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

Evolutionary games in the multiverse

Evolutionary game dynamics of two players with two strategies has been studied in great detail. These games have been used to model many biologically relevant scenarios, ranging from social dilemmas in mammals to microbial diversity. Some of these games may in fact take place between a number of individuals and not just between two. Here, we address one-shot games with multiple players. As long as we have only two strategies, many results from two player games can be generalized to multiple players. For games with multiple players and more than two strategies, we show that statements derived for pairwise interactions do no longer hold. For two player games with any number of strategies there can be at most one isolated internal equilibrium. For any number of players $\boldsymbol{d}$ with any number of strategies n, there can be at most (d-1)^(n-1) isolated internal equilibria. Multiplayer games show a great dynamical complexity that cannot be captured based on pairwise interactions. Our results hold for any game and can easily be applied for specific cases, e.g. public goods games or multiplayer stag hunts

Spatial Invasion of Cooperation

The evolutionary puzzle of cooperation describes situations where cooperators provide a fitness benefit to other individuals at some cost to themselves. Under Darwinian selection, the evolution of cooperation is a conundrum, whereas non-cooperation (or defection) is not. In the absence of supporting mechanisms, cooperators perform poorly and decrease in abundance. Evolutionary game theory provides a powerful mathematical framework to address the problem of cooperation using the prisoner's dilemma. One well-studied possibility to maintain cooperation is to consider structured populations, where each individual interacts only with a limited subset of the population. This enables cooperators to form clusters such that they are more likely to interact with other cooperators instead of being exploited by defectors. Here we present a detailed analysis of how a few cooperators invade and expand in a world of defectors. If the invasion succeeds, the expansion process takes place in two stages: first, cooperators and defectors quickly establish a local equilibrium and then they uniformly expand in space. The second stage provides good estimates for the global equilibrium frequencies of cooperators and defectors. Under hospitable conditions, cooperators typically form a single, ever growing cluster interspersed with specks of defectors, whereas under more hostile conditions, cooperators form isolated, compact clusters that minimize exploitation by defectors. We provide the first quantitative assessment of the way cooperators arrange in space during invasion and find that the macroscopic properties and the emerging spatial patterns reveal information about the characteristics of the underlying microscopic interactions.MathematicsOrganismic and Evolutionary Biolog

Carrier relaxation in GaAs v-groove quantum wires and the effects of localization

Carrier relaxation processes have been investigated in GaAs/AlGaAs v-groove quantum wires (QWRs) with a large subband separation (46 meV). Signatures of inhibited carrier relaxation mechanisms are seen in temperature-dependent photoluminescence (PL) and photoluminescence-excitation (PLE) measurements; we observe strong emission from the first excited state of the QWR below ~50 K. This is attributed to reduced inter-subband relaxation via phonon scattering between localized states. Theoretical calculations and experimental results indicate that the pinch-off regions, which provide additional two-dimensional confinement for the QWR structure, have a blocking effect on relaxation mechanisms for certain structures within the v-groove. Time-resolved PL measurements show that efficient carrier relaxation from excited QWR states into the ground state, occurs only at temperatures > 30 K. Values for the low temperature radiative lifetimes of the ground- and first excited-state excitons have been obtained (340 ps and 160 ps respectively), and their corresponding localization lengths along the wire estimated.Comment: 9 pages, 8 figures, submitted to Phys. Rev. B Attempted to correct corrupt figure

Extrapolating weak selection in evolutionary games

In evolutionary games, reproductive success is determined by payoffs. Weak selection means that even large differences in game outcomes translate into small fitness differences. Many results have been derived using weak selection approximations, in which perturbation analysis facilitates the derivation of analytical results. Here, we ask whether results derived under weak selection are also qualitatively valid for intermediate and strong selection. By ‘‘qualitatively valid’’ we mean that the ranking of strategies induced by an evolutionary process does not change when the intensity of selection increases. For two-strategy games, we show that the ranking obtained under weak selection cannot be carried over to higher selection intensity if the number of players exceeds two. For games with three (or more) strategies, previous examples for multiplayer games have shown that the ranking of strategies can change with the intensity of selection. In particular, rank changes imply that the most abundant strategy at one intensity of selection can become the least abundant for another. We show that this applies already to pairwise interactions for a broad class of evolutionary processes. Even when both weak and strong selection limits lead to consistent predictions, rank changes can occur for intermediate intensities of selection. To analyze how common such games are, we show numerically that for randomly drawn two-player games with three or more strategies, rank changes frequently occur and their likelihood increases rapidly with the number of strategies n. In particular, rank changes are almost certain for n§8, which jeopardizes the predictive power of results derived for weak selection

