Related papers: Conway's game Life perturbed
A model of stochastic games where multiple controllers jointly control the evolution of the state of a dynamic system but have access to different information about the state and action processes is considered. The asymmetry of information…
The research concerns the dynamics of complex autonomous Kauffman networks. The article defines and shows using simulation experiments half-chaotic networks, which exhibit features much more similar to typically modeled systems like a…
We consider a novel model of stochastic replicator dynamics for potential games that converts to a Langevin equation on a sphere after a change of variables. This is distinct from the models studied earlier. In particular, it is ill-posed…
For dynamic situations where the evolution of a player's state is influenced by his own action as well as other players' states and actions, we show that equilibria derived for nonatomic games (NGs) can be used by their large finite…
Two-player stochastic games are games with two 2 players and a randomised entity called "nature". A natural question to ask in this framework is the existence of strategies that ensure that an event happens with probability 1 (almost-sure…
A cellular automaton is presented whose governing rule is that the Kolmogorov complexity of a cell's neighborhood may not increase when the cell's present value is substituted for its future value. Using an approximation of this…
The Minority Game (MG) behaves as a stochastically perturbed deterministic system due to the coin-toss invoked to resolve tied strategies. Averaging over this stochasticity yields a description of the MG's deterministic dynamics via mapping…
Large ensembles of stochastically evolving interacting particles describe phenomena in diverse fields including statistical physics, neuroscience, biology, and engineering. In such systems, the infinitesimal evolution of each particle…
A description of the environment cognition process by intelligent systems with a fixed set of system goals is suggested. Such a system is represented by the set of its goals only without any models of the system elements or the environment.…
We formulate a class of mean field games on a finite state space with variational principles resembling those in continuous-state mean field games. We construct a controlled continuity equation featuring a nonlinear activation function on…
Parrondo's paradox refers to the counter-intuitive situation where a winning strategy results from a suitable combination of losing ones. Simple stochastic games exhibiting this paradox have been introduced around the turn of the…
By modeling the interaction of a system with an environment through a renewal approach, we demonstrate that completely positive non-Markovian dynamics may develop some unexplored non-standard statistical properties. The renewal approach is…
This paper compiles several aspects of the dynamics of stochastic approximation algorithms with Markov iterate-dependent noise when the iterates are not known to be stable beforehand. We achieve the same by extending the lock-in probability…
The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the…
The stochastic simulation algorithm commonly known as Gillespie's algorithm is now used ubiquitously in the modelling of biological processes in which stochastic effects play an important role. In well-mixed scenarios at the sub-cellular…
The paper is concerned with a zero-sum continuous-time stochastic differential game with a dynamics controlled by a Markov process and a terminal payoff. The value function of the original game is estimated using the value function of a…
In this note we consider a Markov chain formed by a finite system of interacting birth-and-death processes on a finite state space. We study an asymptotic behaviour of the Markov chain as its state space becomes large. In particular, we…
We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity,…
We consider exchangeable Markov multi-state survival processes -- temporal processes taking values over a state-space$\mathcal{S}$ with at least one absorbing failure state $\flat \in \mathcal{S}$ that satisfy natural invariance properties…
This paper studies birth and death processes in interactive random environments where the birth and death rates and the dynamics of the state of the environment are dependent on each other. Two models of a random environment are considered:…