Related papers: Deterministic Approximation of a Stochastic Imitat…
This paper is concerned with exploring the microscopic basis for the discrete versions of the standard replicator equation and the adjusted replicator equation. To this end, we introduce frequency-dependent selection -- as a result of…
The goal of this paper is to analyze distributional Markov Decision Processes as a class of control problems in which the objective is to learn policies that steer the distribution of a cumulative reward toward a prescribed target law,…
We study a stochastic model of protein dynamics that explicitly includes delay in the degradation. We rigorously derive the master equation for the processes and solve it exactly. We show that the equations for the mean values obtained…
Diffusive approximations of Markov jump processes often fail to accurately capture large fluctuations. This is confounding, as the rare events triggered by these large fluctuations, such as the failure of electronic memories, are often the…
We study the long-time dynamics in non-Markovian single-population stochastic models, where one or more reactions are modelled as a stochastic process with a fat-tailed non-exponential distribution of waiting times, mimicking long-term…
Understanding the evolutionary dynamics of reinforcement learning under multi-agent settings has long remained an open problem. While previous works primarily focus on 2-player games, we consider population games, which model the strategic…
We study a distributed learning process observed in human groups and other social animals. This learning process appears in settings in which each individual in a group is trying to decide over time, in a distributed manner, which option to…
We study the stability of non-conservative deterministic cross diffusion models and prove that they are approximated by stochastic population models when the populations become locally large. In this model, the individuals of two species…
We study the multi-strategy stochastic evolutionary game with death-birth updating in expanding spatial populations of size $N\to \infty$. The model is a voter model perturbation. For typical populations, we require perturbation strengths…
The origin of the long-range memory in the non-equilibrium systems is still an open problem as the phenomenon can be reproduced using models based on Markov processes. In these cases a notion of spurious memory is introduced. A good example…
Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…
In the last decade, stochastic models have shown to be very useful for quantitative modelling of social processes. Here, a configurational master equation for the description of behavioral changes by pair interactions of individuals is…
Real-world processes often exhibit temporal separation between actions and reactions - a characteristic frequently ignored in many modelling frameworks. Adding temporal aspects, like time delays, introduces a higher complexity of problems…
We consider a broad class of continuous-time two-type population size-dependent Markov Branching Processes. The offspring distribution can depend on the current (alive) and total (dead and alive) populations. Using stochastic approximation…
Stochastic games generalize Markov decision processes (MDPs) to a multiagent setting by allowing the state transitions to depend jointly on all player actions, and having rewards determined by multiplayer matrix games at each state. We…
To investigate the origin of cooperative behaviors, we developed an evolutionary model of sequential strategies and tested our model with computer simulations. The sequential strategies represented by stochastic machines were evaluated…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
Cooperation and defection are social traits whose evolutionary origin is still unresolved. Recent behavioral experiments with humans suggested that strategy changes are driven mainly by the individuals' expectations and not by imitation.…
Continuously changing environments have a paramount role in the evolution of cooperative behavior. Previous works have shown that the transitions among different games, as the feedback between behaviors and environments, can promote…
We study a model of stochastic evolutionary game dynamics in which the probabilities that agents choose suboptimal actions are dependent on payoff consequences. We prove a sample path large deviation principle, characterizing the rate of…