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.