other agents induce bursts of cooperation. The appearance of jokers promotes a rock-paper-scissors dynamics, where jokers outbeat defectors and cooperators outperform jokers, which are subsequently invaded by defectors. Thus, paradoxically, the existence of destructive agents acting indiscriminately promotes cooperation.Comment: Accepted for publication in the Journal of Theoretical Biology (JTB

Structure stability of free copper nanoclusters: FSA-DFT Cubuilding and FDM-XANES study

We present ab initio simulations of X-ray Absorption Near-Edge Structure (XANES) spectra, performed on model clusters built by fast simulated annealing and optimized by Density Functional Theory (DFT) minimization. As is known, larger stability of Cu clusters with 20 atoms was found in comparison with those with 19 and 21 atoms. Based on this knowledge, we show the sensitivity of the XANES technique on the number of atoms n, (c.a 20), and on the morphology of the Cun nanoclusters. For this study we used both L3 and K edges and found the former more sensitive. In addition, in the case of the K XANES edge, we carry out the simulations using four different methods, to observe their performance in arrays of a few atoms. Even more, we obtain a good agreement between our results and previous predictions on the HOMO-LUMO gaps for these systems.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicada

On the influence of resources use and destruction on the evolution of cooperation

La explosiva introducción de la teoría de redes y los métodos estocásticos en el estudio de poblaciones finitas ha llevado a un nuevo nivel en el uso de la teoría de juegos evolutiva. La complejidad de los sistemas representados ha crecido de manera exponencial, y ha atraído el interés de científicos de diferentes especialidades, incluyendo la biología, la física, la economía, la sociología o la lingüística; y en el centro de una gran cantidad de estudios todavía se encuentra el problema de la emergencia y evolución de la cooperación, no sólo en contextos biológicos, sino en el humano, donde la complejidad de las relaciones interpersonales y redes de contactos va en aumento en una sociedad modelada por la aparición de nuevas tecnologías de la información y la comunicación. Sin embargo, el desarrollo de un nuevo marco teórico, la teoría de juegos evolutiva, gracias al cual somos capaces de representar algunas de las complejidades de la sociedad y la naturaleza, no ha acarreado un estudio profundo de uno de los factores más importantes en la evolución: la existencia de una cantidad finita de recursos en ecosistemas, así como en la Tierra. Este factor, junto con la cooperación entre individuos, es de fundamental importancia para la formación de sociedades y de vida multicelular, junto a otras estructuras de orden superior. En este trabajo, mi intención es realizar una primera aproximación a la introducción de restricciones en la cantidad de recursos disponibles en modelos de teoría de juegos evolutiva, estudiando la interrelación entre la emergencia y estabilidad de comportamientos cooperativos y la finitud de recursos. Además, en este estudio proporciono una definición de comportamiento cooperativo, la cual pone de relieve que los comportamientos pacifistas y pacíficos, así como los que evitan activamente los conflictos, son comportamientos cooperativos, incluso si no proporcionan beneficios directos apreciables. Para terminar, también estudio el efecto de los comportamientos destructivos en la evolución de la cooperación, encontrando el primer ejemplo –hasta donde llega mi conocimiento– de comportamiento simple que permite la emergencia de ciclos evolutivos robustos.The explosive introduction of network theory and stochastic methods for the study of finite populations has recently led to a new step in the use of evolutionary game theoretical methods. The complexity of the represented systems has grown exponentially, and has attracted the interest of scientists from many different branches, as biology, physics, economy, sociology or linguistics. And on the core of most studies still lies the same original problem, that of the emergence and evolution of cooperation, not only in biological contexts, but also in a human one, where the complexity of the relationships and contact networks is increasing in a society shaped by the appearance of new information and communication technologies. However, the development of a new theoretical framework, evolutionary game theory, which is able to represent some of the intricacies of our society and nature, did not carry attached a deep analyses of one of the most important factors in evolution: the finiteness of resources in ecosystems as in the Earth. This factor, together with cooperation, is of fundamental importance in the formation of societies and multicellular life (among other higher-order structures). In this work, I aim to make a first approach to the introduction of such resource constraints into evolutionary game theoretical models by studying the interplay between the emergence and stability of cooperative behaviours and finiteness of resources. In addition, I provide in this study a definition of cooperative behaviours, and remark that pacifist, pacific, and conflict avoiding behaviours, are cooperative behaviours, even if they lead to no appreciable direct benefit. To finish, I also study the effect of destructive behaviours on the evolution of cooperation, finding the first example --to my knowledge-- of a simple behaviour that allows for robust evolutionary cycles

