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

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

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

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

Under-dominance constrains the evolution of negative autoregulation in diploids

Regulatory networks have evolved to allow gene expression to rapidly track changes in the environment as well as to buffer perturbations and maintain cellular homeostasis in the absence of change. Theoretical work and empirical investigation in Escherichia coli have shown that negative autoregulation confers both rapid response times and reduced intrinsic noise, which is reflected in the fact that almost half of Escherichia coli transcription factors are negatively autoregulated. However, negative autoregulation is exceedingly rare amongst the transcription factors of Saccharomyces cerevisiae. This difference is all the more surprising because E. coli and S. cerevisiae otherwise have remarkably similar profiles of network motifs. In this study we first show that regulatory interactions amongst the transcription factors of Drosophila melanogaster and humans have a similar dearth of negative autoregulation to that seen in S. cerevisiae. We then present a model demonstrating that this fundamental difference in the noise reduction strategies used amongst species can be explained by constraints on the evolution of negative autoregulation in diploids. We show that regulatory interactions between pairs of homologous genes within the same cell can lead to under-dominance - mutations which result in stronger autoregulation, and decrease noise in homozygotes, paradoxically can cause increased noise in heterozygotes. This severely limits a diploid's ability to evolve negative autoregulation as a noise reduction mechanism. Our work offers a simple and general explanation for a previously unexplained difference between the regulatory architectures of E. coli and yeast, Drosophila and humans. It also demonstrates that the effects of diploidy in gene networks can have counter-intuitive consequences that may profoundly influence the course of evolution

Local-time asymmetries in the Venus thermosphere

Our current understanding of the global structure and dynamics of the Venus thermosphere is embodied in models such as the Venus Thermospheric General Circulation Model (VTGCM) and empirical composition models such as VIRA and VTS3. We have completed an analysis of ultraviolet images of Venus at 130 nm acquired by the Pioneer Venus Orbiter Ultraviolet Spectrometer (PVOUVS). We have examined 97 images spanning the 10-year period between 1980 and 1990, and have developed a technique for global radiative transfer modeling with which we create synthetic models of each image analyzed. We have developed a hypothesis for understanding the persistent local-time asymmetry observed as a signature of vertically propagating internal gravity waves interacting with the thermospheric SS-AS circulation. This hypothesis is presented

Group reciprocity and the evolution of stereotyping

Funding: A.J.S. is supported by the John Templeton Foundation for funding (grant no. 62281). N.R. is supported by the Royal Society and the Leverhulme Trust.Stereotypes are generalized beliefs about groups of people, which are used to make decisions and judgements about them. Although such heuristics can be useful when decisions must be made quickly, or when information is lacking, they can also serve as the basis for prejudice and discrimination. In this paper, we study the evolution of stereotypes through group reciprocity. We characterize the warmth of a stereotype as the willingness to cooperate with an individual based solely on the identity of the group they belong to. We show that when stereotype groups are large, such group reciprocity is less likely to evolve, and stereotypes tend to be negative. We also show that, even when stereotypes are broadly positive, individuals are often overly pessimistic about the willingness of those they stereotype to cooperate. We then show that the tendency for stereotyping itself to evolve is driven by the costs of cognition, so that more people are stereotyped with greater coarseness as costs increase. Finally we show that extrinsic ‘shocks’, in which the benefits of cooperation are suddenly reduced, can cause stereotype warmth and judgement bias to turn sharply negative, consistent with the view that economic and other crises are drivers of out-group animosity.Publisher PDFPeer reviewe

The evolvability of cooperation under local and non-local mutations

Funding: J.B.P. acknowledges funding from the Burroughs Wellcome Fund, the David and Lucile Packard Foundation, US Department of the Interior Grant D12AP00025, and Foundational Questions in Evolutionary Biology Fund Grant RFP-12-16.We study evolutionary dynamics in a population of individuals engaged in pairwise social interactions, encoded as iterated games. We consider evolution within the space of memory-1strategies, and we characterize all evolutionary robust outcomes, as well as their tendency to evolve under the evolutionary dynamics of the system. When mutations are restricted to be local, as opposed to non-local, then a wider range of evolutionary robust outcomes tend to emerge, but mutual cooperation is more difficult to evolve. When we further allow heritable mutations to the player’s investment level in each cooperative interaction, then co-evolution leads to changes in the payoff structure of the game itself and to specific pairings of robust games and strategies in the population. We discuss the implications of these results in the context of the genetic architectures that encode how an individual expresses its strategy or investment.Publisher PDFPeer reviewe

Small groups 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 the question is often how group behaviors such as collective action, or decision making that accounts for memories of past experience, can emerge and persist in an evolving system. 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. We construct a coordinate system for memory-m strategies in iterated n-player games that permits us to characterize all cooperative strategies that resist invasion by any mutant strategy, and stabilize cooperative behavior. We show that, especially when groups are small, longer-memory strategies make cooperation easier to evolve, by increasing the number of ways to stabilize cooperation. We also explore the co-evolution of behavior and memory. We find that even when memory has a cost, longer-memory strategies often evolve, which in turn drives the evolution of cooperation, even when the benefits for cooperation are low.Publisher PDFPeer reviewe

Inequality, identity, and partisanship : how redistribution can stem the tide of mass polarization

The form of political polarization where citizens develop strongly negative attitudes toward out-party members and policies has become increasingly prominent across many democracies. Economic hardship and social inequality, as well as intergroup and racial conflict, have been identified as important contributing factors to this phenomenon known as “affective polarization.” Research shows that partisan animosities are exacerbated when these interests and identities become aligned with existing party cleavages. In this paper, we use a model of cultural evolution to study how these forces combine to generate and maintain affective political polarization. We show that economic events can drive both affective polarization and the sorting of group identities along party lines, which, in turn, can magnify the effects of underlying inequality between those groups. But, on a more optimistic note, we show that sufficiently high levels of wealth redistribution through the provision of public goods can counteract this feedback and limit the rise of polarization. We test some of our key theoretical predictions using survey data on intergroup polarization, sorting of racial groups, and affective polarization in the United States over the past 50 y.PostprintPeer reviewe