The collapse of cooperation in evolving games

Game theory provides a quantitative framework for analyzing the behavior of rational agents. The Iterated Prisoner's Dilemma in particular has become a standard model for studying cooperation and cheating, with cooperation often emerging as a robust outcome in evolving populations. Here we extend evolutionary game theory by allowing players' strategies as well as their payoffs to evolve in response to selection on heritable mutations. In nature, many organisms engage in mutually beneficial interactions, and individuals may seek to change the ratio of risk to reward for cooperation by altering the resources they commit to cooperative interactions. To study this, we construct a general framework for the co-evolution of strategies and payoffs in arbitrary iterated games. We show that, as payoffs evolve, a trade-off between the benefits and costs of cooperation precipitates a dramatic loss of cooperation under the Iterated Prisoner's Dilemma; and eventually to evolution away from the Prisoner's Dilemma altogether. The collapse of cooperation is so extreme that the average payoff in a population may decline, even as the potential payoff for mutual cooperation increases. Our work offers a new perspective on the Prisoner's Dilemma and its predictions for cooperation in natural populations; and it provides a general framework to understand the co-evolution of strategies and payoffs in iterated interactions.Comment: 33 pages, 13 figure

The evolution of complex gene regulation by low specificity binding sites

Transcription factor binding sites vary in their specificity, both within and between species. Binding specificity has a strong impact on the evolution of gene expression, because it determines how easily regulatory interactions are gained and lost. Nevertheless, we have a relatively poor understanding of what evolutionary forces determine the specificity of binding sites. Here we address this question by studying regulatory modules composed of multiple binding sites. Using a population-genetic model, we show that more complex regulatory modules, composed of a greater number of binding sites, must employ binding sites that are individually less specific, compared to less complex regulatory modules. This effect is extremely general, and it hold regardless of the regulatory logic of a module. We attribute this phenomenon to the inability of stabilising selection to maintain highly specific sites in large regulatory modules. Our analysis helps to explain broad empirical trends in the yeast regulatory network: those genes with a greater number of transcriptional regulators feature by less specific binding sites, and there is less variance in their specificity, compared to genes with fewer regulators. Likewise, our results also help to explain the well-known trend towards lower specificity in the transcription factor binding sites of higher eukaryotes, which perform complex regulatory tasks, compared to prokaryotes

Small games and long memories promote cooperation

Complex social behaviors lie at the heart of many of the challenges facing evolutionary biology, sociology, economics, and beyond. For evolutionary biologists in particular the question is often how such behaviors can arise \textit{de novo} in a simple evolving system. How can group behaviors such as collective action, or decision making that accounts for memories of past experience, emerge and persist? Evolutionary game theory provides a framework for formalizing these questions and admitting them to rigorous study. Here we develop such a framework to study the evolution of sustained collective action in multi-player public-goods games, in which players have arbitrarily long memories of prior rounds of play and can react to their experience in an arbitrary way. To study this problem we construct a coordinate system for memory-$m$ strategies in iterated $n$-player games that permits us to characterize all the cooperative strategies that resist invasion by any mutant strategy, and thus stabilize cooperative behavior. We show that while larger games inevitably make cooperation harder to evolve, there nevertheless always exists a positive volume of strategies that stabilize cooperation provided the population size is large enough. We also show that, when games are small, longer-memory strategies make cooperation easier to evolve, by increasing the number of ways to stabilize cooperation. Finally we explore the co-evolution of behavior and memory capacity, and we find that longer-memory strategies tend to evolve in small games, which in turn drives the evolution of cooperation even when the benefits for cooperation are low

Evolutionary consequences of behavioral diversity

Iterated games provide a framework to describe social interactions among groups of individuals. Recent work stimulated by the discovery of "zero-determinant" strategies has rapidly expanded our ability to analyze such interactions. This body of work has primarily focused on games in which players face a simple binary choice, to "cooperate" or "defect". Real individuals, however, often exhibit behavioral diversity, varying their input to a social interaction both qualitatively and quantitatively. Here we explore how access to a greater diversity of behavioral choices impacts the evolution of social dynamics in finite populations. We show that, in public goods games, some two-choice strategies can nonetheless resist invasion by all possible multi-choice invaders, even while engaging in relatively little punishment. We also show that access to greater behavioral choice results in more "rugged " fitness landscapes, with populations able to stabilize cooperation at multiple levels of investment, such that choice facilitates cooperation when returns on investments are low, but hinders cooperation when returns on investments are high. Finally, we analyze iterated rock-paper-scissors games, whose non-transitive payoff structure means unilateral control is difficult and zero-determinant strategies do not exist in general. Despite this, we find that a large portion of multi-choice strategies can invade and resist invasion by strategies that lack behavioral diversity -- so that even well-mixed populations will tend to evolve behavioral diversity.Comment: 26 pages, 4 figure

Sonic Boom

A status of the knowledge of sonic booms is provided, with emphasis on their generation, propagation and prediction. For completeness, however, material related to the potential for sonic boom alleviation and the response to sonic booms is also included. The material is presented in the following sections: (1) nature of sonic booms; (2) review and status of theory; (3) measurements and predictions; (4) sonic boom minimization; and (5) responses to sonic booms

Transcriptional errors and the drift barrier

Population genetics predicts that the balance between natural selection and genetic drift is determined by the population size. Species with large population sizes are predicted to have properties governed mainly by selective forces; whereas species with small population sizes should exhibit features governed by mutational processes alone. This “drift-barrier hypothesis” has been successful in explaining extensive variation in genome size, mutation rate, transposable element abundance, and other molecular features across diverse taxa (1⇓–3). However, in PNAS Traverse and Ochman (4) report a striking exception to this theory by showing that transcriptional error rates are nearly equal across several bacterial species with very different population sizes

Practical rare event sampling for extreme mesoscale weather

Extreme mesoscale weather, including tropical cyclones, squall lines, and floods, can be enormously damaging and yet challenging to simulate; hence, there is a pressing need for more efficient simulation strategies. Here we present a new rare event sampling algorithm called Quantile Diffusion Monte Carlo (Quantile DMC). Quantile DMC is a simple-to-use algorithm that can sample extreme tail behavior for a wide class of processes. We demonstrate the advantages of Quantile DMC compared to other sampling methods and discuss practical aspects of implementing Quantile DMC. To test the feasibility of Quantile DMC for extreme mesoscale weather, we sample extremely intense realizations of two historical tropical cyclones, 2010 Hurricane Earl and 2015 Hurricane Joaquin. Our results demonstrate Quantile DMC's potential to provide low-variance extreme weather statistics while highlighting the work that is necessary for Quantile DMC to attain greater efficiency in future applications.Comment: 18 pages, 9 figure

Influx of pwm-modulation upon torque harmonics of induction machines

Influx of pwm-modulation upon torque harmonics of induction machines

Hilbert-Post completeness for the state and the exception effects

In this paper, we present a novel framework for studying the syntactic completeness of computational effects and we apply it to the exception effect. When applied to the states effect, our framework can be seen as a generalization of Pretnar's work on this subject. We first introduce a relative notion of Hilbert-Post completeness, well-suited to the composition of effects. Then we prove that the exception effect is relatively Hilbert-Post complete, as well as the "core" language which may be used for implementing it; these proofs have been formalized and checked with the proof assistant Coq.Comment: Siegfried Rump (Hamburg University of Technology), Chee Yap (Courant Institute, NYU). Sixth International Conference on Mathematical Aspects of Computer and Information Sciences , Nov 2015, Berlin, Germany. 2015, LNC