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.
Traditionally, resource limitation in evolutionary game theory (EGT) is assumed just to impose a constant population size. Here we show that resource limitations may generate dynamical payoffs able to alter an original prisoner's dilemma (PD), and to allow for stable coexistence between unconditional cooperators and defectors in well-mixed populations. This is a consequence of a selforganizing process that turns the interaction payoff matrix into evolutionary neutral, and represents a resource-based control mechanism preventing the spread of defectors. To our knowledge, this is the first example of coexistence in well-mixed populations with a game structure different from a snowdrift game.PACS numbers: 02.50. Le, Cooperative behaviors are common in nature, and necessary for the evolutionary appearance of higher selective units -such as eukaryotic cells or multicellular lifefrom simpler components [1]. However, the survival of the fittest under the action of natural selection seems to foster selfish behaviors taking advantage of other individuals [2,3]. It is therefore intriguing how cooperative behaviors can emerge and survive in a world ruled by natural selection. This issue is frequently addressed in the context of evolutionary game theory (EGT), where the prisoner's dilemma (PD) game [4] has been used as a paradigm for understanding the evolution of cooperation, as its simplified non-iterated version is the worst scenario for the survival of cooperation [5]; if interactions between individuals follow a PD and reproductive success grows with payoffs, cooperative behavior is led to extinction in large well-mixed populations [5,6]. In the last decades some mechanisms have been found allowing cooperative behaviors to survive in the absence of genetic relatedness, but none of them works for the simplified PD in the absence of features such as memory [7,8], reputation gain [9], network structure [10][11][12] or other sensory inputs [13,14].Here we study the influence of resource limitation on the emergence of cooperation. We find that in addition to imposing a finite population size, as usually assumed in EGT [4,5,[7][8][9][10][11][12][13][14][15], it may generate dynamic payoffs [16][17][18]. In the absence of resource limitation the interactions between cooperators and defectors fulfil a simplified PD, as determined by the selfish strategy, and thus cooperators extinguish, as expected in evolving well-mixed populations. Surprisingly, resource limitation may drive a self-organizing process that allows for stable coexistence between cooperators and defectors. In contrast to previous studies including ecological features, in which coexistence happens only in public goods games with variable interaction group sizes [19], it is transient [20] or requires spatial structure [21,22], here we find stable coexistence for pairwise interactions without population structure. This stable coexistence resembles the homeostatic equilibrium in the daisy world [23,24], as both are mediated by environmental factors driving the syste...
To cite this version:Rubén J. Requejo, Juan Camacho. Evolution of cooperation mediated by limiting resources: Connecting resource based models and evolutionary game theory. Journal of Theoretical Biology, Elsevier, 2011, 272 (1) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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.
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.
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