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Concept: Evolutionary game theory

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We study evolutionary game dynamics on structured populations in which individuals take part in several layers of networks of interactions simultaneously. This multiplex of interdependent networks accounts for the different kind of social ties each individual has. By coupling the evolutionary dynamics of a Prisoner’s Dilemma game in each of the networks, we show that the resilience of cooperative behaviors for extremely large values of the temptation to defect is enhanced by the multiplex structure. Furthermore, this resilience is intrinsically related to a non-trivial organization of cooperation across the network layers, thus providing a new way out for cooperation to survive in structured populations.

Concepts: Structure, Nash equilibrium, Evolutionary game theory, Evolutionarily stable strategy, Game theory, The Evolution of Cooperation, Sociology, Prisoner's dilemma

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It is often assumed that in public goods games, contributors are either strong or weak players and each individual has an equal probability of exhibiting cooperation. It is difficult to explain why the public good is produced by strong individuals in some cooperation systems, and by weak individuals in others. Viewing the asymmetric volunteer’s dilemma game as an evolutionary game, we find that whether the strong or the weak players produce the public good depends on the initial condition (i.e., phenotype or initial strategy of individuals). These different evolutionarily stable strategies (ESS) associated with different initial conditions, can be interpreted as the production modes of public goods of different cooperation systems. A further analysis revealed that the strong player adopts a pure strategy but mixed strategies for the weak players to produce the public good, and that the probability of volunteering by weak players decreases with increasing group size or decreasing cost-benefit ratio. Our model shows that the defection probability of a “strong” player is greater than the “weak” players in the model of Diekmann (1993). This contradicts Selten’s (1980) model that public goods can only be produced by a strong player, is not an evolutionarily stable strategy, and will therefore disappear over evolutionary time. Our public good model with ESS has thus extended previous interpretations that the public good can only be produced by strong players in an asymmetric game.

Concepts: Evolution and the Theory of Games, Matching pennies, Chicken, Goods, Evolutionary game theory, Evolutionarily stable strategy, Nash equilibrium, Game theory

25

A tragedy of the commons occurs when individuals take actions to maximize their payoffs even as their combined payoff is less than the global maximum had the players coordinated. The originating example is that of overgrazing of common pasture lands. In game-theoretic treatments of this example, there is rarely consideration of how individual behavior subsequently modifies the commons and associated payoffs. Here, we generalize evolutionary game theory by proposing a class of replicator dynamics with feedback-evolving games in which environment-dependent payoffs and strategies coevolve. We initially apply our formulation to a system in which the payoffs favor unilateral defection and cooperation, given replete and depleted environments, respectively. Using this approach, we identify and characterize a class of dynamics: an oscillatory tragedy of the commons in which the system cycles between deplete and replete environmental states and cooperation and defection behavior states. We generalize the approach to consider outcomes given all possible rational choices of individual behavior in the depleted state when defection is favored in the replete state. In so doing, we find that incentivizing cooperation when others defect in the depleted state is necessary to avert the tragedy of the commons. In closing, we propose directions for the study of control and influence in games in which individual actions exert a substantive effect on the environmental state.

Concepts: Evolutionary dynamics, Evolution and the Theory of Games, Replicator equation, Maxima and minima, Evolutionarily stable strategy, Evolutionary game theory, Game theory

11

Abiraterone treats metastatic castrate-resistant prostate cancer by inhibiting CYP17A, an enzyme for testosterone auto-production. With standard dosing, evolution of resistance with treatment failure (radiographic progression) occurs at a median of ~16.5 months. We hypothesize time to progression (TTP) could be increased by integrating evolutionary dynamics into therapy. We developed an evolutionary game theory model using Lotka-Volterra equations with three competing cancer “species”: androgen dependent, androgen producing, and androgen¬†independent. Simulations with standard abiraterone dosing demonstrate strong selection for androgen-independent cells and rapid treatment failure. Adaptive therapy, using patient-specific tumor dynamics to inform on/off treatment cycles, suppresses proliferation of androgen-independent cells and lowers cumulative drug dose. In a pilot clinical trial, 10 of 11 patients maintained stable oscillations of tumor burdens; median TTP is at least 27 months with reduced cumulative drug use of 47% of standard dosing. The outcomes show significant improvement over published studies and a contemporaneous population.

Concepts: Estrogen, Evolutionary game theory, Androgen, Metastasis, Testosterone, Cancer, Game theory, Prostate cancer

11

Most examples of the application of evolutionary game theory to problems in biology involve highly simplified models. I contend that it is time to move on and include much more richness in models. In particular, more thought needs to be given to the importance of (i) between-individual variation; (ii) the interaction between individuals, and hence the process by which decisions are reached; (iii) the ecological and life-history context of the situation; (iv) the traits that are under selection, and (v) the underlying psychological mechanisms that lead to behaviour. I give examples where including variation between individuals fundamentally changes predicted outcomes of a game. Variation also selects for real-time responses, again resulting in changed outcomes. Variation can select for other traits, such as choosiness and social sensitivity. More generally, many problems involve coevolution of more than one trait. I identify situations where a reductionist approach, in which a game is isolated from is ecological setting, can be misleading. I also highlight the need to consider flexibility of behaviour, mental states and other issues concerned with the evolution of mechanism.

