Bounded learning and planning in public goods games.

A previously developed agent model, based on bounded rational planning, is extended by introducing learning, with bounds on the memory of the agents. The exclusive impact of learning, especially in longer games, is investigated. Based on our results, we provide testable predictions for experiments on repeated public goods games (PGG) with synchronized actions. We observe that noise in player contributions can have a positive impact of group cooperation in PGG. We theoretically explain the experimental results on the impact of group size as well as mean per capita return (MPCR) on cooperation.

Bounded rational agents playing a public goods game.

An agent-based model for human behavior in the well-known public goods game (PGG) is developed making use of bounded rationality, but without invoking mechanisms of learning. The underlying Markov decision process is driven by a path integral formulation of reward maximization. The parameters of the model can be related to human preferences accessible to measurement. Fitting simulated game trajectories to available experimental data, we demonstrate that our agents are capable of modeling human behavior in PGG quite well, including aspects of cooperation emerging from the game. We find that only two fitting parameters are relevant to account for the variations in playing behavior observed in 16 cities from all over the world. We thereby find that learning is not a necessary ingredient to account for empirical data.

A control theory approach to optimal pandemic mitigation.

In the framework of homogeneous susceptible-infected-recovered (SIR) models, we use a control theory approach to identify optimal pandemic mitigation strategies. We derive rather general conditions for reaching herd immunity while minimizing the costs incurred by the introduction of societal control measures (such as closing schools, social distancing, lockdowns, etc.), under the constraint that the infected fraction of the population does never exceed a certain maximum corresponding to public health system capacity. Optimality is derived and verified by variational and numerical methods for a number of model cost functions. The effects of immune response decay after recovery are taken into account and discussed in terms of the feasibility of strategies based on herd immunity.

New topological tool for multistable dynamical systems.

We introduce a new method for investigation of dynamical systems which allows us to extract as much information as possible about potential system dynamics, based only on the form of equations describing it. The discussed tool of critical surfaces, defined by the zero velocity (and/or) acceleration field for particular variables of the system is related to the geometry of the attractors. Particularly, the developed method provides a new and simple procedure allowing to localize hidden oscillations. Our approach is based on the dimension reduction of the searched area in the phase space and has an advantage (in terms of complexity) over standard procedures for investigating full-dimensional space. The two approaches have been compared using typical examples of oscillators with hidden states. Our topological tool allows us not only to develop alternate ways of extracting information from the equations of motion of the dynamical system, but also provides a better understanding of attractors geometry and their capturing in complex cases, especially including multistable and hidden attractors. We believe that the introduced method can be widely used in the studies of dynamical systems and their applications in science and engineering.

Understanding transient uncoupling induced synchronization through modified dynamic coupling.

An important aspect of the recently introduced transient uncoupling scheme is that it induces synchronization for large values of coupling strength at which the coupled chaotic systems resist synchronization when continuously coupled. However, why this is so is an open problem? To answer this question, we recall the conventional wisdom that the eigenvalues of the Jacobian of the transverse dynamics measure whether a trajectory at a phase point is locally contracting or diverging with respect to another nearby trajectory. Subsequently, we go on to highlight a lesser appreciated fact that even when, under the corresponding linearised flow, the nearby trajectory asymptotically diverges away, its distance from the reference trajectory may still be contracting for some intermediate period. We term this phenomenon transient decay in line with the phenomenon of the transient growth. Using these facts, we show that an optimal coupling region, i.e., a region of the phase space where coupling is on, should ideally be such that at any of the constituent phase point either the maximum of the real parts of the eigenvalues is negative or the magnitude of the positive maximum is lesser than that of the negative minimum. We also invent and employ a modified dynamics coupling scheme-a significant improvement over the well-known dynamic coupling scheme-as a decisive tool to justify our results.