Related papers: Intrinsic noise in game dynamical learning
We introduce a simple stochastic dynamics for game theory. It assumes ``local'' rationality in the sense that any player climbs the gradient of his utility function in the presence of a stochastic force which represents deviation from…
We discuss stochastic dynamics of finite populations of individuals playing games. We review recent results concerning the dependence of the long-run behavior of such systems on the number of players and the noise level. In the case of…
Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control…
While noise is generally associated with uncertainties and often has a negative connotation in engineering, living organisms have evolved to adapt to (and even exploit) such uncertainty to ensure the survival of a species or implement…
A key goal of systems biology is the predictive mathematical description of gene regulatory circuits. Different approaches are used such as deterministic and stochastic models, models that describe cell growth and division explicitly or…
We discuss the long-run behavior of stochastic dynamics of many interacting players in spatial evolutionary games. In particular, we investigate the effect of the number of players and the noise level on the stochastic stability of Nash…
Neutral dynamics, where taxa are assumed to be demographically equivalent and their abundance is governed solely by the stochasticity of the underlying birth-death process, has proved itself as an important minimal model that accounts for…
We study the quality of outcomes in repeated games when the population of players is dynamically changing and participants use learning algorithms to adapt to the changing environment. Game theory classically considers Nash equilibria of…
Spatial evolutionary games model individuals who are distributed in a spatial domain and update their strategies upon playing a normal form game with their neighbors. We derive integro-differential equations as deterministic approximations…
It is well known that the kinetics of an intracellular biochemical network is stochastic. This is due to intrinsic noise arising from the random timing of biochemical reactions in the network as well as due to extrinsic noise stemming from…
We consider the influence of local noise on a generalized network of populations having positive and negative feedbacks. The population dynamics at the nodes is nonlinear, typically chaotic, and allows cessation of activity if the…
We derive a class of macroscopic differential equations that describe collective adaptation, starting from a discrete-time stochastic microscopic model. The behavior of each agent is a dynamic balance between adaptation that locally…
Evolutionary game dynamics describes not only frequency dependent genetical evolution, but also cultural evolution in humans. In this context, successful strategies spread by imitation. It has been shown that the details of strategy update…
We present a general framework to describe the evolutionary dynamics of an arbitrary number of types in finite populations based on stochastic differential equations (SDE). For large, but finite populations this allows to include…
The multi-population replicator dynamics (RD) can be considered a dynamic approach to the study of multi-player games, where it was shown to be related to Cross' learning, as well as of systems of coevolving populations. However, not all of…
Noise is usually regarded as adversarial to extract the effective dynamics from time series, such that the conventional data-driven approaches usually aim at learning the dynamics by mitigating the noisy effect. However, noise can have a…
Different strains competing for a common pool of susceptible individuals is a key problem in mathematical epidemiology. To address this problem, we investigate a two-strain model within a Susceptible-Infected-Recovered (SIR) framework.…
Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator…
We study the dynamics of a version of the batch minority game, with random external information and with different types of inhomogeneous decision noise (additive and multiplicative), using generating functional techniques \`{a} la De…
Trusting in others and reciprocating that trust with trustworthy actions are crucial to successful and prosperous societies. The Trust Game has been widely used to quantitatively study trust and trustworthiness, involving a sequential…