An oscillating tragedy of the commons in replicator dynamics with game-environment feedback.

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.

Information sharing for a coordination game in fluctuating environments.

Collective action dilemmas pervade the social and biological sciences - from human decision-making to bacterial quorum sensing. In these scenarios, individuals sense cues from the environment to adopt a suitable phenotype or change in behavior. However, when cues include signals from other individuals, then the appropriate behavior of each individual is linked. Here, we develop a framework to quantify the influence of information sharing on individual behavior in the context of two player coordination games. In this framework, the environment stochastically switches between two states, and the state determines which one of two actions players must coordinate on. Given a stochastically switching environment, we then consider two versions of the game that differ in the way players acquire information. In the first model, players independently sense private environmental cues, but do not communicate with each other. We find there are two types of strategies that emerge as Nash equilibria and fitness maximizers - players prefer to commit to one particular action when private information is poor, or prefer to employ phenotypic plasticity when it is good. The second model adds an additional layer of communication, where players share social cues as well. When the quality of social information is high, we find the socially optimal strategy is a novel "majority logic" strategy that bases decision-making on social cues. Our game-theoretic approach offers a principled way of investigating the role of communication in group decision-making under uncertain conditions.

Systematic biases in disease forecasting - The role of behavior change.

In a simple susceptible-infected-recovered (SIR) model, the initial speed at which infected cases increase is indicative of the long-term trajectory of the outbreak. Yet during real-world outbreaks, individuals may modify their behavior and take preventative steps to reduce infection risk. As a consequence, the relationship between the initial rate of spread and the final case count may become tenuous. Here, we evaluate this hypothesis by comparing the dynamics arising from a simple SIR epidemic model with those from a modified SIR model in which individuals reduce contacts as a function of the current or cumulative number of cases. Dynamics with behavior change exhibit significantly reduced final case counts even though the initial speed of disease spread is nearly identical for both of the models. We show that this difference in final size projections depends critically in the behavior change of individuals. These results also provide a rationale for integrating behavior change into iterative forecast models. Hence, we propose to use a Kalman filter to update models with and without behavior change as part of iterative forecasts. When the ground truth outbreak includes behavior change, sequential predictions using a simple SIR model perform poorly despite repeated observations while predictions using the modified SIR model are able to correct for initial forecast errors. These findings highlight the value of incorporating behavior change into baseline epidemic and dynamic forecast models.