Non-equilibrium time-dependent solution to discrete choice with social interactions

  title={Non-equilibrium time-dependent solution to discrete choice with social interactions},
  author={James Holehouse and Hector Pollitt},
  journal={PLoS ONE},
We solve the binary decision model of Brock and Durlauf (2001) in time using a method reliant on the resolvent of the master operator of the stochastic process. Our solution is valid when not at equilibrium and can be used to exemplify path-dependent behaviours of the binary decision model. The solution is computationally fast and is indistinguishable from Monte Carlo simulation. Well-known metastable effects are observed in regions of the model’s parameter space where agent rationality is… 

Figures from this paper

Exact time-dependent dynamics of discrete binary choice models

We provide a generic method to find full dynamical solutions to binary decision models with interactions. In these models, agents follow a stochastic evolution where they must choose between two

A Binary Decision Model and Fat Tails in Financial Market

Binary decision models have been the subject of renewed research in recent years. In these models, agents follow a stochastic evolution where they must choose between two possible choices by taking

Regulation of stem cell dynamics through volume exclusion

This study suggests that the size distribution of a stem cell population bears signatures that are useful to detect negative feedback mediated via volume exclusion, and approximate solutions to the vBD master equation using a renormalized system-size expansion, QSS approximation and the Wentzel–Kramers–Brillouin method.



Discrete Choice with Social Interactions

This paper provides an analysis of aggregate behavioural outcomes when individual utility exhibits social interaction effects. We study generalized logistic models of individual choice which

Dynamic Models of Residential Ségrégation: An Analytical Solution

We propose an analytical solution to a Schelling segregation model for a relatively broad range of utility functions. Using evolutionary game theory, we provide existence conditions for a potential

Self-Fulfilling Prophecies, Quasi Non-Ergodicity & Wealth Inequality

We construct a model where people trade assets contingent on an observable signal that reflects public opinion. The agents in our model are replaced occasionally and each person updates beliefs in

Of songs and men: a model for multiple choice with herding

We propose a generic model for multiple choice situations in the presence of herding and compare it with recent empirical results from a Web-based music market experiment. The model predicts a phase

Crises and Collective Socio-Economic Phenomena: Simple Models and Challenges

Financial and economic history is strewn with bubbles and crashes, booms and busts, crises and upheavals of all sorts. Understanding the origin of these events is arguably one of the most important

Whom Or What Does the Representative Individual Represent

Macroeconomic models often assume that the choices of all the diverse agents in one sector—consumers for example—can be considered as the choices of one "representative" standard utility maximizing

Competition between collective and individual dynamics

This work solves exactly a Schelling-like segregation model, which interpolates continuously between cooperative and individual dynamics, and shows that increasing the degree of cooperativity induces a qualitative transition from a segregated phase of low utility toward a mixed phase of high utility.

Fixation of Strategies for an Evolutionary Game in Finite Populations

It is shown that fixation is fast when there is at least one pure evolutionary stable strategy in the infinite population size limit, while fixation is slow when the ESS is the coexistence of the two strategies.

General transient solution of the one-step master equation in one dimension.

A linear algebraic method is proposed for simplifying the solution of any master equation as the exponential of a matrix, which requires the calculation of the eigenvalues and eigenvectors of the matrix, and it is shown that the computational time is significantly reduced.

Hysteresis of economic networks in an XY model