Concepts: Evolution and the Theory of Games, Biology, Evolutionarily stable strategy, Evolutionary game theory, Psychology, Evolution, Natural selection, Game theory

9

Recent empirical work highlights the heterogeneity of social competitions such as political campaigns: proponents of some ideologies seek debate and conversation, others create echo chambers. While symmetric and static network structure is typically used as a substrate to study such competitor dynamics, network structure can instead be interpreted as a signature of the competitor strategies, yielding competition dynamics on adaptive networks. Here we demonstrate that tradeoffs between aggressiveness and defensiveness (i.e., targeting adversaries vs. targeting like-minded individuals) creates paradoxical behaviour such as non-transitive dynamics. And while there is an optimal strategy in a two competitor system, three competitor systems have no such solution; the introduction of extreme strategies can easily affect the outcome of a competition, even if the extreme strategies have no chance of winning. Not only are these results reminiscent of classic paradoxical results from evolutionary game theory, but the structure of social networks created by our model can be mapped to particular forms of payoff matrices. Consequently, social structure can act as a measurable metric for social games which in turn allows us to provide a game theoretical perspective on online political debates.

Concepts: Strategy, Evolutionarily stable strategy, Scientific method, Evolutionary game theory, Competition, Social network, Sociology, Game theory

5

In the animal world, the competition between individuals belonging to different species for a resource often requires the cooperation of several individuals in groups. This paper proposes a generalization of the Hawk-Dove Game for an arbitrary number of agents: the N-person Hawk-Dove Game. In this model, doves exemplify the cooperative behavior without intraspecies conflict, while hawks represent the aggressive behavior. In the absence of hawks, doves share the resource equally and avoid conflict, but having hawks around lead to doves escaping without fighting. Conversely, hawks fight for the resource at the cost of getting injured. Nevertheless, if doves are present in sufficient number to expel the hawks, they can aggregate to protect the resource, and thus avoid being plundered by hawks. We derive and numerically solve an exact equation for the evolution of the system in both finite and infinite well-mixed populations, finding the conditions for stable coexistence between both species. Furthermore, by varying the different parameters, we found a scenario of bifurcations that leads the system from dominating hawks and coexistence to bi-stability, multiple interior equilibria and dominating doves.

Concepts: Evolutionarily stable strategy, Prisoner's dilemma, Chicken, Conflict, Evolutionary game theory, Species, Evolution, Aggression

5

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' payoffs as well as their strategies 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 coevolution of strategies and payoffs in arbitrary iterated games. We show that, when there is a tradeoff between the benefits and costs of cooperation, coevolution often leads to a dramatic loss of cooperation in the Iterated Prisoner’s Dilemma. The collapse of cooperation is so extreme that the average payoff in a population can decline even as the potential reward for mutual cooperation increases. Depending upon the form of tradeoffs, evolution may even move away from the Iterated Prisoner’s Dilemma game altogether. 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 coevolution of strategies and payoffs in iterated interactions.

Concepts: Biology, Nash equilibrium, Evolutionary game theory, Evolution, Natural selection, Evolutionarily stable strategy, Game theory, Prisoner's dilemma

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Recognition of behavioral types can facilitate the evolution of cooperation by enabling altruistic behavior to be directed at other cooperators and withheld from defectors. While much is known about the tendency for recognition to promote cooperation, relatively little is known about whether such a capacity can coevolve with the social behavior it supports. Here we use evolutionary game theory and multi-population dynamics to model the coevolution of social behavior and recognition. We show that conditional harming behavior enables the evolution and stability of social recognition, whereas conditional helping leads to a deterioration of recognition ability. Expanding the model to include a complex game where both helping and harming interactions are possible, we find that conditional harming behavior can stabilize recognition, and thereby lead to the evolution of conditional helping. Our model identifies a novel hypothesis for the evolution of cooperation: conditional harm may have coevolved with recognition first, thereby helping to establish the mechanisms necessary for the evolution of cooperation.

Concepts: Evolutionary psychology, Evolution and the Theory of Games, Altruism, Coevolution, Evolutionarily stable strategy, Evolutionary game theory, Game theory, The Evolution of Cooperation

4

The most common assumption in evolutionary game theory is that players should adopt a strategy that warrants the highest payoff. However, recent studies indicate that the spatial selection for cooperation is enhanced if an appropriate fraction of the population chooses the most common rather than the most profitable strategy within the interaction range. Such conformity might be due to herding instincts or crowd behavior in humans and social animals. In a heterogeneous population where individuals differ in their degree, collective influence, or other traits, an unanswered question remains who should conform. Selecting conformists randomly is the simplest choice, but it is neither a realistic nor the optimal one. We show that, regardless of the source of heterogeneity and game parametrization, socially the most favorable outcomes emerge if the masses conform. On the other hand, forcing leaders to conform significantly hinders the constructive interplay between heterogeneity and coordination, leading to evolutionary outcomes that are worse still than if conformists were chosen randomly. We conclude that leaders must be able to create a following for network reciprocity to be optimally augmented by conformity. In the opposite case, when leaders are castrated and made to follow, the failure of coordination impairs the evolution of cooperation.

Concepts: Evolution and the Theory of Games, The Evolution of Cooperation, Nash equilibrium, Evolutionarily stable strategy, Evolutionary game theory, Sociology, Natural selection, Game theory