The analysis of the stochastic stability for an economic game

TL;DR

This paper examines a stochastic economic game model using Wiener processes, analyzing its stability through Lyapunov exponents and functions, supported by numerical simulations.

Contribution

It introduces a stochastic model for an economic game and analyzes its stability properties using Lyapunov methods and numerical validation.

Findings

Stochastic stability in the stationary state is established.

Lyapunov exponents depend on model parameters.

Numerical simulations confirm theoretical stability results.

Abstract

In this paper we investigate a stochastic model for an economic game. To describe this model we have used a Wiener process, as the noise has a stabilization effect. The dynamics are studied in terms of stochastic stability in the stationary state, by constructing the Lyapunov exponent, depending on the parameters that describe the model. Also, the Lyapunov function is determined in order to analyze the mean square stability. The numerical simulation that we did justifies the theoretical results.