Related papers: The long-run behavior of the stochastic replicator…
Continuous-time game dynamics are typically first order systems where payoffs determine the growth rate of the players' strategy shares. In this paper, we investigate what happens beyond first order by viewing payoffs as higher order forces…
This paper investigates the long-term behavior of an interacting particle system of interest in the hot topic of evolutionary game theory. Each site of the $d$-dimensional integer lattice is occupied by a player who is characterized by one…
We study the influence of a dissipation process on diffusion dynamics triggered by slow fluctuations. We study both strong- and weak-friction regime. When the latter regime applies, the system is attracted by the basin of either Gauss or…
We study an atomic signaling game under stochastic evolutionary dynamics. There is a finite number of players who repeatedly update from a finite number of available languages/signaling strategies. Players imitate the most fit agents with…
How and to what extent will new activities spread through social ties? Here, we develop a more sophisticated framework than the standard mean-field approach to describe the diffusion dynamics of multiple activities on complex networks. We…
Macroevolution is considered as a problem of stochastic dynamics in a system with many competing agents. Evolutionary events (speciations and extinctions) are triggered by fitness records found by random exploration of the agents' fitness…
We study adaptive dynamics in games where players abandon the population at a given rate, and are replaced by naive players characterized by a prior distribution over the admitted strategies. We demonstrate how such process leads…
This paper considers a class of reinforcement-learning that belongs to the family of Learning Automata and provides a stochastic-stability analysis in strategic-form games. For this class of dynamics, convergence to pure Nash equilibria has…
This work develops a distributed optimization strategy with guaranteed exact convergence for a broad class of left-stochastic combination policies. The resulting exact diffusion strategy is shown in Part II to have a wider stability range…
Evolutionary strategies have recently been shown to achieve competing levels of performance for complex optimization problems in reinforcement learning. In such problems, one often needs to optimize an objective function subject to a set of…
Vaccination is widely recognised as one of the most effective forms of public health interventions. Individuals decisions regarding vaccination creates a complex social dilemma between individual and collective interests, where each…
Evolutionary game theory is used to model the evolution of competing strategies in a population of players. Evolutionary stability of a strategy is a dynamic equilibrium, in which any competing mutated strategy would be wiped out from a…
We consider a system of two competing populations in two-dimensional heterogeneous environments. The populations are assumed to move horizontally and vertically with different probabilities, but are otherwise identical. We regard these…
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…
Winner-take-all phenomena are observed in various competitive systems. We find similar phenomena in replicator models with randomly fluctuating growth rates. The disparity between winners and losers increases indefinitely, even if all…
Since Press and Dyson's ingenious discovery of ZD (zero-determinant) strategy in the repeated Prisoner's Dilemma game, several studies have confirmed the existence of ZD strategy in repeated multiplayer social dilemmas. However, few…
In this paper, we discuss the fitness landscape evolution of permanent replicator systems using a hypothesis that the specific time of evolutionary adaptation of the system parameters is much slower than the time of internal evolutionary…
Many biological activities are induced by cellular chemical reactions of diffusing reactants. The dynamics of such systems can be captured by stochastic reaction networks. A recent numerical study has shown that diffusion can significantly…
The recently developed short-time linear response algorithm, which predicts the average response of a nonlinear chaotic system with forcing and dissipation to small external perturbation, generally yields high precision of the response…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…