Laser Repair of Superalloy Single Crystals with Varying Substrate Orientations

The casting and repair of single-crystal gas turbine blades require specific solidification conditions that prevent the formation of new grains, equiaxed or columnar, ahead of the epitaxial columnar dendrites. These conditions are best determined by microstructure modeling. Present day analytical models of the columnar-to-equiaxed transition (CET) relate the microstructure to local solidification conditions (temperature gradient and interface velocity) without taking into account the effects of (1) a preferred growth direction of the columnar dendrites and (2) a growth competition between columnar grains of different orientations. In this article, the infiuence of these effects on the grain structure of nickel-base superalloy single crystals, which have been resolidified after laser treatment or directionally cast, is determined by experiment and by analytical and numerical modeling. It is shown that two effects arise for the case of a nonzero angle between the local heat flux direction and the preferred dendrite growth axis: (1) the regime of equiaxed growth is extended and (2) a loss of the crystal orientation of the substrate often occurs by growth competition of columnar grains leading to an "oriented-to-misoriented transition” (OMT). The results are essential for the definition of the single-crystal processing window and are important for the service life extension of expensive components in land-based or aircraft gas turbine

Synergy and Discounting of Cooperation in Social Dilemmas

The emergence and maintenance of cooperation by natural selection is an enduring conundrum in evolutionary biology, which has been studied using a variety of game theoretical models inspired by different biological situations. The most widely studied games are the Prisoner's Dilemma, the Snowdrift game and by-product mutualism for pairwise interactions, as well as Public Goods games in larger groups of interacting individuals. Here, we present a general framework for cooperation in social dilemmas in which all the traditional scenarios can be recovered as special cases. In social dilemmas, cooperators provide a benefit to the group at some cost, while defectors exploit the group by reaping the benefits without bearing the costs of cooperation. Using the concepts of discounting and synergy for describing how benefits accumulate when more than one cooperator is present in a group of interacting individuals, we recover the four basic scenarios of evolutionary dynamics given by (i) dominating defection, (ii) coexistence of defectors and cooperators, (iii) dominating cooperation and (iv) bi-stability, in which cooperators and defectors cannot invade each other. Generically, for groups of three or more interacting individuals further, more complex, dynamics can occur. Our framework provides the first unifying approach to model cooperation in different kinds of social dilemmas.Mathematic

Evolutionary Dynamics on Graphs: Efficient Method for Weak Selection

Investigating the evolutionary dynamics of game theoretical interactions in populations where individuals are arranged on a graph can be challenging in terms of computation time. Here, we propose an efficient method to study any type of game on arbitrary graph structures for weak selection. In this limit, evolutionary game dynamics represents a first-order correction to neutral evolution. Spatial correlations can be empirically determined under neutral evolution and provide the basis for formulating the game dynamics as a discrete Markov process by incorporating a detailed description of the microscopic dynamics based on the neutral correlations. This framework is then applied to one of the most intriguing questions in evolutionary biology: the evolution of cooperation. We demonstrate that the degree heterogeneity of a graph impedes cooperation and that the success of tit for tat depends not only on the number of rounds but also on the degree of the graph. Moreover, considering the mutation-selection equilibrium shows that the symmetry of the stationary distribution of states under weak selection is skewed in favor of defectors for larger selection strengths. In particular, degree heterogeneity—a prominent feature of scale-free networks—generally results in a more pronounced increase in the critical benefit-to-cost ratio required for evolution to favor cooperation as compared to regular graphs. This conclusion is corroborated by an analysis of the effects of population structures on the fixation probabilities of strategies in general 2×2 games for different types of graphs. Computer simulations confirm the predictive power of our method and illustrate the improved accuracy as compared to previous studies.MathematicsOrganismic and Evolutionary Biolog