Scarcity may promote cooperation in populations of simple agents

In the study of the evolution of cooperation, resource limitations are usually assumed just to provide a finite population size. Recently, however, it has been pointed out that resource limitation may also generate dynamical payoffs able to modify the original structure of the games. Here we study analytically a phase transition from a homogeneous population of defectors when resources are abundant to the survival of unconditional cooperators when resources reduce below a threshold. To this end, we introduce a model of simple agents, with no memory or ability of recognition, interacting in well-mixed populations. The result might shed light on the role played by resource constraints on the origin of multicellularity

Analytical models for well-mixed populations of cooperators and defectors under limiting resources

In the study of the evolution of cooperation, resource limitations are usually assumed just to provide a finite population size. Recently, however, agent-based models have pointed out that resource limitation may modify the original structure of the interactions and allow for the survival of unconditional cooperators in well-mixed populations. Here, we present analytical simplified versions of two types of agent-based models recently published: one in which the limiting resource constrains the ability of reproduction of individuals but not their survival, and a second one where the limiting resource is necessary for both reproduction and survival. One finds that the analytical models display, with a few differences, the same qualitative behavior of the more complex agent-based models. In addition, the analytical models allow us to expand the study and identify the dimensionless parameters governing the final fate of the system, such as coexistence of cooperators and defectors, or dominance of defectors or of cooperators. We provide a detailed analysis of the occurring phase transitions as these parameters are varied

On the influence of resources use and destruction on the evolution of cooperation

La explosiva introducción de la teoría de redes y los métodos estocásticos en el estudio de poblaciones finitas ha llevado a un nuevo nivel en el uso de la teoría de juegos evolutiva. La complejidad de los sistemas representados ha crecido de manera exponencial, y ha atraído el interés de científicos de diferentes especialidades, incluyendo la biología, la física, la economía, la sociología o la lingüística; y en el centro de una gran cantidad de estudios todavía se encuentra el problema de la emergencia y evolución de la cooperación, no sólo en contextos biológicos, sino en el humano, donde la complejidad de las relaciones interpersonales y redes de contactos va en aumento en una sociedad modelada por la aparición de nuevas tecnologías de la información y la comunicación. Sin embargo, el desarrollo de un nuevo marco teórico, la teoría de juegos evolutiva, gracias al cual somos capaces de representar algunas de las complejidades de la sociedad y la naturaleza, no ha acarreado un estudio profundo de uno de los factores más importantes en la evolución: la existencia de una cantidad finita de recursos en ecosistemas, así como en la Tierra. Este factor, junto con la cooperación entre individuos, es de fundamental importancia para la formación de sociedades y de vida multicelular, junto a otras estructuras de orden superior. En este trabajo, mi intención es realizar una primera aproximación a la introducción de restricciones en la cantidad de recursos disponibles en modelos de teoría de juegos evolutiva, estudiando la interrelación entre la emergencia y estabilidad de comportamientos cooperativos y la finitud de recursos. Además, en este estudio proporciono una definición de comportamiento cooperativo, la cual pone de relieve que los comportamientos pacifistas y pacíficos, así como los que evitan activamente los conflictos, son comportamientos cooperativos, incluso si no proporcionan beneficios directos apreciables. Para terminar, también estudio el efecto de los comportamientos destructivos en la evolución de la cooperación, encontrando el primer ejemplo -hasta donde llega mi conocimiento- de comportamiento simple que permite la emergencia de ciclos evolutivos robustos.The explosive introduction of network theory and stochastic methods for the study of finite populations has recently led to a new step in the use of evolutionary game theoretical methods. The complexity of the represented systems has grown exponentially, and has attracted the interest of scientists from many different branches, as biology, physics, economy, sociology or linguistics. And on the core of most studies still lies the same original problem, that of the emergence and evolution of cooperation, not only in biological contexts, but also in a human one, where the complexity of the relationships and contact networks is increasing in a society shaped by the appearance of new information and communication technologies. However, the development of a new theoretical framework, evolutionary game theory, which is able to represent some of the intricacies of our society and nature, did not carry attached a deep analyses of one of the most important factors in evolution: the finiteness of resources in ecosystems as in the Earth. This factor, together with cooperation, is of fundamental importance in the formation of societies and multicellular life (among other higher-order structures). In this work, I aim to make a first approach to the introduction of such resource constraints into evolutionary game theoretical models by studying the interplay between the emergence and stability of cooperative behaviours and finiteness of resources. In addition, I provide in this study a definition of cooperative behaviours, and remark that pacifist, pacific, and conflict avoiding behaviours, are cooperative behaviours, even if they lead to no appreciable direct benefit. To finish, I also study the effect of destructive behaviours on the evolution of cooperation, finding the first example --to my knowledge-- of a simple behaviour that allows for robust evolutionary cycles