An economic game with stochastic dynamics

TL;DR

This paper introduces a stochastic economic game model using Wiener processes, analyzing its stability through Lyapunov exponents and supporting findings with numerical simulations.

Contribution

It presents a novel stochastic model for an economic game and provides a stability analysis based on Lyapunov exponents, supported by numerical simulations.

Findings

The model exhibits stochastic stability in the stationary state.

Numerical simulations confirm the theoretical stability results.

Wiener process noise has a stabilizing effect on the dynamics.

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. The numerical simulation that we did justifies the theoretical results.