Related papers: Broken ergodicity and memory in the minority game
We study the dynamics and statics of a dilute batch minority game with random external information. We focus on the case in which the number of connections per agent is infinite in the thermodynamic limit. The dynamical scenario of…
Using generating functional and replica techniques, respectively, we study the dynamics and statics of a spherical Minority Game (MG), which in contrast with a spherical MG previously presented in J.Phys A: Math. Gen. 36 11159 (2003)…
We show that spatial quenched disorder affects polar active matter in ways more complex and far-reaching than believed heretofore. Using simulations of the 2D Vicsek model subjected to random couplings or a disordered scattering field, we…
We study the phenomenon of weak ergodicity breaking for a class of globally correlated random walk dynamics defined over a finite set of states. The persistence in a given state or the transition to another one depends on the whole previous…
The influence of a fixed number of agents with the same fixed behavior on the dynamics of the minority game is studied. Alternatively, the system studied can be considered the minority game with a change in the comfort threshold away from…
We discuss the interplay between the degree of dynamical stochasticity, memory persistence and violation of the self-averaging property in the aging kinetics of quenched ferromagnets. We show that, in general, the longest possible memory…
We study the role of strategy correlations and timing of adaptation for the dynamics of Minority Games, both simulationally and analytically. Using the exact generating functional approach a la De Dominicis we compute the phase diagram and…
It is known that the memory is relevant in the symmetric phase of the minority game. In our previous work we have successfully explained the quasi-periodic behavior of the game in the symmetric phase with the help of the probability theory.…
Both the phenomenology and the theory of minority games (MG) with more than two strategies per agent are different from those of the conventional and extensively studied case S=2. MGs with $S>2$ exhibit nontrivial statistics of the…
The concept of weak ergodicity breaking is defined and studied in the context of deterministic dynamics. We show that weak ergodicity breaking describes a weakly chaotic dynamical system: a nonlinear map which generates subdiffusion…
A finite memory is introduced in the score dynamics of Minority Games. As expected, this removes the dependence of the stationary state on the initial conditions. However, it also causes an unexpected increase of fluctuations in…
We discuss the Euclidean quantum $O(N)$ model with $N=2$ in a continuous broken symmetry phase. We study the system at low temperatures in the presence of quenched disorder linearly coupled to the scalar field. Performing an average over…
Ergodic stationary states of Minority Games with S strategies per agent can be characterised in terms of the asymptotic probabilities $\phi_a$ with which an agent uses $a$ of his strategies. We propose here a simple and general method to…
Minority game is a simple-mined econophysical model capturing the cooperative behavior among selfish players. Previous investigations, which were based on numerical simulations up to about 100 players for a certain parameter $\alpha$ in the…
The stochastic processes underlying the growth and stability of biological and psychological systems reveal themselves when far from equilibrium. Far from equilibrium, nonergodicity reigns. Nonergodicity implies that the average outcome for…
The reduced density matrix of many-body systems possessing an additive conserved quantity can be decomposed in orthogonal sectors which can be independently analyzed. Recently, these have been proven to equally contribute to entanglement…
We explore the mechanism responsible for the ergodicity breaking in systems with long-range forces. In thermodynamic limit such systems do not evolve to the Boltzmann-Gibbs equilibrium, but become trapped in an out-of-equilibrium…
We introduce a simple analysis of the structural complexity of infinite-memory processes built from random samples of stationary, ergodic finite-memory component processes. Such processes are familiar from the well known multi-arm Bandit…
We study analytically and by computer simulations a complex system of adaptive agents with finite memory. Borrowing the framework of the Minority Game and using the replica formalism we show the existence of an equilibrium phase transition…
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…