Evolution and equilibrium under inexact information.
type: Item
instance of: scholarly article
title: Evolution and equilibrium under inexact information.
zbMATH Open document ID: 1089.91007
DOI: 10.1016/S0899-8256(03)00026-5
author: William H. Sandholm
published in: Games and Economic Behavior
publication date: 2003-09-25T00:00:00Z
review text: The article is devoted to a general model of stochastic evolution in games. Let \(X_t^N=\{(R_t^N,U_t^N)\}_{t\geq 0}\) be the behavior process describing the proportions of players in a population of \(N\) individuals choosing strategies \(R\) and \(U\). The author defines the local behavior process at \(x^*\) \(Z_t^N=\sqrt{N}(X_t^N-x^*)\) and admits that it satisfies the stochastic differential equation \(dZ_t=DZ_tdt+\frac{1}{\sqrt{2}}IdB_t\) where \(D\) is a linear operator and \(B_t\) denotes white noise. A new notion of stability called local probabilistic stability (LPS) is proposed, which requires that a population which begins to play in equilibrium settles into a fixed stochastic pattern around the equilibrium. Then LPS is compared with standard deterministic notions of stability.
Mathematics Subject Classification ID: 91A22
Mathematics Subject Classification ID: 91A15
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 1985838
zbMATH Keywords: equilibrium
zbMATH Keywords: inexact information
zbMATH Keywords: behavior process
zbMATH Keywords: stochastic differential equation
zbMATH Keywords: local probabilistic stability
MaRDI profile type: Publication
cites work: Stochastic evolution with slow learning
cites work: Mixed equilibria and dynamical systems arising from fictitious play in perturbed games
cites work: Deterministic Approximation of Stochastic Evolution in Games
cites work: Evolutionary Drift and Equilibrium Selection
cites work: Musical chairs: Modeling noisy evolution
cites work: Learning through reinforcement and replicator dynamics
cites work: Continuous approximation of dynamical systems with randomly matched individuals
cites work: Continuous approximations of stochastic evolutionary game dynamics
cites work: Stochastic Calculus
cites work: Evolutionary dynamics with aggregate shocks
cites work: Learning mixed equilibria
cites work: Social Stability and Equilibrium
cites work: On the Global Convergence of Stochastic Fictitious Play
cites work: Learning, Mutation, and Long Run Equilibria in Games
cites work: Learning dynamics in games with stochastic perturbations
cites work: Q4002114
cites work: Solutions of ordinary differential equations as limits of pure jump markov processes
cites work: Q4888828
cites work: Almost global convergence to \(p\)-dominant equilibrium
cites work: Evolution, population growth, and history dependence
cites work: Why imitate, and if so, how? A boundedly rational approach to multi-armed bandits
cites work: Q3862204
cites work: The Evolution of Conventions
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description: scientific article; zbMATH DE number 1985838